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 THE ELEMENTS OF QUALITATIVE CHEMICAL ANALYSIS

 WITH

 SPECIAL CONSIDERATION OF THE APPLICATION OF
 THE LAWS OF EQUILIBRIUM AND OF THE
 MODERN THEORIES OF SOLUTION

 BY
 JULIUS STIEGLITZ
 ‹Professor of Chemistry in the University of Chicago›

 VOLUME I
 PARTS I AND II
 FUNDAMENTAL PRINCIPLES AND THEIR APPLICATION

 [Illustration]

 NEW YORK
 THE CENTURY CO.
 1920




 COPYRIGHT, 1911,
 BY
 THE CENTURY CO.

 ‹Printed, October, 1911›
 ‹Reprinted, August, 1912›
 ‹Reprinted, October, 1913›
 ‹Reprinted, October, 1915›
 ‹Reprinted, August, 1917›
 ‹Reprinted, January, 1919›
 ‹Reprinted, August, 1919›
 ‹Reprinted, November, 1919›
 ‹Reprinted, July, 1920›




 PREFACE


In venturing to add another book on Qualitative Chemical Analysis to
the long list of publications on this subject, the author has been
moved chiefly by the often expressed wish of students and friends
to have his lectures on qualitative analysis rendered available for
reference and for a wider circle of instruction. Parts I and II of
the present book embody these lectures in the form to which they have
developed in the course of the last sixteen years, since, in 1894,
the teaching of analytical chemistry, along the lines followed, was
first suggested by Ostwald's pioneer "Wissenschaftliche Grundlagen
der Analytischen Chemie."

The author believes that instruction in qualitative analysis, besides
teaching analysis proper, should demand of the student a very
distinct advance in the study of general chemistry, and should also,
consciously, pave the way for work in quantitative analysis, if it is
not, indeed, accompanied by work in that subject. The professional
method of work, whether routine or research work of the academic or
the industrial laboratory is involved, inevitably consists in first
making an exhaustive study of the ‹general chemical› aspects of the
subject under examination: it includes a thorough study of books of
reference and of the original literature on the subject; and when
the experimental work is finally undertaken, it is carried out with
a critical, searching mind, which questions every observation made,
every process used. The method of instruction in this book aims at
developing these habits of the professional, productive chemist.
For the reasons given, a rather thorough and somewhat critical
study is first made (in Part I) of the fundamental general chemical
principles which are most widely involved in analytical work. The
applications of these principles to the subject matter of elementary
qualitative analysis are then discussed (in Part II), in closest
connection with the laboratory work covering the study of analytical
reactions (in Part III). The material is presented, not as a finished
subject, but as a growing one, with which the present generation of
chemists is still busy, and which contains many important, unsolved
problems of a fundamental character. Numerous references to standard
works and to the current literature are given, of which those
suitable for reading by the young student are specially designated.
The obvious demand is thereby made on the student to aim to remain
in touch with the growth of the science, after he has completed his
studies under the guidance of an instructor. Finally, to arouse
and develop the critical, questioning attitude of the professional
chemist, referred to above, the subject matter of the laboratory
work, given in Part III, is put very largely in the form of
questions, which demand not only careful observation on the part of
the student, but also a thoughtful interpretation of the observations
made.

In the experience of the author, although the majority of students
attending his lectures had already acquired some knowledge of
chemical and physical equilibrium, of the theories of solutions
and of ionization and of their applications, the more exhaustive
treatment of parts of these subjects and of related topics, to which
a course in qualitative analysis lends itself, has been of particular
benefit to them, bringing them into closer touch with the method of
detailed study of a chemical topic, than the broader, more varied
work of general chemistry courses usually does. Throughout the
theoretical treatment of the subject, the attempt is made to prepare
the student for a more general ‹quantitative› expression of chemical
relations. For this reason, chemical and physical equilibrium
constants are given and used, wherever it is possible. The author
is aware that these "constants" have, in part, only a temporary
standing; that more exact work will continually modify their
numerical values and, probably, limit the field for their ‹rigorous›
application. The latter facts can be impressed on the student and
still the invaluable principle be inculcated in his mind, that
chemistry is striving to express its relations, as far as possible,
in mathematical terms, exactly as its sister science, physics, has
long been doing. At the same time the treatment of physicochemical
topics has been kept within the bounds set by the subject matter, and
by the chemical maturity of the students addressed: it is elementary
in form, and quantitative relations are used, in the main, only to
elucidate qualitative facts. The rigorous development of the subjects
presented and their elaboration from a purely physicochemical
standpoint are left to advanced courses. It has been found that
this method interests the better class of students in seeking such
advanced courses.

The relations of qualitative to quantitative analysis are touched
upon in the theoretical treatment, where it has been feasible to do
so. The laboratory methods aim also at beginning the training of
students in the habit of accuracy demanded by quantitative analysis,
by laying special emphasis on the methods of detecting traces of
a number of the common elements and by requiring a report on the
relative quantities of components found. The study of reactions is
carried out, almost wholly, with solutions of known and uniform
molar concentration. However, the actual development of quantitative
accuracy is left to the instruction in the courses in quantitative
analysis, in which a successful training in this direction is far
more readily attained. Simultaneous courses in the two branches
of analysis seem to the author to be highly desirable, whenever
practicable. The study of quantitative analysis adds neatness of
manipulation and accuracy to the work in qualitative analysis; and
the latter supplies the opportunity for the further development of a
student's knowledge of general chemistry, for which there is a much
smaller scope in quantitative analysis courses, and thus relieves a
condition where a serious pedagogical defect is likely to exist in
the development of our students.

Parts III and IV of this book are published in a separate volume,
as a laboratory manual for qualitative analysis. They comprise the
instructions for laboratory work introductory to systematic analysis
(the study of reactions and of the analysis of groups, in Part III)
and an outline for elementary systematic analysis (Part IV). The
attempt has been made, in particular, to bring the laboratory work,
which otherwise follows the usual lines of instruction in systematic
analysis, ‹also into closest relations to the development of the
scientific foundations of analytical chemistry›, as represented in
Parts I and II. It is believed that the subject matter lends itself
especially well to such a close interweaving of the two sides of the
study, without any special loss of time to the student, and with the
result, it is hoped, of a greatly increased interest on his part and
an increased stimulus of the habit of scientific thought.

The following plan of work is used by the author with his classes:
The first section (lasting eleven weeks) of the course in qualitative
analysis is started with some seven to ten (according to the ability
of the class) lectures or classroom exercises, given daily, and
covering the first seven or the eight chapters of Part I. At the
end of the second week the laboratory work is started. During the
remainder of this section of the course, two hours of classroom work
and eight hours of laboratory work per week are required, and, in
this period, Part III, comprising the first half of the laboratory
manual, is studied in the laboratory in closest connection with
the classroom work on Part II of the book. As far as possible, the
laboratory work on a given topic ‹precedes› the classroom work. This
first course is followed by an eleven weeks' course in systematic
analysis, covering Part IV of the book. A third (graduate) course,
optional for students specializing in chemistry, is offered, in which
very complex commercial and natural products are analyzed and in
which special attention is also given to rare elements. During this
course, particular care is taken to familiarize students with other
works on qualitative analysis, such as the outlines of A. A. Noyes
and Bray, and the special parts of Fresenius's manual.

Students who have been prepared in general chemistry along
physicochemical lines, as represented, for instance, by Smith's
textbooks, make more rapid and more easy progress in the first
course than do students otherwise prepared. But the treatment of the
subject is intended to make it possible for students, who have not
paid particular attention to chemical equilibrium and to the modern
theories of solution in their general chemistry course, to complete
the course within the time limit indicated. Perhaps one-third of the
students in an average class, in the past, have taken the course
under these conditions and no special difficulty was encountered by
them.

In the theoretical treatment the author is particularly indebted to
the original articles and to the larger works of Arrhenius, van 't
Hoff, Nernst, A. A. Noyes, Ostwald, and Walker. For the systematic
analytical material acknowledgment is due, in particular, to
Fresenius's "Qualitative Chemical Analysis," and to the important
publications by A. A. Noyes and Bray in the ‹Journal of the American
Chemical Society›. Some of the excellent methods of the latter
authors have been adopted outright, as indicated in the text. For
some special matters the author is indebted to the texts of W.
A. Noyes and of Böttger. Constant references to his sources of
information have been made by the author, partly as a matter of
acknowledgment, and more particularly to give students and teachers
the opportunity for more extended, first-hand reading on any topic of
interest. References suitable for college students are indicated by
the addition of («Stud.»). In two or three instances, the original
source of information has been forgotten and diligent search has
failed to trace it. For use in preparing any future edition of the
book, the author will be glad to have his attention called to the
facts by authors.

The author wishes to express here his particular appreciation of
the generous assistance given him by his former colleague, Prof.
Alexander Smith of Columbia University, whose suggestions and
advice, especially in the editing of the manuscript and proof, have
been invaluable. He also wishes to make grateful acknowledgment to
his colleagues, Profs. H. N. McCoy, H. Schlesinger, and Dr. Edith
Barnard, to Prof. L. W. Jones of the University of Cincinnati, Prof.
E. P. Schoch of the University of Texas, Prof. B. B. Freud of Armour
Institute, and Prof. W. J. Hale of the University of Michigan, who
have assisted him by reading the proofs or the manuscript, or by
carrying out experimental studies underlying part of the work, or in
other ways. Corrections of his mistakes of omission and commission,
and suggestions, will be gratefully received by the author.

 JULIUS STIEGLITZ.

 CHICAGO, ‹September, 1911›.




 CONTENTS


 PART I

 FUNDAMENTAL PRINCIPLES

 CHAPTER                                                          PAGE

    I. INTRODUCTION                                                  3

   II. OSMOTIC PRESSURE AND THE THEORY OF SOLUTION, I                8

  III. OSMOTIC PRESSURE AND THE THEORY OF SOLUTION, II              21

   IV. THE THEORY OF IONIZATION: IONIZATION AND ELECTRICAL
       CONDUCTIVITY                                                 33

    V. THE THEORY OF IONIZATION, II: IONIZATION AND OSMOTIC
       PRESSURE; IONIZATION AND CHEMICAL ACTIVITY                   67

   VI. CHEMICAL EQUILIBRIUM. THE LAW OF MASS ACTION                 90

  VII. PHYSICAL OR HETEROGENEOUS EQUILIBRIUM.—THE COLLOIDAL
       CONDITION                                                   118

 VIII. SIMULTANEOUS CHEMICAL AND PHYSICAL EQUILIBRIUM.—THE
       SOLUBILITY- OR ION-PRODUCT                                  139


 PART II

 SYSTEMATIC ANALYSIS AND THE APPLICATION OF FUNDAMENTAL
 PRINCIPLES

   IX. SYSTEMATIC ANALYSIS FOR THE COMMON METAL IONS. THE IONS
       OF THE ALKALIES AND OF THE ALKALINE EARTHS. ORDER OF
       PRECIPITATION OF DIFFICULTLY SOLUBLE SALTS WITH A
       COMMON ION                                                  157

    X. ALUMINIUM; AMPHOTERIC HYDROXIDES; HYDROLYSIS OF SALTS.
       THE ALUMINIUM AND ZINC GROUPS                               171

   XI. THE COPPER AND SILVER GROUPS. PRECIPITATION WITH HYDROGEN
       SULPHIDE                                                    199

  XII. THE COPPER AND SILVER GROUPS (‹Continued›). THE THEORY OF
       COMPLEX IONS                                                216

 XIII. THE ARSENIC GROUP. SULPHO-ACIDS AND SULPHO-SALTS            242

  XIV. OXIDATION AND REDUCTION REACTIONS, I                        251

   XV. OXIDATION AND REDUCTION, II. OXIDATION BY OXYGEN,
       PERMANGANATES, ETC.; OXIDATION OF ORGANIC COMPOUNDS         277

  XVI. SYSTEMATIC ANALYSIS FOR ACID IONS                           299




 LIST OF REFERENCES AND THEIR ABBREVIATIONS

NOTE.—(«Stud.») affixed to a reference indicates that the original
article is recommended as suitable reading for college students
taking their second year of work in chemistry.

 ‹Am. Chem. J.›—American Chemical Journal.
 ‹Ann. de Chim. et de Phys.›—Annales de Chimie et de Physique.
 ‹Ber. d. chem. Ges.›—Berichte der deutschen chemischen Gesellschaft.
 LE BLANC'S ‹Lehrbuch der Elektrochemie› (1903).
 BÖTTGER'S ‹Qualitative Analyse› (1908).
 ‹Compt. rend.›—Comptes rendus.
 FRESENIUS'S ‹Manual of Qualitative Chemical Analysis› (1909).
 FRESENIUS'S ‹Quantitative Chemical Analysis› (1904).
 VAN 'T HOFF'S ‹Lectures on Theoretical and Physical Chemistry› (1898).
 H. C. JONES'S ‹The Elements of Physical Chemistry›.
 ‹J. Am. Chem. Soc.›—Journal of the American Chemical Society.
 ‹J. Chem. Soc.› (London).—Journal of the Chemical Society (London).
 ‹J. of Physiology.›—Journal of Physiology.
 ‹J. Phys. Chem.›—Journal of Physical Chemistry.
 ‹J. prakt. Chem.›—Journal für praktische Chemie.
 KOHLRAUSCH UND HOLBORN'S ‹Leitvermögen der Elektrolyte› (1898).
 LANDOLT-BÖRNSTEIN-MEYERHOFFER'S ‹Physikalisch-Chemische Tabellen›.
 ‹Liebig's Ann.›—Liebig's Annalen der Chemie.
 NERNST'S ‹Theoretical Chemistry› (1904).
 NERNST'S ‹Theoretische Chemie› (1909).
 OSTWALD'S ‹Lehrbuch der allgemeinen Chemie› (1893).
 OSTWALD'S ‹Scientific Foundations of Analytical Chemistry› (1908).
 OSTWALD'S ‹Wissenschaftliche Grundlagen der analytischen Chemie›
   (1894).
 ‹Phil. Mag.›—Philosophical Magazine.
 ‹Phil. Trans. Royal Soc.›—Philosophical Transactions of the Royal
   Society.
 ‹Poggendorff's Ann.›—Poggendorff's Annalen der Physik und Chemie.
 ‹Proc. Am. Acad.›—Proceedings of the American Academy.
 REMSEN'S ‹Inorganic Chemistry›, Advanced Course, 1904.
 SMITH'S ‹General Inorganic Chemistry› (1909).
 SMITH'S ‹General Chemistry for Colleges› (1908).
 TREADWELL'S ‹Qualitative Analyse› (1902).
 WALKER'S ‹Introduction to Physical Chemistry› (1909).
 ‹Wiedemann's Ann.›—Wiedemann's Annalen der Physik und Chemie.
 ‹Z. analyt. Chem.›—Zeitschrift für analytische Chemie.
 ‹Z. anorg. Chem.›—Zeitschrift für anorganische Chemie.
 ‹Z. für Elektrochem.›—Zeitschrift für Elektrochemie.
 ‹Z. phys. Chem.›—Zeitschrift für physikalische Chemie.




 QUALITATIVE CHEMICAL ANALYSIS




 PART I

 «FUNDAMENTAL PRINCIPLES»




 CHAPTER I

 «INTRODUCTION»


Qualitative chemical analysis is concerned with the determination of
the kinds of matter present in any given substance. In its broadest
sense it includes the determination of all kinds of matter, the
elements, rare as well as common, and all their combinations, organic
compounds as well as inorganic. The recognition of the presence of
rare elements, such as radium, uranium, thorium, tungsten, cerium,
etc., is becoming a matter of growing importance with the modern
development of the subject of radioactivity and the technical
exploitation of the rarer elements, and it is a common experience for
an analytical chemist to be called upon to determine the presence
or absence of alcohol in beverages, of formalin in milk or other
foods, and not a rare experience to be obliged to make tests for
the presence of alkaloids like strychnine, morphine, cocaine, or
for the presence of numerous other organic compounds. In this book,
however, we shall limit our material to the more common elements and
their most important inorganic combinations, including only a few
typical organic acids. The limitation of our experimental material
will make it possible to devote special attention to the scientific
principles underlying analysis, to secure a clear and definite grasp
of them, and to impart with simple material such experience in the
technique and methods of analysis as will train the student to apply
both his theoretical and practical knowledge to any field of analysis
occasion may require. Accurate qualitative analysis, [p004] in any
field, will depend on the care taken in mastering the theoretical
significance and the technique of the methods recommended for the
specific problem before the analyst; the details of the methods
themselves, in any problem involving more than elementary analysis,
are sought and found by him as a matter of practice in suitable
larger works, in monographs and in the original literature. With
the object of suggesting this broader application of the training
acquired and of cultivating the invaluable habit of the professional
chemist of consulting larger works and the literature, frequent
reference will be made to such larger works, and to original papers
in which more special subjects of analysis or theory are elaborately
treated.

To recognize, in a substance, the presence of any element or
compound, one must know its characteristic reactions, which will make
it possible to distinguish it from all other elements or compounds.
Further, in order to reach conclusions with the greatest possible
speed, directness, and conclusiveness, it is usually best to carry
out an examination in some systematic way, rather than in a haphazard
and irregular fashion. We distinguish, accordingly, two parts in
our laboratory work: first, the study of characteristic tests or
‹reactions› of the common elements and such of their compounds as
are of importance in elementary analysis (Part III), and, secondly,
practice in a ‹systematic› method of analysis (Part IV). In the study
of the reactions, the way will be paved for systematic analysis, by
taking the elements in the groups, which form the basis of the system
of analysis employed, and by analyses of mixtures of the elements of
a group immediately after the group has been studied.

Reliable and intelligent analysis is possible only with a clear
knowledge of the chemistry of the reactions used, and the chemistry
of the most important typical reactions will therefore be considered
(in Part II), simultaneously with the laboratory study of the
reactions and of systematic analysis.

The reactions for identifying an element or compound must bring
physical evidence which can be recognized by our senses. The sense
of ‹touch› is scarcely ever appealed to; perhaps the numbness or
paralysis of the sense of touch imparted to the tongue or eyelid by
the alkaloid cocaine and a few modern substitutes for it, and the
tingling sensation produced on the tongue [p005] by aconite and
its preparations, are the most important, but rare, instances of an
appeal to this sense in analytical work. The sense of ‹taste› is also
rarely used, and always with the greatest care to prevent poisonous
effects. Acids and bases, bitter alkaloids, such as strychnine and
brucine, sweet substances, such as cane sugar, glucose, glycerine,
are instances of compounds which affect our sense of taste. In all
these cases the taste is used rather as a confirmative test than as a
conclusive proof of the identity of a suspected substance.

The sense of ‹smell› is rather more useful in qualitative analysis
than that of taste or of touch. Hydrogen sulphide and ammonia,
unless present in traces only, readily reveal themselves by their
odor. Every chemist should be familiar with the faint but very
characteristic odor of hydrocyanic acid,[1] which should instantly
and automatically warn him of the presence of this potent poison.
Owing to partial decomposition by the moisture and carbonic acid
absorbed from the atmosphere, alkali cyanides also give this
important warning signal. Tests based on the odors of compounds are
particularly valuable in the field of organic chemistry, where the
sense of smell is extensively used for qualitative purposes; for
instance, the pleasant smell of acetic ester, and the nauseating odor
of an organic arsenic derivative, cacodyl oxide, may be used with
advantage in identifying acetic acid.

But the evidence of touch, taste, and smell is, on the whole, only
occasionally available in chemical analysis—almost all the tests
employed are ‹visual› ones. A small proportion of these are ‹color›
tests. The color of iodine vapor or of the solution of iodine in
chloroform, the colors of metallic copper or gold, of copper salts in
ammoniacal solutions, of sulphides, such as the orange sulphide of
antimony (‹exps.›), may be mentioned as instances, in which a test
of identity depends on the observation of some characteristic color.
But the great majority of analytical tests depend on ‹observations
of changes of state›; evidence consisting in the solution of solids,
the formation of precipitates, the evolution of gases, forms the most
important part of the observations, [p006] on which our conclusions
are based. In organic chemistry, determinations of melting-points
and of boiling-points, which are very commonly used for the
qualitative identification of compounds, form further instances of
the application, to qualitative purposes, of observations based on
changes of state.

In very many cases, where the formation or nonformation of a
precipitate is intended to be used as an indication of the presence
or absence of a given substance, the precipitating agent may throw
down one or more of several different precipitates, which, seen
without the aid of a microscope, cannot be identified without further
examination. It is, thus, commonly necessary to use a sequence
of such tests for the complete identification. For instance, the
addition of hydrochloric acid to a solution of lead, mercurous or
silver nitrate will produce a white precipitate. The precipitates may
be distinguished by a further examination of their solubilities: hot
water will dissolve the lead chloride, ammonia readily dissolves the
chloride of silver and converts the mercurous chloride into a black
insoluble mixture containing finely divided mercury (‹exps.›). By the
same means the chlorides, if present together, may be separated from
one another and subsequently identified. Systematic analysis consists
very largely in the use of a proper, logical sequence of such
precipitation and solution reactions, and in the drawing of definite
conclusions from the results obtained.

By far the greatest part of the experimental work in qualitative
analysis has to do, then, with solution and precipitation. For
intelligent and accurate analytical work a clear knowledge of the
nature of solution and, in particular, of the simple ‹laws governing
chemical action in solution›, and of those ‹governing the formation
and the solution of precipitates›, is indispensable. The discoveries
of van 't Hoff, in 1885–8, concerning the nature of solution, and
the subsequent discoveries of Arrhenius, Nernst, Ostwald and others,
have advanced every branch of chemistry, but perhaps no branch has
profited quite so much as the theory of analytical chemistry, which,
as a result of these discoveries, for the first time, received a
clear, precise and satisfying scientific formulation of its empirical
processes.[2] [p007]

On account of the fundamental importance of this modern scientific
formulation of the principles of analytical chemistry for the proper
understanding of our subject, we shall consider first (in Part I) the
modern theories of solution, with their experimental foundations, and
we shall then develop the simpler fundamental laws governing chemical
action and physical changes in solution. The analytical reactions
themselves will be utilized as far as possible as the material for
developing these general principles, so that this study may lead to
the desired grasp of the theory of analysis and yet, at the same
time, advance the student's knowledge of the practice of analysis.


  FOOTNOTES:

  [1] On account of the poisonous character of this and other vapors,
  the vessel containing a substance whose odor one wishes to test is
  not brought to the nose, but a little of the vapor is carefully
  wafted towards one by a motion of the hand, the vapor being thus
  greatly diluted with air.

  [2] We owe the first modern scientific treatment of the principles
  of Analytical Chemistry to Ostwald's ‹Wissenschaftliche Grundlagen
  der analytischen Chemie›, 1894.

[p008]




 CHAPTER II

 «OSMOTIC PRESSURE AND THE THEORY OF SOLUTION I»


If a concentrated solution of a substance like sugar or cupric
nitrate is allowed to flow into a cylinder of water (‹exp.› with
cupric nitrate), we find that the outside forces—gravity—tend to draw
the solution, whose specific gravity is greater than that of water,
to the bottom of the cylinder. In this method of proceeding there
is some inevitable mixing of the solution with the solvent, as the
result of friction, but the main portion of the deep blue solution is
drawn to the bottom of the vessel and forms a blue layer under the
colorless water. A much sharper line of separation may be obtained
by allowing the cupric nitrate solution to enter a cylinder of water
from under the water (see Fig. 1), the great density of the nitrate
solution causing it to displace the water without perceptible mixing
of the two liquids (‹exp.›). If these vessels are left at rest, it
may be noted, from day to day, that the copper nitrate diffuses
further and further into the pure solvent, and careful examination
would show that the solvent, in turn, diffuses also into the copper
nitrate solution. The process is a very slow one, but it will
continue until a solution of ‹uniform concentration› is reached, and
this will be the case, whatever the shape of the vessel may be. If,
for the moment, only the copper nitrate be considered—and what we
are developing for the copper nitrate may be applied equally well,
‹mutatis mutandis›, to the diffusion of water into the copper nitrate
solution—it is obvious then that copper nitrate in solution ‹diffuses
in all directions›, even against the force of gravity, and it is
plain also, that any object, resisting or arresting such a motion
of material particles, must have a force or pressure exerted upon
it. Whatever the ultimate [p009] cause of the motion, whether it is
the result of inherent molecular velocities of the dissolved copper
nitrate, or of an attraction between the solute and the solvent, or
both, it is inevitable that a pressure must result from the impact of
the moving solute against the solvent.[3]

 [Illustration: FIG. 1.]

We have thus phenomena of diffusion of solutes through solvents,
exactly as we have the well-known diffusion of gases, and the two
phenomena are unquestionably very much alike, the solute, like the
gas, tending to diffuse from the place of higher, to that of lower
concentration.[4] Likewise, if a solution of uniform concentration
is heated in one part and not in another, the solute,[4] like a gas
under similar conditions, will move from the warmer to the colder
part of the solution, as was demonstrated by Soret.[5] Without
committing ourselves for the present to any given reason for the
diffusion, we note that the tendency to diffusion is a fact, and we
must accept the conclusion that every obstacle to such diffusion must
have a ‹pressure› exerted upon it.

Now, if a solution is separated from the pure solvent by means of
a so-called ‹semipermeable membrane›, some of the results of this
tendency to diffusion may be demonstrated.

 EXP. A concentrated solution of cane sugar in water, colored with
 some aniline dye, is enclosed in a thimble of parchment paper firmly
 fastened to a long narrow glass tube (see Fig. 2) and the cell is
 placed in a vessel of pure water. The parchment is not absolutely
 semipermeable, but it is approximately so, allowing the solvent,
 water, to pass, but being practically impervious to the solute
 sugar. A Schleicher and Schüll diffusion-thimble, No. 579, may be
 used, with advantage, as the thimble. (‹Cf.› Smith's ‹Introduction
 to Inorganic Chemistry›, p. 284.) [p010]

We observe, presently, that the system is not in a condition
of equilibrium; water passes through the thimble into the sugar
solution and the latter expands, producing a decided difference of
level, and consequently a hydrostatic pressure, between the liquid
in the cell and the solvent outside of it. We may note two facts:
first, that the change includes an expansion of the solute,[6] the
sugar, in the solution—that is, the tendency of the solute to expand
into larger volumes of the solvent is satisfied exactly as in the
experiment (Fig. 1) described above. In the second place, like all
natural phenomena which proceed spontaneously, ‹the change is in
the direction of equilibrium›; for when the hydrostatic pressure on
the solution in the cell becomes sufficiently great, or if it is
made sufficiently great at once by the application of some outside
pressure, ‹a point of equilibrium is reached, at which water will
pass neither into the cell nor out of it›. At that point, the
tendency to expansion, both of the solute and of the solvent in the
solution, is just overcome by the pressure on the solution.

 [Illustration: FIG. 2.]

«Definition of Osmotic Pressure.»—‹The hydrostatic pressure which
is necessary to bring the solution into equilibrium with the pure
solvent, when the two are separated by a semipermeable membrane,
may be defined, according to van 't Hoff, as the measure of› what
is called the ‹osmotic pressure of the solution›. We note that this
definition still does not commit us to any theory as to the origin of
the pressure, but merely ‹formulates› an ‹experimental relation›.

«Measurement of Osmotic Pressure.»—More perfect semipermeable
membranes can be produced. These make possible quantitative
measurements of the hydrostatic pressure on a solution, when
equilibrium between the solution and the pure solvent [p011] has
been reached. Such membranes were first used by Pfeffer. They consist
of certain gelatinous precipitates, notably copper ferrocyanide.
Films of these precipitates may be formed, under proper conditions,
which are permeable to water but not to certain solutes, such as cane
sugar, glucose and galactose.

 [Illustration: FIG. 3.]

By precipitating these membranes in the pores of unglazed clay
cells, especially by the process devised by Morse,[7] we may make
them sufficiently strong to resist enormous pressures—some used
by the Earl of Berkeley were found to withstand a pressure of 130
atmospheres. The hydrostatic pressure required to produce equilibrium
may then be measured in either of two ways. The first method, used
originally by Pfeffer and more recently by Morse and Frazer[8] and
their collaborators in a wonderfully conscientious study of osmotic
pressures, consists in allowing the hydrostatic pressure to establish
itself by the passage of very small quantities of the solvent,
through the membrane, into the tightly closed cell containing the
solution. When the resulting pressure produces a condition of
equilibrium, it is measured[9] by a manometer connected with the
solution, much as a gas pressure may be measured (Fig. 3).[10] This
process requires considerable time for exact measurements—weeks,
during which the cell must be kept at a constant temperature. The
second method, which has been used by Berkeley and Hartley,[11]
is very much more rapid and requires only a few hours for the
measurement. It consists in having the pure solvent within the
cell, instead of outside of it, and in [p012] exerting an external
pressure on the solution outside of the cell, until a delicate
manometer, communicating with the pure solvent, shows that water does
not pass through the membrane in either direction—equilibrium having
been reached.

«Osmotic Pressure and the Laws of Gases.»—The work of van 't
Hoff, which has proved of inestimable value to the development of
chemistry, succeeded in demonstrating that, ‹for dilute solutions,
the osmotic pressure›, as defined above, ‹obeys the common laws of
gases›,[12]—‹that, in fact, a substance in a dilute solution has an
osmotic pressure equal to the gas pressure which it would exert if it
were a gas of the same volume and at the same temperature›.[13]

Space does not permit the presentation of all the details of the
evidence confirming this conclusion, but some of the most direct
experimental proofs[14] will be considered. [p013]

«Boyle's Law.»—Boyle's law for gases states that, at a constant
temperature, the pressure of a gas changes inversely as its
volume, or directly as its concentration. Mathematically we have
‹P› : ‹P′› = ‹V′› : ‹V› or ‹P› ‹V› = ‹P′› ‹V′› = a constant, and
‹P› : ‹P′› = ‹C› : ‹C′› or ‹P› : ‹C› = ‹P′› : ‹C′› = a constant.
When van 't Hoff published his first paper on the subject, Pfeffer's
results from the direct measurement of the osmotic pressures of
cane-sugar solutions were available, and even these, although
experimentally not as exact as more recent determinations, showed
plainly that, at a given temperature, the osmotic pressure of a sugar
solution varies directly as the concentration, or inversely as the
volume containing a given weight of the sugar. At 13–16° we have:

  Concentration.   Osmotic Pressure.     Pressure/
                    mm. Mercury.      Concentration.
     1.00%               535                535
     2.00%              1016                508
     2.74%              1518                554
     4.00%              2082                521
     6.00%              3075                513

The ratio of pressure to concentration varies irregularly round a
mean value of 526, and is approximately constant. The more recent,
exceedingly careful measurements of Morse and Frazer confirm the
conclusion, that Boyle's law holds for the osmotic [p014] pressures
of dilute solutions; they find that the osmotic pressures of glucose
and of cane-sugar solutions vary directly as the concentrations of
the solutions, at a constant temperature.[15]

«Gay-Lussac's Law.»—Gay-Lussac's law for gases states that,
if the volume of gas is kept constant, its pressure increases
by 1 / 273 of its value for every degree above 0° C., or
‹P›_{‹t›} = ‹P›_{0} (1 + ‹t› / 273).

Expressing the temperature in absolute degrees, we have more simply:

 ‹P›_{‹t›} = ‹P›_{0} (‹T› / 273) or
   P_{t} / T = ‹P›_{0} / 273 = a constant.[16]

That is, the pressure of a gas varies directly as its absolute
temperature, if the volume is kept constant.

Pfeffer's results, on the osmotic pressure of sugar solutions
at different temperatures, were not sufficiently accurate to
enable van 't Hoff to use them to confirm positively the rigorous
thermodynamic proof (footnote 3, p. 12), that the osmotic pressure
must increase proportionally to the absolute temperature, as
required by Gay-Lussac's law. But the data did show, uniformly, a
marked increase of the osmotic pressure with the temperature and,
frequently, excellent agreement between theory and experiment.
More striking were the results obtained by van 't Hoff in testing
the correctness of this extension of Gay-Lussac's law by means of
Soret's results on the diffusion of a solute from a warmer to a
colder place. It was found that the concentrations, obtained by
Soret when equilibrium was reached, agreed closely with the demand
that the osmotic pressures in the colder and the warmer parts of the
solution should be equal, and that the osmotic pressure of a given
weight of solute in a given volume should increase proportionally
to the absolute temperature. An elevation of temperature, in a
portion of a uniform solution, will increase the osmotic pressure of
this part. Diffusion will follow, until the loss in concentration
of the solute, and therefore the loss of osmotic pressure (Boyle's
law), of the warmer part, and the increased concentration and
increased pressure of the colder portion result in all parts of the
solution having the same osmotic pressure. [p015] As an example,
a concentration of 17.33% copper sulphate at 20° was found to be
in equilibrium with a concentration of 14.03% at 80°. Now, if
the 17.33% solution had an osmotic pressure of ‹P› mm. at 20°, a
14.03% solution at the same temperature would have a pressure of
(14.03 / 17.33) × ‹P› mm. (Boyle's law), and this would increase
to (14.03 / 17.33) × ‹P› × (353 / 293) mm. at 80° C., or 0.975 ‹P›
mm.—a result showing that the osmotic pressure in the hot part
was practically the same as that, (‹P›), in the cold part of the
solution.[17]

It is a source of great satisfaction, that the recent very exact
and painstaking work of Morse and Frazer,[18] in measuring osmotic
pressures directly, completely confirms this fundamentally important
conclusion, that the osmotic pressure of a solution does increase
proportionally to its absolute temperature.

«The Avogadro-van 't Hoff Hypothesis.»—For chemists, the most
important part of van 't Hoff's work lies in the extension of ‹the
Avogadro Hypothesis› to solutions. As van 't Hoff expresses it,
"equal volumes of the most different solutions, having the same
osmotic pressure and the same temperature, contain the same number of
dissolved molecules,—that number, namely, which would be found in the
same volume of a gas at the same gas pressure and temperature."[19]
[p016]

Pfeffer's measurements, with solutions of 1 g. of sugar in 100 c.c.
of water (the volume of the solution is 100.6 c.c.), were shown to
prove, that the observed osmotic pressures agreed excellently with
the gas pressures, calculated for the equimolar weight of hydrogen,
in the same volume and at the same temperature:

                     Osmotic Pressure
  Temperature.  ──────────────────────────

                   Found.    Calculated.[20]
                Atmosphere.    Atmosphere.
      6.8          0.664          0.665
     13.7          0.691          0.681
     14.2          0.671          0.682
     15.5          0.684          0.686
     22            0.721          0.701
     32            0.716          0.725
     36            0.746          0.735

Morse's more recent and more exact results show, that the osmotic
pressure of solutions of cane sugar and of glucose (corrected for
the volume occupied by the sugar, see footnote, p. 15) agrees within
6% with the values demanded by van 't Hoff's theory, being about
6% larger for concentrations ranging from 0.1 to 1.0 molar. The
difference of 6% is noteworthy and is probably due to secondary
causes, but suggests extended investigation of its source.

«Indirect Determinations of Osmotic Pressure.»—The experimental
results given have been obtained by direct measurements of osmotic
pressures with the aid of semipermeable membranes. [p017] Perfect
membranes are very difficult to prepare, and membranes of this kind
can be used only with a few solutes. Nature offers us, however, forms
of semipermeable "walls" between solutions and pure solvents, which
in many instances are perfect. The atmosphere, above a volatile pure
solvent and a solution of a nonvolatile substance in that solvent,
when both liquids are placed side by side in a closed space, would
serve as a semipermeable wall: the solvent vaporizes and may pass
freely from solvent to solution and ‹vice versa›, but the solute, in
the case under consideration, is nonvolatile and therefore cannot
pass through the atmosphere. The vapor pressure of a pure solvent
being always found to be higher than that of a solution in this
solvent, at the same temperature, the solvent would pass in such a
closed space as vapor ‹from the pure solvent› and would ‹condense›
in the solution; it thereby dilutes the solution and the solute, and
the solvent in the solution, expand, exactly as in the absorption
of a solvent by a solution through a semipermeable membrane. Again,
the vapor pressure of a solution being lower than that of the pure
solvent, the solution (of a nonvolatile solute) must be heated higher
than the pure solvent, to bring both to the boiling-point; that is,
there is an ‹elevation of the boiling-point›, when a nonvolatile
solute is dissolved in a solvent. The solute being nonvolatile, only
the solvent passes off in the process of boiling, the solute becomes
‹more concentrated›, and, according to van 't Hoff's extension of
Boyle's law, the ‹osmotic pressure of the solution increases›.
Similarly, when a solution is cooled until freezing occurs,
provided the solute does not crystallize out with the solvent, the
concentration of the solute is again increased, and therefore the
‹osmotic pressure› of the solution is also increased. Van 't Hoff
recognized the relations existing between the freezing, boiling
and vaporization of solutions, on the one hand, and the changes of
their osmotic pressures on the other. By developing rigorously the
‹relations between the lowering of the vapor tension, the raising of
the boiling-point, the lowering of the freezing-point› of a solvent
by a solute ‹and the osmotic pressure of the solution›, he made it
possible[21] to use [p018] extensive experimental material,[22] on
the elevation of boiling-points and the lowering of freezing-points
and of vapor tensions, to determine the osmotic pressures of
solutions. The theory of the relation of osmotic pressure to gas
pressure is fully confirmed by these measurements, for those cases
to which it may properly be applied, namely, to sufficiently dilute
solutions and such as have only negligible heats of dilution, ‹i.e.›
in which dilution does not involve chemical changes.

 «Apparent Exceptions.»—Instead of discussing the vast amount of
 material of this kind, which agrees with van 't Hoff's theory,
 we may consider, more profitably, typical cases of ‹apparent
 exceptions›. The most important instance of this kind, the case of
 solutions of compounds which undergo ‹electrolytic dissociation or
 ionization›, will be separately discussed in the next chapter, and
 we shall find that van 't Hoff's great generalization is a vital
 element in the evidence of this important form of dissociation. Of
 other apparent exceptions, we may note the fact that some solutes
 seem to give "abnormally" ‹low› osmotic pressures[23] in certain
 solutions. For instance, benzoic acid, in benzene solutions, gives
 only a little more than half as great an osmotic pressure as it does
 in aqueous solutions of the same concentration and temperature, and
 as would be calculated on the basis of the Avogadro-van 't Hoff
 Hypothesis for a compound of the formula C_{6}H_{5}COOH and the
 molecular weight 122. But a rigorous study[24] of the distribution
 of benzoic acid between water and benzene, when solutions of the
 acid in the two solvents are shaken together until equilibrium
 is established (Chapter VIII), has proved that the distribution
 is strictly in accord with the assumption that benzoic acid, in
 aqueous solution, has the molecular weight 122 and the composition
 C_{6}H_{5}COOH, and that, in benzene solution, it has the molecular
 weight 244 and the composition (C_{6}H_{5}COOH)_{2}; only a
 ‹small part› of the acid (C_{6}H_{5}COOH)_{2} is decomposed in
 benzene solution into the simpler molecules, of the composition
 C_{6}H_{5}COOH. In other words, the simpler molecules C_{6}H_{5}COOH
 are ‹polymerized› or ‹associated› to form larger molecules in
 benzene solution, much as the gas nitrogen dioxide NO_{2} goes
 over more or less into the gas N_{2}O_{4}, especially at low
 temperatures, and as hydrogen fluoride at low temperatures has
 the composition H_{2}F_{2}, while at higher temperatures it is
 HF. The divergence of the benzene solutions of benzoic acid from
 the Avogadro-van 't Hoff principle is therefore only an ‹apparent
 one›, not a real one, inasmuch as the osmotic pressure of the
 solutions agrees perfectly with that calculated for solutions of
 a substance (C_{6}H_{5}COOH)_{2}, of molecular weight 244. Such
 associated molecules (of organic acids, alcohols, phenols, etc.)
 occur [p019] particularly readily in liquids of small dissociating
 power, like benzene, and such solutions show marked ‹absorption of
 heat on dilution›,[25] the dilution being accompanied by a ‹chemical
 change›. The associated molecules are dissociated more and more
 completely [(C_{6}H_{5}COOH)_{2} ⇄ 2 C_{6}H_{5}COOH], even in these
 solvents, as the solutions are diluted. Since dilution results in a
 ‹chemical increase› in the number of molecules, the osmotic pressure
 cannot decrease proportionally with the increase of volume in such
 a case as this. Nor does gas pressure, it must be remembered,
 decrease proportionally to the volume in the case of gases which
 show ‹chemical changes› with change of volume, ‹e.g.› in the case of
 nitrogen tetroxide, for which we have N_{2}O_{4} ⇄ 2 NO_{2}.

 In still other instances, apparently too high osmotic pressures, or
 too low molecular weights, have been found by the application of
 the Avogadro-van 't Hoff Hypothesis to solutions: for instance, the
 molecular weight of sodium, when dissolved in mercury, was found
 by Ramsay to vary from 21.6, in dilute, to 15.1 in concentrated
 solutions. But Cady found that the heat of dilution of sodium in
 mercury solution is considerable, and by taking this properly into
 account, Bancroft was able to show that the molecular weight,
 correctly calculated in a given experiment, is 22.7 (agreeing well
 with the theoretical weight 23), in place of 16.5, as calculated
 without making the required allowance for the heat of dilution.[26]
 These determinations are most instructive in showing that the
 sources of some of the most important deviations from the van 't
 Hoff-Avogadro principle, deviations which have been brought
 forward as arguments against its assumptions, are due, not to any
 untrustworthiness of the general principle, but to the error of
 neglecting to observe the limiting conditions of the formulation,
 or of neglecting to make corresponding corrections for the
 non-observance thereof.

«Summary.»—Van 't Hoff's theory of solution—that the osmotic
pressure of substances in solution obeys the laws of gases, and
that equal volumes of the most varied dilute solutions, having
the same temperature and osmotic pressure, contain the same
number of dissolved molecules, that number, namely, which would
be found in the same volume of a gas at the same temperature
and gas pressure,—accords thus, not only with the demands of
thermodynamics,[27] but is also, within the limits demanded by the
theory itself, in agreement with the best experimental measurements
of osmotic pressures that have been made in recent years. The
apparent exceptions, as in the cases just described and, as we shall
find, in the case of electrolytic dissociation, are found to be no
exceptions, when the conclusions, reached on the assumption that
[p020] the theory is correct, are tested rigorously by independent
methods of investigation.[28]

 The fundamental laws of gases and the Avogadro Hypothesis may be
 condensed into the following general equation, expressing all
 of the laws, viz.: ‹P› ‹V› = ‹n› ‹R› ‹T›. This equation applies
 equally to the osmotic pressures of dilute solutions, the osmotic
 pressure being substituted for the gas pressure. In the equation,
 ‹T› is the absolute temperature of the gas or solution, ‹P› the
 gaseous or osmotic pressure, ‹V› the free space of the gas volume,
 ‹i.e.› the volume of the gas less the volume occupied by the gas
 molecules, or the volume of the pure solvent in the solution used,
 ‹i.e.› the volume of the solution less the volume of the solute.
 ‹R› is the so-called ‹gas-constant›, and represents ‹the work›
 done against the external pressure when one gram molecule, or
 mole, of the gas is heated one degree and allowed to expand, say
 at constant pressure ‹P›, against an external pressure ‹P›; ‹n›
 represents the number of gram molecules or moles of gas or solute
 used (the total weight of solute or gas, divided by the average
 weight of a mole in the gas or solute). If a given weight of a
 gas or solute is taken, and no dissociation or association occurs
 (such as would involve appreciable heats of dilution), then ‹n›
 is a given number; and, therefore, at a given temperature ‹T›,
 all the factors on the right side of the general equation being
 given numbers, ‹P› ‹V› ‹is a constant› (Boyle's law). For a given
 quantity of gas or solute (‹n› is a given number), kept at ‹constant
 volume› ‹V›, the pressure must vary as the absolute temperature
 (Gay-Lussac's law); ‹P› / ‹T› = ‹n› ‹R› / ‹V› = ‹a constant›. When
 the pressure, volume and temperature of two gases, or two dilute
 solutions, are equal, ‹n›, the number of gas or solute molecules
 present, must be the same (Avogadro-van 't Hoff Hypothesis);
 ‹n› = ‹P› ‹V› / (‹R› ‹T›), and all the factors of the right side
 are the same for the gases and solutions which we are comparing.
 Finally, if the pressure is expressed in atmospheres, the volume in
 litres, and the temperature in absolute degrees, the ‹gas-constant›
 ‹R› = ‹P› ‹V› / ‹T› = 1 × 22.4 / 273 = 0.082.


  FOOTNOTES:

  [3] Even after a solution of uniform concentration of the solute is
  formed, the tendency toward diffusion, and the diffusion itself,
  and the resulting pressure must still persist. But a state of
  ‹dynamic› (or flowing) ‹equilibrium› must be considered now to
  exist, the loss caused by the moving away of the solute, from a
  given part of the solution, being balanced by the diffusion (into
  that part) of the solute from the neighboring parts. Whether
  one ascribes the diffusion to inherent molecular velocities of
  the solute, or to an attraction between solvent and solute,
  the discrete particles of the solute in a solution of uniform
  concentration will continue to have such inherent velocities (Chap.
  III), and will also continue to be surrounded by pure solvent,
  exactly as in solutions of unequal concentrations, where the
  diffusion may be observed, because the net result, in such a case,
  is a one-sided action.

  [4] This again holds equally for the solvent.

  [5] See below.

  [6] At the same time, the change is also in the direction of an
  expansion of the ‹solvent in the solution›. The two changes are not
  opposed to each other, but supplementary.

  [7] ‹Am. Chem. J.›, «28», 1 (1902); «40», 266, 325 (1908) («Stud.»).

  [8] ‹Am. Chem. J.›, «34», 1 (1905); «36», 39 (1906); «37», 324,
  425, 558 (1907); «38», 175 (1907).

  [9] The exact concentration of the solution at the point of
  equilibrium is determined by subsequent analysis.

  [10] ‹Cf.› Smith's ‹Inorganic Chemistry›, p. 287.

  [11] Berkeley and Hartley, ‹Phil. Trans. Roy. Soc.› A, «206», 481
  (1906).

  [12] When appreciable ‹heat of dilution› is shown by a solution,
  some chemical change, resulting from dilution, is indicated (such
  as, dissociation of the solute, hydration, hydrolysis, etc.). In
  such a case, the Avogadro-van 't Hoff principle holds for each
  concentration for its actual composition, and the principle may
  often be used to determine the extent of the chemical change
  produced by dilution. But then the osmotic pressure will not obey
  Boyle's and Gay-Lussac's laws. The same exception applies also to
  gases which undergo chemical changes, as the result of dilution
  or change of temperature. In the case, for instance, of nitrogen
  tetroxide, which dissociates according to N_{2}O_{4} ⇄ 2 NO_{2},
  the extent of the dissociation varies with changes of concentration
  (pressure) and of temperature, and the gas does not obey the laws
  of Gay-Lussac and of Boyle. In regard to the rôle of heat of
  dilution in connection with osmotic pressure, see Bancroft, ‹J.
  Phys. Chem.›, «10», 319 (1906).

  [13] See p. «15» for a more rigorous statement concerning the
  volume. ‹Cf.› Morse and Frazer, ‹Am. Chem. J.›, «34», 1 (1905).

  [14] As a result of numerous vain endeavors, as well as of much
  direct evidence of a positive character, the scientific world has,
  for many years, held the opinion that any sort of "perpetual motion
  machine" is impossible. Every one now admits that a machine which
  would be able to work continuously, without consuming energy, is
  an impossibility—that is, that a "‹perpetuum mobile of the first
  class›," as it is called, is impossible (law of the conservation of
  energy or ‹first law› of thermodynamics). From this law it does not
  of necessity follow, however, that it would be impossible to make a
  machine or device that would convert ‹continuously› into available
  energy or work, say, the enormous amounts of heat energy of the
  earth or of large bodies of water ("dissipated energy") which would
  thereby be ‹cooled below› the temperatures of their surroundings.
  Such a hypothetical process has been termed a "‹perpetuum mobile of
  the second class›"; it has never been realized and is universally
  conceded to be an impossibility; the so-called "‹second law› of
  thermodynamics" gives expression to this fact.

  Now van 't Hoff [‹Z. phys. Chem.›, «1», 481 (1887)] showed, first,
  that a gas like oxygen, nitrogen, hydrogen, etc., which is soluble
  in proportion to its gas pressure (Henry's law), must exert, in
  solution, an osmotic pressure equal to the gas pressure, which it
  would have, if present in the same quantity as a gas in the same
  volume at the same temperature; for, if such were not the case,
  the solution and gas could be used to produce a ‹perpetuum mobile
  of the second class›, which, according to the above law, is an
  impossibility. Similar proofs were given by Rayleigh [‹Nature›,
  «55», 253 (1897)] and by Larmor [‹Phil. Trans.›, «190», 266 (1897),
  ‹Nature›, «55», 545 (1897)] that the principle applies to solutions
  of other solutes.

  Provided, then, that we have (1) perfect semipermeable membranes,
  (2) sufficiently dilute solutions, and (3) none but negligible
  heats of dilution (p. 12), van 't Hoff's generalization, concerning
  the relation of osmotic pressure and the laws of gases, must hold,
  if the ‹perpetuum mobile of the second class› is impossible, as is
  demanded by the second law of thermodynamics.

  [15] See p. 15 in regard to the relation for concentrated solutions.

  [16] The pressure ‹P›_{0} of a given quantity (weight) of a gas
  at 0° C., in a given constant volume, is also a given number and
  consequently ‹P›_{0}/273 is a constant under these conditions.

  [17] The slight differences in the ionization of copper sulphate
  solutions of 14% and 17% and at 20° and 80° are not included in the
  calculation, ionization being unknown, when van 't Hoff made his
  calculations.

  [18] ‹Am. Chem. J.›, 41, 258 (1909).

  [19] In the light of recent work, especially by Morse and Frazer,
  the law would state, more exactly, that a substance in solution
  produces the osmotic pressure, at a given temperature, which
  it would exert, if it were contained as a gas, at the same
  temperature, ‹in the volume occupied by the pure solvent› of the
  solution. For sufficiently dilute solutions, the volume of the
  solution and the volume of the solvent may be considered identical;
  for more concentrated solutions, there is a decided difference,
  and the correct volume to use in calculation is the volume of the
  solvent alone, ‹i.e.› the volume of the solution reduced by the
  volume of the pure solute. This corresponds to the correction of
  the volume in the more accurate expression for the behavior of
  gases, developed by van der Waals; in place of ‹v›, the total
  gas volume, (‹v› − ‹b›), the total volume of the gas less the
  volume of the spheres of action of the gas particles, is used,
  especially for strongly compressed or concentrated gases. It may
  be added that van 't Hoff's thermodynamic proof involves the same
  correct definition of the volume that Morse and Frazer subsequently
  developed experimentally. ‹Cf.› Bancroft, ‹J. Phys. Chem.›, «10»,
  319 (1906).

  [20] One gram of cane sugar, C_{12}H_{22}O_{11} (the mol.
  wt. is 342) corresponds to 1 / 342 gram molecule or mole
  and, therefore, to 2.02 / 342 gram of hydrogen. The volume
  containing this quantity of hydrogen is 100.6 c.c.; a liter
  would contain 2.02 / 342 × 1000 / 100.6 gram of hydrogen.
  The pressure of a mole or 2.02 grams of hydrogen, contained
  in a liter at 0°, is 22.4 atmospheres, and the pressure of
  the quantity of hydrogen given above, in a liter, would be
  (2.02 × 1000) / (342 × 100.6) × (22.4 / 2.02) at 0°. At 36°
  C., for instance, the pressure would be 309 / 273 times as
  great, or ‹P›_{calculated} = (2.02 × 1000 × 22.4 × 309) /
  (342 × 100.6 × 2.02 × 273) = 0.735 atmosphere.

  [21] The exact relations are discussed in van 't Hoff's ‹Lectures
  on Physical Chemistry›, Part II, pp. 42–59, Nernst's ‹Theoretical
  Chemistry› (1904), pp. 142 and 148, and H. C. Jones's ‹The Elements
  of Physical Chemistry› (1909), pp. 252, 271.

  [22] ‹Vide› Raoult, ‹Scientific Memoir Series›, «4», 71, 127.

  [23] ‹I.e.› abnormally small depressions of freezing-points or
  elevations of boiling-points.

  [24] Nernst, ‹Theoretical Chemistry›, p. 486; Hendrixson, ‹Z.
  anorg. Chem.›, «13», 73 (1897).

  [25] ‹Cf.› Bancroft, ‹J. Phys. Chem.›, «10», 319 (1906).

  [26] For the discussion of other instances, ‹vide› Bancroft, ‹loc.
  cit.›

  [27] Footnote 3, p. 12.

  [28] For example, determinations of distribution coefficients
  (p. 18), heats of dilution (p. 19), conductivities and chemical
  activity (Chapters IV–VI).

[p021]




 CHAPTER III

 «OSMOTIC PRESSURE AND THE THEORY OF SOLUTION II»


Accepting van 't Hoff's theory of solutions, then, as based on
experimental evidence as well as on sound thermodynamic reasoning,
we find a number of interesting questions still confronting us.
Most insistent is the question as to the source of the remarkable
agreement between the osmotic pressure of a solute and the gas
pressure, which it would exert in the same volume, as a gas, at the
same temperature, and as to the identity of the laws governing the
two forms of pressure. Then, we may also ask, what is the mechanism
of the process by which osmotic pressure reveals itself, especially
in the case of cells with semipermeable membranes. And, finally, we
may ask what is the cause of the semipermeability of the membranes.

«Semipermeability.»—Taking up the last question first, as the
simplest one, we find that it was long ago recognized that
permeability depends on the power of membranes to dissolve certain
substances, or to form unstable combinations with them. A membrane is
semipermeable if it will dissolve one component only of a solution,
the solute or the solvent, and not the other.[29]

We find the simplest evidence of the cause of semipermeability in
the case of gases. Palladium, especially when heated, dissolves
hydrogen readily, but not nitrogen or oxygen, and a wall of palladium
may be used as a semipermeable membrane to separate a mixture of
hydrogen and nitrogen from pure hydrogen, just as copper ferrocyanide
membranes are used with aqueous sugar solutions and water. The
results with the gases duplicate in every particular the observations
made on the solutions (see below, p. 24). Certain gases, such as
ammonia and hydrogen chloride, are easily soluble in water, while
others, like oxygen, nitrogen and hydrogen, are very difficultly
soluble, and a film of [p022] water may be used as a semipermeable
membrane for such gases.[30]

 EXP. If the moist membrane of a cell (Fig. 4), containing air, is
 covered with an atmosphere of hydrogen, there is no increase of
 pressure produced in the cell, as indicated by the column of colored
 oil in the manometer in which the cell ends: hydrogen, being very
 little soluble in water, cannot pass through the film of water
 in the few minutes it is allowed to act. If now an atmosphere of
 ammonia is substituted for the hydrogen, the gas passes through the
 film into the cell. It turns the color of a piece of litmus paper
 placed in the cell and produces an increased pressure in the cell,
 the air remaining in the latter, because oxygen and nitrogen are
 very little soluble in water.

 [Illustration: FIG. 4.]

Membranes will be, similarly, semipermeable to solvent or solute,
when only one of these is soluble in the membrane, or is capable of
forming an unstable compound with it. For instance, salts, holding
water of crystallization which is readily lost and recovered,
may easily be conceived of as assuming the rôle of semipermeable
membranes, allowing the passage of water say from a wet atmosphere
to a dry one, or from pure water to a solution; and Tammann[31] has
realized such membranes by the use of zeolites—silicates, which hold
water of crystallization but are insoluble in water. Kahlenberg[32]
has recently used rubber membranes, that are permeable for solvents
like benzene, pyridine, etc., which are soluble in rubber, but not
permeable for water, which is insoluble in rubber.

 [Illustration: FIG. 5.]

«Osmosis.»—The recognition of this rôle of the semipermeable membrane
leads to the second question raised, namely as to the mechanism of
the process by means of which osmotic pressures are measured directly
with the aid of such membranes (p. 11). [p023] The answer hinges on
the question of the mechanism of the diffusion of the solvent into
the cell, a diffusion which is called its osmosis.[33] If we consider
the pure solvent, say water, on one side of a semipermeable membrane,
and a solution (‹e.g.› of sugar in water) on the other side, it is
obvious that the ‹solvent› itself has a ‹higher concentration› on the
side where it is pure, than on the side of the solution, where it is
diluted—distended by the solute in it. The solvent is soluble in the
membrane, and its solubility will be proportional[34] to its own (the
solvent's) concentration; it will, consequently, be more soluble in
the membrane on the side of the pure solvent than on the side of the
solution. If we bring such a membrane first into contact with the
pure solvent (Fig. 5), the membrane will take up the solvent (from
the side ‹A›) until it is ‹saturated› with it. Let the solubility,
which represents the concentration of the solvent in the membrane at
this stage, be called ‹c›. The membrane may then be considered to
be taking up in unit time just as many molecules from the solvent
as it gives up to it (dynamic equilibrium), exactly as, when water
is in equilibrium with water vapor, we consider the water to be
vaporizing just as fast as vapor is condensing to form water. Now, if
a solution of sugar is placed on the other side of the membrane, the
solvent will pass out of the membrane into the solution just as fast
as it passes back into the pure solvent. At first the concentration
of the solvent on the surface ‹B› of the membrane is just as great
(‹c›) as on the surface ‹A›; but ‹the membrane will here receive the
solvent more slowly from the solution, which is less concentrated as
to the solvent›; and consequently the membrane ‹will lose water to
the solution›. The solubility (‹c′›) of the solvent at this surface
‹B› of the membrane, corresponding to the smaller concentration of
the solvent in the solution, will be less than the solubility (‹c›)
at ‹A›, where the membrane is in contact with the pure solvent, and
water will pass into the solution at ‹B›, until the concentration of
the water in the membrane at ‹B› has fallen [p024] from (‹c›) to
(‹c′›). In such a membrane, as in every solution or gas, there must
be a tendency towards the establishing of uniform concentration by
diffusion from points of higher concentration to those of lower, and
the solvent will, therefore, ‹diffuse from points along the surface
A of the membrane to points along the surface B›; the surface ‹A›
will become ‹unsaturated› and will take up solvent from the pure
liquid bathing it, and the surface ‹B› will be kept continuously
supersaturated and will lose solvent continually to the solution.
Consequently, the solvent will pass continuously through the
membrane from the pure solvent to the solution. Equilibrium will be
reached, and the flow will cease, only ‹when the solution has become
infinitely dilute›, equal hydrostatic pressure obtaining on solution
and solvent, or ‹when the disturbing influence of the solute, which
dilutes the solvent in the solution, is exactly counterbalanced by an
external hydrostatic pressure, exerted on the solution›. When such a
pressure on the surface of the solution balances the force exerted
against the solvent by the solute we shall have equilibrium. It is
clear, then, that the ‹osmosis›, or passage of the solvent through
the membrane, is brought about by the unequal concentrations (or,
more exactly, the resulting ‹unequal partial pressures›) ‹of the
solvent itself. But this inequality is produced by the presence of
the solute, and it is a characteristic and significant fact, that
the effect of the latter, in dilute solutions, may be overcome by a
hydrostatic pressure, corresponding to the gas pressure which the
same number of molecules of a gas in the same volume at the same
temperature would exert against this hydrostatic pressure›.

 [Illustration: FIG. 6.]

«Osmosis and Gas Pressure.»—The legitimacy of the interpretation
given is most strikingly shown by experiments with a membrane,
semipermeable for gases, which enables us to measure gas pressures,
that may be unknown, by exactly the same process as is used to
measure the unknown osmotic pressure of a solute in solution. Van 't
Hoff[35] and Arrhenius[36] predicted such a result, and Ramsay[37]
proved by experiment the correctness of their assumptions. A
mixture of nitrogen and hydrogen may be enclosed in a palladium
vessel connected with a manometer (see Fig. 6).[38] The partial
pressure ‹P›_{‹N›} of the nitrogen may be [p025] determined by
surrounding the palladium vessel with pure hydrogen, at a pressure
which is known and is greater than the partial pressure of the
hydrogen in the vessel, and by observing the final total gas
pressure which is obtained in the vessel. The hydrogen diffuses
from the point of higher concentration, outside of the vessel,
through the palladium, into the interior where the concentration
of the hydrogen is lower. The experiment may be carried out at
280°, a temperature at which palladium readily dissolves hydrogen
and is permeable to it. The metal does not dissolve nitrogen and
is not permeable to it. The volume of the enclosed gas is kept
constant by raising the mercury level in the outside arm of the
manometer, and the total pressure of the enclosed gas is measured
when equilibrium is reached. If this total pressure is ‹P›_{final}
and the known pressure of the hydrogen outside of the vessel is
‹P›_{‹H›}, then, if equilibrium is reached when the hydrogen on
both sides of the semipermeable palladium membrane has the same
concentration (pressure), ‹P›_{‹H›} + ‹P›_{‹N›} = ‹P›_{final} and
‹P›_{‹N›} = ‹P›_{final} − ‹P›_{‹H›}. In other words, the excess of
the final combined pressure inside, over the outside pressure of the
hydrogen, ‹is equal to the pressure of the nitrogen in the vessel›.
Ramsay's results showed that the amount of hydrogen actually entering
the vessel was 90–97% of the amount predicted by the theory on the
basis of the assumption that equilibrium will be reached, when the
hydrogen has the same concentration (pressure) on both sides of the
palladium membrane.

The experiment is particularly instructive, in the first place,
because it illustrates with a gas, subject to the laws of gases, why
and how osmosis takes place through a semipermeable membrane—namely
as a result of the solubility of the diffusing substance in the
membrane, and through the flow of the diffusing substance [p026]
from higher to lower concentrations. In the second place, while
the increase in total pressure in the inner chamber undoubtedly is
‹brought about› by the ‹osmosis› of ‹hydrogen› into the chamber,
the excess pressure when equilibrium has been reached, necessarily
measures accurately the partial pressure of the ‹nitrogen›. In other
words, the semipermeable membrane is merely a means or ‹device for
measuring› the partial pressure of the nitrogen—the membrane is not
the ‹cause› of the pressure; the latter is a definite one, whether we
know what it is or not, and the osmosis of the hydrogen through the
palladium merely gives us a means of ascertaining it. Similarly, it
would be wrong to consider that the osmotic pressure of a solution
is caused, or brought about, by the flow of the solvent through a
semipermeable membrane (osmosis); the latter simply is a ‹device›
which enables us to recognize and ‹measure› the pressure that exists
in the solution, both in the presence and the absence of such a
membrane.

We may consider, then, that the osmosis, or migration of the solvent
through a semipermeable membrane into a solution, is the result of
the reduced concentration (or ‹partial pressure›) of the solvent in
the solution, resulting from the presence of the solute.

Inasmuch as the ‹effect› of the ‹solute› on the solvent can be
overcome by a ‹pressure› on the surface of the solution, one is led
to the conclusion that the solute acts by exerting, in turn, ‹a force
or pressure› against the surfaces of the solvent, in the directions
opposite to the hydrostatic pressure required to overcome it. The
significant identity of the value of this pressure, as thus measured,
with the gas pressure that would be exerted by a gas of the same
number of molecules, in the same volume and at the same temperature,
leads us to the last of the three questions which have been raised,
namely, the question concerning the theory of the intimate relations
between gas and osmotic pressures (p. 21).

«The Kinetic Theory and Osmotic Pressure.»—For an answer to this
fundamentally interesting theoretical question one turns, naturally,
to the kinetic theory, which, in the hands of Clausius, Joule,
van der Waals and others, has given us a very satisfactory and
essentially complete theoretical interpretation of the behavior of
gases, and of the liquids to which they may be compressed.

The laws of gases, it is known, are in accord with the two simple
assumptions of the kinetic theory. The first assumption is that
[p027] gases consist of ultimate discrete particles (molecules),
which move in all directions through the space filled by the gas and,
at ordinary pressures, are so far apart, that the forces of molecular
attraction between them are negligible; the ‹pressure› of the gas
is simply the net result of the impacts of these flying particles
upon the walls of the containing vessel. The second assumption of
the kinetic theory is that ‹temperature› is a function of the mean
kinetic energy of the moving molecules, and that the molecules of
gases of the same temperature have the same mean kinetic energy. The
kinetic energy of particles is a function of their mass ‹m› and their
velocity ‹u› (K.E. = ½ ‹m› ‹u›^2). When a gas is heated, the kinetic
energy of its molecules is increased, and, since their masses remain
unchanged, their velocity must increase. As a result, the number
and the force of their impacts against the walls of a given space
increase, and thus the pressure is increased.

We may ask, whether this theory cannot be used to explain the
connection between osmotic and gaseous pressure. If temperature
is a function of the kinetic energy of the molecules of which
a substance consists,—and the whole behavior of gases confirms
such a conception,—then one must conclude, that the mean kinetic
energy of molecules, at a given temperature, must always be the
same, irrespective of whether they are present in gaseous, or
liquid, or solid form, or even in solution.[39] The tendency of the
molecules to move, resulting from the kinetic energy inherent at a
given temperature, may be largely balanced (liquids), or overcome
(solids), by molecular attractions of surrounding particles, but
such conditions are altogether in harmony with the conception of
a definite mean molecular kinetic energy, persisting at a given
temperature, irrespective of the physical surroundings of the
molecule. According to the kinetic theory, then, when we have a
dilute solution, say of alcohol in water, the molecules of alcohol,
at a given temperature, would have a given mean kinetic energy,
[p028] and would be tending to move in all directions with a
mass[40] and velocity, the same as if the alcohol were present as a
gas or vapor at the same temperature. If the solution is sufficiently
dilute, the dissolved alcohol molecules are sufficiently far apart,
for average time, to make the molecular attractions between them
negligible, just as is assumed for gases. As far as the alcohol
(solute) molecules alone are concerned, they may, evidently, be
assumed to be present in the solution, in the same condition, as to
number, mean kinetic energy and mean velocity, as they would be in
alcohol vapor of the same concentration and temperature. We may ask,
now, whether the osmotic pressure of the solution may not result from
the pressure on the solvent, growing out of its bombardment by the
solute molecules. And we may ask, further, what numerical relation
would subsist between such a pressure and the pressure of the solute,
if the latter were present as a gas, under the same conditions of
temperature and concentration. In order to be prepared to answer
these questions, we must consider, in what way the presence of the
solvent must modify the motions and the forces of impact of solute
molecules.

One great difference between the dissolved substance and the gas
would be, that, in the solution, the solute is in intimate contact
with the ‹solvent›. A decided attraction must exist between the
solute molecules and the solvent molecules, since we could not
otherwise understand how a solvent, like water, in dissolving a
nonvolatile substance like sugar, could overcome those molecular
attractions between the sugar molecules, which make sugar a solid.
But we note, that all the solute molecules in a solution, except
those at the surface, are surrounded on all sides equally by the
solvent. The attractive forces, exerted upon the single molecules
of the solute by the solvent molecules, thus sum up to ‹zero›, and
need not be considered further. Only the small number of solute
molecules, which are at the surface of the liquid, would involve a
minor correction in the application of the kinetic theory, and this
need not be considered here.

A second point of difference between a substance in solution, and
the same substance as a gas or vapor at the same temperature [p029]
in the same volume, lies in the fact that a gas molecule will go a
much greater distance without colliding with some second molecule and
changing its path, than would a solute molecule, the latter molecule
being closely surrounded by the molecules of the solvent. The mean
‹free path›, as it is called, will be very much shorter for a solute
molecule than for a gas molecule, and we note, as a matter of fact,
how slow is the diffusion through a solvent (see ‹exp.› p. 8). But
the shortness of the previous path ‹does not affect the force of a
blow resulting from the impact of a moving mass›, the force of the
impact being dependent only on the mass and the change in speed of
the striking particle, at the moment of impact. Thus the short free
mean path of a dissolved molecule does not affect the mean ‹force› of
the blow, ‹delivered when it strikes the resisting medium›.

 The slow diffusion of a dissolved substance represents a difference
 in degree, not in kind, between gases and dissolved substances. Even
 in gases, we have such frequent collisions that the mean free path
 of an oxygen molecule at 0° and atmospheric pressure is only 0.00001
 cm., whereas the velocity, the total path covered in one second, is
 42,500 cm.

 EXP. If a bulb containing a few drops of bromine is broken at the
 bottom of a tall cylinder, the bromine vapor is seen to diffuse
 rather slowly into the upper part of the cylinder, the bromine
 molecules, in their passage upward, rebounding from the air
 molecules, with which the cylinder is filled. If a second cylinder
 is first evacuated, and the bromine bulb is broken ‹in vacuo›, the
 vapor is seen to fill the cylinder instantly, the high velocity of
 the bromine molecules being thus revealed.

But a third question, of fundamental importance in the comparison
of the condition of a substance existing as a gas and its condition
in a solution of the same concentration and temperature, results
from a consideration of the ‹frequency of the impacts› of the solute
molecules against the solvent, growing out of the reduction of the
lengths of the mean free paths of the solute molecules.[41] In order
to be able to take this fact properly into account, it will be
necessary to consider somewhat more precisely the manner in which,
according to the kinetic theory, gas pressure is produced.

We may consider that we have in a cube of unit volume (1 c.c.) ‹n›
molecules of a gas, each of mass ‹m› and average velocity ‹u› cm. per
second. We may assume that one-third of the total number [p030] of
molecules moves in each of the three dimensional directions.[42] A
single molecule of mass ‹m›, striking the surface with a velocity ‹u›
and rebounding with the same velocity in the opposite direction, will
exert on the surface a force of 2 ‹m› ‹u› units. But, with a velocity
of ‹u› cm. per second, it will reach the opposite wall and return
to the surface we are considering, ‹u› / 2 times in one second. A
single molecule will consequently exert a force 2 ‹m› ‹u› × ‹u› / 2
or ‹m› ‹u›^2 on the surface, and the ‹n› / 3 molecules moving in the
same direction will exert a force ‹n› / 3 × ‹m› ‹u›^2 on the unit
surface. This represents, therefore, the pressure of such a gas, as
calculated on the basis of the assumptions of the kinetic theory.
Now, when a gas is so strongly compressed, that the bulk of the
molecules is not negligible in comparison with the total volume of
the gas, the number of impacts on unit surface in unit time becomes
sensibly greater than ‹n› / 3 × ‹u› / 2, since the distance to be
covered between successive blows on the surface will be sensibly
less than 2 cm., in a cube of unit volume. If we imagine, for the
sake of a rough illustration, that one-third of the molecules in 1
c.c. are united into one spherical mass (indicated by A in Fig. 7),
moving upwards and downwards, it is obvious that the distance covered
between two successive blows on a surface is not 2 cm., but that
distance diminished by twice the diameter of the sphere. For strongly
compressed gases, the total number of impacts on unit surface is
therefore sensibly greater than ‹n› / 3 × ‹u› / 2, and the pressure
is proportionately greater. According to van der Waal's correction
for this effect, ‹P› = ‹n› / 3 × ‹m› ‹u›^2 / (1 − ‹b›), where ‹b›
represents the volume actually occupied by the molecules in 1 c.c. of
the gas.[43]

 [Illustration: FIG. 7.]

Now, for solute molecules, the "free space" of movement, as we may
call it, is, similarly, very considerably reduced by the presence
[p031] of the solvent, and the reduction of this free space, as
Nernst has shown, will have the same effect on the pressure produced
against unit surface of the solvent by the bombardment of the solvent
by the solute, as the reduction of the free space has on the gas
pressure when a gas is strongly compressed. The resulting pressure
on unit surface of the solution must thus be increased, from the
pressure ‹P›_{gas}, which would be exerted by the solute against
the walls of a vessel, if it were present as a gas of the same
concentration, at the same temperature, to ‹P›_{gas} / (1 − ‹v›),
where ‹v› represents the real volume occupied by the solvent and
(1 − ‹v›) the ‹free space› for the solute molecules ‹in unit volume›
of solution.[44] If osmotic pressure is the result of such a
bombardment of the solvent by the molecules of the solute, one might,
therefore, expect to find the osmotic pressure ‹very much greater›
than the gas pressure of the same substance in the same volume at the
same temperature. However, in all the ‹experimental determinations›
(by means of semipermeable membrane, vapor pressure, boiling-point
and freezing-point measurements) of the osmotic pressure as defined
on p. 10, this ‹corrective factor cancels› out again.[45] ‹According
to the kinetic theory›, the osmotic pressure of a substance in
‹dilute solution should, consequently, be found by experiment to
be equal to the gas pressure which a gas, of the same molecular
concentration, would exert at the same temperature›.[46]

We find thus that the significant coincidence between the osmotic
pressure of a substance in dilute solution, as defined and measured
according to van 't Hoff, and the gas pressure which the substance
would exert, if it were present as a gas in the same volume and
at the same temperature, is in agreement with the fundamental
assumptions of the kinetic theory. This theory, consequently, gives
us an adequate theoretical explanation of [p032] osmotic pressure,
as it does of gas pressure. As van 't Hoff says,[47] "if the osmotic
pressure follows Gay-Lussac's law and is proportional to the absolute
temperature, then, like gas pressure, it will become zero at 0°
absolute temperature and will vanish when molecular movements come
to rest. It is therefore natural to look for the cause of osmotic
pressure in kinetic phenomena and not in attractions."[48]


  FOOTNOTES:

  [29] L'Hermite, ‹Compt. rend.›, «39», 1177 (1854); van 't Hoff,
  ‹Lectures on Physical Chemistry›, ‹Part II›, p. 37.

  [30] Nernst, ‹Theoretical Chemistry›, p. 103.

  [31] Van 't Hoff, ‹Lectures on Physical Chemistry, Part II›, p. 37.

  [32] ‹J. Phys. Chem.›, «10», 141 (1906).

  [33] This term ‹must not be confounded with the term osmotic
  pressure›, which has been defined on p. 10.

  [34] See Chapter VII on the law of physical or heterogeneous
  equilibrium, where the relations are discussed in detail.

  [35] ‹Z. phys. Chem.›, «5», 175 (1890).

  [36] ‹Ibid.›, «3», 119 (1889).

  [37] ‹Phil. Mag.›, «38», 206 (1894).

  [38] ‹Cf.› van 't Hoff's ‹Lectures on Physical Chemistry›, Vol. II,
  40 (1899).

  [39] The molecules may have different masses in the different
  conditions, and the principle of the mean kinetic energy would
  always apply to them as ‹they are›, in the condition under
  observation, and not as they are in some other condition; any
  change in mass, in solution, for instance, would show itself in
  the osmotic pressure measurements (see p. 18), just as it is
  shown in the measurements of gases, when the gas molecules show
  a change in composition, as is the case with hydrogen fluoride
  (H_{2}F_{2} ⇄ 2 HF), nitrogen tetroxide (N_{2}O_{4} ⇄ 2 NO_{2}),
  phosphorus pentachloride (PCl_{5} ⇄ PCl_{3} + Cl_{2}) and other
  compounds.

  [40] The molecular weight of alcohol in dilute aqueous solution is
  the same (46) as in vapor form. Raoult, ‹Z. phys. Chem.›, «27»,
  656; Loomis, ‹ibid.›, «32», 592.

  [41] Nernst, ‹Theoretical Chemistry›, p. 245.

  [42] This assumption is not made in the rigorous development of the
  above relations on the basis of the kinetic theory, but it leads to
  the same net result.

  [43] Even for gases of ordinary concentration, the introduction
  of the same correction gives an expression for the relation of
  pressure and volume, which is more exact than Boyle's law and is
  used in all exact calculations with gases.

  [44] One may imagine, first, ‹n› molecules of the solute as
  a ‹gas›, with the pressure ‹P›_{gas}, in 1 c.c. Then, one
  may imagine, crudely, the ‹n› molecules of solute, in a free
  (gas) space of (1 − ‹v›) c.c., in the center of 1 c.c. of the
  solvent, and exerting by their impacts a pressure ‹P›_{osm.},
  against the solvent. According to Boyle's law, we should then
  have, ‹P›_{gas} × 1 = ‹P›_{osm.} × (1 − ‹v›), and therefore
  ‹P›_{osm.} = ‹P›_{gas} / (1 − ‹v›).

  [45] ‹Vide› Nernst, ‹Theoretical Chemistry›, p. 245, for the
  detailed discussion of this relation.

  [46] This conclusion is reached more rigorously and more simply by
  thermodynamic analysis.

  [47] ‹Lectures on Physical Chemistry›, Part II, p. 35.

  [48] Rigorous developments of the relations between solute and
  solvent, for dilute and concentrated solutions, have been made
  by van der Waals, ‹Z. phys. Chem.›, «5», 133 (1890); van Laar,
  ‹ibid.›, «15», 457 (1894); G. N. Lewis, ‹J. Am. Chem. Soc.›, «30»,
  675 (1908), and Washburn, ‹ibid.›, «32», 653 (1910). An admirable
  review of the theories of osmotic pressure, by Lovelace, will be
  found in the ‹Am. Chem. J.›, «39», 546 (1908) («Stud.»).

[p033]




 CHAPTER IV

 «THE THEORY OF IONIZATION; IONIZATION AND ELECTRICAL CONDUCTIVITY»


Of the laws and hypotheses concerning gases, the one that is perhaps
of most importance to chemistry is Avogadro's hypothesis. With
the aid of this hypothesis, we are able to determine the relative
molecular weights[49] of such elements and compounds as are gases,
or are volatile at higher temperatures. If equal volumes of gases,
under the same conditions of temperature and pressure, contain the
same number of molecules, then the weights of such equal volumes
also represent the relative weights of the molecules composing the
gases. As a standard, for expressing the relative molecular weights
in definite numbers, the molecular weight of oxygen is taken by
convention to be 32, and all other molecular weights are expressed
in terms of this standard. The density, or weight of one liter of
oxygen at 0° and 760 mm., is 1.429 grams, and the ‹molecular weight
expressed in grams (molar weight)› of oxygen, 32 grams, occupies,
therefore, 32 / 1.429, or 22.4 liters. The weights of ‹this same
volume›, 22.4 liters, of gases and vapors, calculated for 0° and
760 mm. pressure,[50] express then directly, in terms of the oxygen
standard, the relative molecular weights of the elements or compounds
forming the gases. The weights themselves give us directly their
gram-molecular or molar weights.

When molecular weights are determined in this way, with the aid of
Avogadro's hypothesis, results are obtained which agree [p034]
perfectly with the chemical behavior of the compounds or elements in
question. The molecular weights of hydrogen chloride, water, ammonia,
and marsh gas, for instance, are found to be 36.5, 18, 17 and 16,
respectively, corresponding to the formulæ[51] HCl, H_{2}O, NH_{3}
and CH_{4}, and in confirmation of these results we find, by methods
used especially in organic chemistry, that these compounds show a
chemical behavior agreeing perfectly with the presence of one, two,
three and four hydrogen atoms, respectively, in their molecules.
Marsh gas, for instance, by treatment with chlorine, yields a
monochloride, CH_{3}Cl, a dichloride, CH_{2}Cl_{2}, a trichloride
(chloroform), CHCl_{3}, and a tetrachloride, CCl_{4}. Water, by
proper treatment, may be converted in successive stages into alcohol,
(C_{2}H_{5})OH, and then into ether, (C_{2}H_{5})O(C_{2}H_{5}), or
into sodium hydroxide, NaOH, and sodium oxide, Na_{2}O.

 It is this perfect agreement between the chemical behavior and the
 formulæ (as based on these molecular weights and on the analysis of
 compounds), which forms the strongest ‹experimental evidence› of the
 correctness of the fundamental assumption of Avogadro's hypothesis.
 The agreement has been shown to hold for innumerable compounds,
 even for those of greatest complexity, and it was such agreement
 which finally led to the general acceptance of the hypothesis. The
 experimental evidence of this nature is so strong, so extensive and
 so completely corroborative of the hypothesis, that many chemists,
 rather justly, consider the hypothesis to have been established as a
 law, although the evidence is circumstantial rather than direct.

While the application of Avogadro's hypothesis thus gives results
agreeing well with the observed chemical behavior of very many
important compounds, observations have been made which, at first
sight, do not appear to agree with the requirements of the hypothesis
and which seem to raise a doubt as to the ‹universal truth› of its
fundamental assumption. Thus, if equal volumes of hydrogen chloride
and ammonia, of the same temperature and pressure, are brought
together, ammonium chloride is formed, both gases being totally
consumed. Since, according to the hypothesis, equal volumes, under
the conditions obtaining, contain the same numbers of molecules,
the formation of ammonium chloride takes place according to the
equation NH_{3} + HCl → NH_{4}Cl, and we should anticipate that the
molecular weight of [p035] ammonium chloride would be 17 + 36.5 or
53.5. However, when the molecular weight is determined by obtaining
the weight of a measured volume of ammonium chloride vapor, at
a temperature sufficiently high to vaporize the salt, and the
observations are reduced to standard conditions of temperature and
pressure, 26.75 grams is found as the calculated weight of 22.4
liters, and this weight, according to this hypothesis, should be
the molecular weight of the chloride. This contradiction in two
conclusions, each reached by the application of Avogadro's hypothesis
to experimental observations, would, at the first glance, make one
hesitate to accept the hypothesis as representing a universal truth;
it might seem as if in some gases, such as ammonium chloride vapor,
there might be only half as many molecules in a given volume as in
the same volume of the majority of gases.

«Gaseous Dissociation.»—The discrepancy between the two conclusions
and any doubt as to the universal soundness of the great
generalization expressed in Avogadro's hypothesis disappear, however,
in the light of a closer study of the composition of ammonium
chloride vapor. It was suggested simultaneously by Cannizzaro, by
Kopp and by Kékulé[52] that the abnormally low result, obtained
for the molecular weight of ammonium chloride from a study of its
vapor density, is due to the ‹dissociation› of the salt at high
temperatures into its components, ammonia and hydrogen chloride, the
‹average› of whose ‹molecular weights› is, in fact, (17 + 36.5) / 2,
or 26.75, the value found experimentally for the vapor of ammonium
chloride. Proof of the correctness of this interpretation was
furnished by Pébal,[53] who showed that ammonium chloride vapor does
consist of the two gases, the lighter of which, ammonia, diffuses
more rapidly through porous walls (Pébal used an asbestos stopper)
than does the heavier, hydrogen chloride. The dissociation may be
easily demonstrated by using an air cushion as a porous wall.[54]
From the mixture produced by vaporizing ammonium chloride,[55] the
ammonia will diffuse more rapidly through the layer of air than will
the hydrogen [p036] chloride, and the gases may be recognized in
succession by their action on litmus paper (‹exp.›).

The ‹gaseous dissociation› of other ammonium salts, of phosphorus
pentachloride and pentabromide (PX_{5} ⇄ PX_{3} + X_{2}), and of a
number of less common compounds, has been demonstrated in similar
ways. As a result of the study of each case, the important conclusion
has been reached that, as far as our knowledge goes, there are no
exceptions to Avogadro's hypothesis, and this hypothesis seems
therefore to represent a universal truth.[56]

«Molecular Weight Determinations in Solution.»—Van 't Hoff's
extension of the Avogadro Hypothesis, so that it shall apply to
solutes in dilute solutions, is the basis of another general method
of greatest value for determining molecular weights. Equal volumes
of dilute solutions of the same osmotic pressure and the same
temperature contain, according to van 't Hoff, the same numbers of
dissolved molecules, irrespective of the solvent used. Furthermore,
the number of dissolved molecules is identical with that which a
gas of the same pressure and at the same temperature would contain
in the same volume. To determine the molecular weight of a solute,
therefore, we may calculate, from the osmotic pressure, the
temperature and the concentration of the solution,[57] that weight of
the solute which, in 22.4 liters of the solution, at 0° would give
760 mm. osmotic pressure; the weight found represents, in grams, the
‹molecular weight› of the solute ‹in the solution used›. [p037]

The fact that ‹all solvents› and ‹all solutes› are included in this
hypothesis, with the sole limiting condition that the solution must
be dilute, is one of great significance and of greatest practical
importance, as we may use any suitable solvent for determinations.

When molecular weights are determined in this way, a very large
number of compounds give the same molecular weight by the solution
method as by the gas method. For instance we have:

       Substance.                   Mol. Wt.     Mol. Wt.    Solvent.
                                  Gas Method.  Sol. Method.
  Chloroform, CHCl_{3}                119.5      119.5       Benzene
  Carbon bisulphide, CS_{2}            76         76         Benzene
  Methyl (wood) alcohol, CH_{4}O       32         32         Water
  Ethyl (ordinary) alcohol,
    C_{2}H_{6}O                        46         46         Water
  Ether, C_{4}H_{10}O                  74         74         Acet. Acid

Further, the molecular weight of glucose is found in aqueous
solutions to be 180, conforming to the formula C_{6}H_{12}O_{6}, and
agreeing with the molecular weight as obtained by a chemical study of
compounds derived from glucose.

While there are, then, very many agreements in the molecular
weights determined by the solution and by the older methods, it was
recognized, at the outset,[58] that there is also a large number of
apparently ‹abnormal› cases, in which, in particular, ‹much lower
molecular weights› are obtained by the solution methods than by the
gas method,—lower even than the weights consistent with the accepted
atomic weights of the elements in the compounds in question.[59]
For instance, we find 36.5 to be the molecular weight of hydrogen
chloride in the gas form, but in ‹aqueous› solution its apparent
molecular weight, as determined on the basis of van 't Hoff's
hypothesis, is not even a constant; it is found to be less than
36.5 and approaches the limit 18.25, the more dilute the solution,
[p038] the lower being the apparent molecular weight.[60] For sodium
chloride, the formula weight, corresponding to the formula NaCl, is
58.5. This would also represent its smallest molecular weight in gas
form, consistent with the accepted atomic weights for sodium and
chlorine. In ‹aqueous› solution, again, the apparent molecular weight
of sodium chloride is found to be less than 58.5, and more than
29.25, the value found depending on the concentration of the solution
used. For zinc chloride we have, likewise, in aqueous solution values
much less than 136 and tending toward the limit 45, whereas the
formula weight for ZnCl_{2} is 136.

These are instances of a very large class of apparent gross
discrepancies between the requirements of the Avogadro-van 't Hoff
principle and the generally accepted molecular weights of common
compounds. There are three ways, in particular, in which one might
be inclined to regard such results: in the first place, one might
be tempted to consider that van 't Hoff's extension of Avogadro's
hypothesis to solutions is justified in a considerable number of
cases, but not as a ‹universal› expression, applicable to ‹all›
dilute solutions. This seems, indeed, to have been van 't Hoff's own
attitude originally. Such a view, since it does not throw new light
on the matter, but simply shelves the question of the source of the
discrepancy, would be tenable only after all other explanations had
been found unsatisfactory.

In the second place, we might be inclined to consider whether a
molecule like hydrogen chloride is not dissociated in aqueous
solution into two smaller molecules, ‹h›‹cl›, in which hydrogen
and chlorine would appear as atoms with the weights ‹h› = 0.5
and ‹cl› = 17.75, which are half as large as the atomic weights
determined from a study of volatile compounds of hydrogen and
chlorine. If we remember that our atomic weights are confessedly
maximum weights, and not minimum weights—although they are almost
certainly also the true atomic weights—such a view would be, at
least, worthy of some consideration. But, in the first place,
it would be extraordinary that we should never have found, in
the thousands of [p039] hydrogen derivatives that have been
investigated, any compound, the molecule of which, in the gaseous
condition, contained a ‹single› such atom of hydrogen, with the
weight 0.5, or an ‹uneven› multiple of it: that only ‹even› multiples
or pairs ‹h›_{2}, corresponding to the atom H, should always
have been found. In the second place, such an explanation of the
results of the molecular weight determinations in aqueous solutions
given above, would soon lead to difficulties, which make the view
altogether untenable. For instance, the molecule of zinc chloride,
according to the data given, would have to break down into three
molecules and, if these were of uniform composition, we would have to
assume chlorine atoms two-thirds or one-third as large as Cl. Since a
moment ago we had to assume chlorine atoms one-half as large as Cl,
we would have to conclude that the atomic weight of chlorine could
be, at most, Cl / 6, which is the largest common divisor of Cl / 2
and Cl / 3. No chemist would seriously consider an atomic weight
for chlorine one-sixth as large as the accepted weight, for that
would mean that, in all the chlorine compounds investigated in the
condition of gases, we have always at least six such atoms occurring
together, and otherwise always multiples of six. Consequently such
an interpretation of the so-called "abnormal" behavior of solutions
of hydrogen chloride, sodium and zinc chlorides, etc., although at
one time advanced by some chemists, must be considered as altogether
untenable.

A third explanation of the "abnormally" low molecular weights,
which certain substances in aqueous solutions possess, is, that
the molecules of these compounds are ‹capable of dissociation into
smaller molecules of unlike composition›, somewhat like ammonium
chloride when it is heated, and that the substances in question
are dissociated more or less considerably in this fashion in the
solutions under consideration. Hydrogen chloride, for instance,
besides existing as such (as HCl), in aqueous solutions, might
be capable of dissociating, and actually be dissociated, to a
considerable degree into molecules containing either only hydrogen
or only chlorine (HCl ⇄ H + Cl); the ‹average› of the weights of
the molecules in a mixture of molecules, HCl, H, and Cl, would be
‹less› than 36.5, and, according to the proportion of dissociated and
undissociated molecules of hydrogen chloride, the average would lie
between the limits 36.5 and (1 + 35.5) / 2, or 18.25. Such an [p040]
explanation,[61] made with ‹certain additions and restrictions›, was
advanced in 1885 by Arrhenius, a Swedish chemist and physicist, when
he learned of the exceptional behavior of these solutions, as noted
by van 't Hoff. Although at first this interpretation occasioned
considerable criticism, it has maintained itself successfully for
twenty years, on the basis of a wide range of accumulated facts, and
it has been of remarkable value and benefit in the development of all
branches of chemistry and the allied sciences.

«The Theory of Ionization.»—Arrhenius[2] made the simple observation
that all those solutions, in which the dissolved compounds seem to
have abnormally low molecular weights, are solutions through which an
‹electric current› may be readily passed, they are ‹electrolytes›,
whereas the solutions which give normal results (see, for instance,
the table on p. 37) do not allow the ready passage of a current, they
are ‹nonelectrolytes›.

 EXP. The fundamental difference between the two classes of solutions
 may readily be demonstrated. To water contained in an electrolytic
 cell, which is connected with a lighting circuit and with an
 electric lamp, first some alcohol, and later a small quantity of
 hydrochloric acid are added. The lamp is seen to glow, instantly,
 when the acid is added.

This simple fact, that the very solutions which give abnormally
low molecular weights for the dissolved compounds are also good
conductors of electricity, was explained by a theory of ‹electrolytic
dissociation› or of ‹ionization›, which Arrhenius had developed[62]
from a study of the conductivity of electrolytes. The same fact has
aided in establishing this theory which has led to the elucidation
of vital problems of ‹electrical conductivity› and to a successful
[p041] explanation of the problem of the apparently abnormal
‹osmotic pressures› (and ‹molecular weights›) of electrolyte solutes.
It has thus removed the last difficulty in the way of accepting
the van 't Hoff-Avogadro Hypothesis (p. 15) as true for all dilute
solutions, exactly as the discovery of ‹gaseous dissociation› made it
possible to recognize in the original Avogadro Hypothesis a universal
truth (p. 36) about gases. And to these results was added, chiefly
as the fruit of the work of Ostwald, with the aid of the theory
of Arrhenius, the most successful and accurate formulation of the
problem of the ‹chemical activity› of electrolytes, known in the
history of chemistry.

«Main Assumptions of Arrhenius's Theory of Ionization.»—The main
assumptions of the theory of electrolytic dissociation or ionization
are the following: (1) When an ionogen is dissolved in water, its
molecules are immediately, more or less completely, ‹dissociated by
the water› into smaller fragments or molecules of unlike composition.
(2) These new molecules are charged with ‹electricity›; the molecules
of the one product are charged with ‹positive›, the molecules of the
other product[63] with ‹negative electricity›, the unit positive
charge being equal in quantity, but opposite in kind, to the unit
negative charge; the sum of all the positive charges in a solution is
equal to the sum of all the negative charges, and the whole solution
is electrically neutral. (3) The dissociation is a reversible
reaction, and all electrolytes must be considered to be ‹completely
ionized at infinite dilution›. (4) Except for the dependence
resulting from the electrical charges and the consequent attractions
and repulsions between ions, the ions must be considered independent
molecules with their own ‹specific chemical› and ‹physical›
properties.

When a current is passed through the solution of an ionogen, the
electrified particles carry their charges to the electrodes (see
[p042] below). They are called the ‹ions›[64] of the electrolyte;
the positively charged ions are distinguished as ‹cations› from the
negatively charged ‹anions›, and the electrode toward which the
cations move is called the cathode (negative electrode), and the
electrode to which the anions move is called the ‹anode› (positive
electrode).

The dissociation of hydrogen chloride may be expressed, in
the terms of the assumptions made, in the following equation:
HCl ⇄ H^{+} + Cl^{−}; that is, hydrogen chloride is dissociated, to a
greater or smaller extent and in reversible fashion, into positively
charged hydrogen ions H^{+}, and negatively charged chloride ions
Cl^{−}, and the charge on each chloride ion is equal in quantity
to the positive charge on each hydrogen ion. Zinc chloride is
dissociated according to the equation ZnCl_{2} ⇄ Zn^{2+} + 2 Cl^{−},
and, according to (2), the charge on each zinc ion is twice as great
in quantity as the charge on each chloride ion, and therefore twice
as great also as the charge on each hydrogen ion (see below, p.
58). It is practically certain, according to more recent results,
that the ions are combined with water to form hydrates, such as
H^{+}(H_{2}O)_{‹x›} and Cl^{−}(H_{2}O)_{‹y›}.[65] This does not
modify, essentially, the fundamental assumptions of the theory, but
contributes rather to a satisfactory explanation of the rôle of water
as an ionizing agent, a question to which we shall return later.

«The Theory of Ionization and the Electron Theory of Electricity
and of Matter.»[66]—According to the views held by many leading
physicists at the present time, ‹negative electricity› consists
of ultimate particles of matter called electrons or corpuscles.
The mass of an electron is about 1 / 1000 the mass of an atom of
hydrogen, and the electric charge of the electron is equal to that
carried by a chloride ion in solution.[67] The atoms of the elements
are considered to consist of aggregations of large numbers of
electrons in a kind of "shell" or "body" of positive electricity.
This positive electricity, in a given atom, is equal in quantity to
the total negative charge of the electrons in the atom, the atoms
as such [p043] containing no excess of either positive or negative
electricity. The number of electrons in the atom of an element is
considered to be definite and constant for that element, but the
number varies as we go from the atoms of one element to those of a
second element, the number increasing with the atomic weight of the
element.

One of the most fundamental and most characteristic properties of
elements is considered to be the ‹affinity which their atoms show
for electrons›; thus, the atoms of metals like sodium and potassium,
which are generally called "electropositive" elements,[68] show an
enormous tendency ‹to lose one electron› each and to form positively
charged particles[69] Na^{-ε} (= Na^{+}) and K^{-ε} (= K^{+}).[70]
The atoms of strongly electronegative elements, like chlorine, have
a tremendous tendency for ‹gaining› and ‹holding electrons› beyond
the number originally in such atoms. Thus, chlorine atoms tend to
‹assume an electron› each; they thereby become ‹negatively charged›
particles, Cl^{+ε} ( = Cl^{−}).

On the basis of these views, we have in sodium chloride NaCl a
substance, whose molecules contain an atom, Na, with a tremendous
‹tendency to lose an electron›, and an atom, Cl, which has
a tremendous ‹affinity for an electron›. It is natural to
suppose, then, that ‹both tendencies will be satisfied by the
passage of an electron from the sodium to the chlorine atom›,
NaCl → Na^{-ε}Cl^{+ε}. Or, if we use the sign + to designate the
positive charge produced on an atom by the loss of an electron and
the sign − to indicate the charge gained through the assumption of
an electron, we have[71]: NaCl is Na^{+}Cl^{−}. Similarly we have
in hydrogen chloride H^{-ε}Cl^{+ε} or H^{+}Cl^{−}. It is altogether
likely, therefore, that the atoms in a molecule of sodium chloride
or of hydrogen chloride already possess electric charges,[72] so
that, even while combined, [p044] their tendencies to lose or gain
electrons are satisfied. It is also possible that the atoms are held
together in the molecule by the electrical attraction of the opposite
charges.[73] The force with which opposite electrical charges
attract each other depends, as is well known, on the nature of the
‹surrounding medium›. Now, when molecular sodium chloride or hydrogen
chloride is dissolved in water (a favorable medium), a decided
decrease in the attraction (see p. 62), between the charged atoms
within the molecules is brought about, and a process of ‹ionization›
results: H^{+}Cl^{−} ⇄ H^{+} + Cl^{−}. The charged particles are
called ‹ions› only after they have separated from one another and
have become independent molecules, capable, for example, of moving in
‹opposite› directions.

While the atoms of some metallic elements tend to lose a single
electron and form ions Me^{+} (‹e.g.› Na^{+}, K^{+}), the atoms of
other elements tend to lose two or more electrons, forming bivalent
ions, Me^{2+} (‹e.g.› Zn^{2+}, Fe^{2+}, etc.), or trivalent ions,
Me^{3+} (‹e.g.› Bi^{3+}, Fe^{3+}), and so forth. Similarly, atoms of
the so-called negative elements may assume two or more electrons,
forming bivalent ions, X^{2−} (‹e.g.› S^{2−}), and so forth.

«The Validity of the Theory of Ionization.»—In determining the
validity of the theory of ionization, we may consider, first, the
sufficiency of the explanations which it offers for observed facts
and important phenomena. We may then weigh, more critically, by any
evidence offering itself, the facts which will enable us to decide
between this theory and the older theory of ionization, that of
Clausius (p. 51). The latter, although displaced, is still often
revived by opponents of the modern theory. Such facts as we will
consider are found, first, in the domain of ‹conductivity phenomena›,
next, in the ‹osmotic pressure› and related properties of solutions,
and, finally, in the study of the ‹chemical activity› of electrolytes
(see Chapter V).

«Ionization and Electrical Conductivity.»—Turning our attention first
to the field of electrical phenomena, and developing the theory
for the present descriptively, we find that the conductivity of a
solution depends, according to this theory, on the fact that when
two oppositely charged poles are placed in a solution, the [p045]
positive charge on the anode attracts all the negative particles
within its field of action, and repels all the positive particles,
exactly as a positive static charge of electricity would attract a
negatively charged pith-ball and repel a positively charged one. In
the case of a solution of hydrochloric acid, the negative charge on
the cathode would attract the hydrogen ions and repel the chloride
ions, and the positive charge of the anode would attract the
chloride ions and repel the hydrogen ions. The net result would be a
migration of all the chloride ions with their negative charges toward
the anode, and of the positively charged hydrogen ions toward the
cathode,—a flow or ‹current of electricity› being thus produced. The
fact, then, that a current of electricity does readily pass through
such a solution of an ionogen, is easily understood on the basis of
these views.

 [Illustration: FIG. 8.]

 EXP. The migration of the ions throughout the whole solution may
 be demonstrated by the passage of a current through a large U-tube
 containing a mixture of a cupric salt and a permanganate,[74]
 placed under some dilute sulphuric acid. The cupric-ion is blue,
 all ionized solutions of cupric salts, with a colorless negative
 ion, being blue, while the permanganate-ion is of an intense purple
 color. In the limb of the U-tube, in which the cathode is placed, a
 blue zone, containing cupric ions, is soon seen emerging from the
 purple liquid and rising toward the cathode (see Fig. 8). It will
 take some time for any cupric ions actually to reach the electrode
 and be deposited as metallic copper. On the anode side, purple
 permanganate ions are seen rising toward the positive electrode.

The movement of the electrically charged particles in opposite
directions through the solution constitutes an electric current,
and such a current has the properties of a current through a [p046]
wire—producing, for instance, heat, or being capable of deflecting a
magnet placed in its field of action.[75]

«Electrolysis.»—When ions touch an electrode, they are discharged,
and with the discharge, are changed chemically, and, according to the
electron theory, also materially. Cupric ions, Cu^{2+} or Cu^{−2 ε},
receiving two electrons at the cathode, are precipitated as metallic
copper. When a current is passed through a solution of hydrochloric
acid, the hydrogen ions, by the pairing of the discharged ions,
yield hydrogen gas consisting of molecules, H_{2}; the chloride ions
are converted at the anode into chlorine Cl_{2}. The formation of
these molecules, X_{2}, may be variously interpreted, as resulting
either from the union of two discharged or neutral atoms, or as
consisting, for instance in the case of hydrogen, in the discharge
of a hydrogen ion H^{+}, at the negative electrode, ‹followed by
the assumption of a negative charge or electron by the neutral
atom›, the new ion H^{−} combining at once with the positive ion
H^{+} to form the molecule H^{+}H^{−}. At the positive pole, by an
analogous recharging of a discharged negative chloride-ion Cl^{−},
we should obtain a positive ion,[76] Cl^{+}, and immediately the
formation of Cl_{2} or Cl^{+}Cl^{−} would follow. Helmholtz advocated
the latter conception of the action at the electrodes, and, more
recently, J. J. Thomson[77] brings forward, as a very important
argument in favor of it, the fact that iodine, which according to
vapor density determinations dissociates into monatomic molecules
at high temperatures (I_{2} ⇄ 2 I), becomes, simultaneously
with this dissociation, also an excellent ‹gaseous conductor
of electricity›, as would be anticipated from a dissociation,
I^{+}I^{−} ⇄ I^{+} + I^{−}. This fact is emphasized here, because
in it we seem to have a case of ‹conductivity› coinciding with
‹gaseous dissociation›, the existence of which is recognized by the
universally accepted laws of gases, and differing in no important
respect from the dissociation assumed for conductors in solution.

«Conductivity and Dilution.»—The passage of a current through an
electrolyte consists, then, in a transfer of electricity by material
particles, the ions. According to the theory of ionization only
[p047] the ionized portion of an electrolyte can carry the current
at any moment, and, consequently, a ‹given weight› of an ionogen
should, under comparable conditions, be the more efficient as a
conductor, the more completely it is dissociated into ions.

If the conductivity of a given weight of hydrogen chloride, for
instance, is measured under comparable conditions, it should be
found to be greater, the more completely the acid is ionized. Now,
in aqueous solutions, hydrogen chloride ionizes under the influence
of the ‹solvent water› (pp. 41, 61), and the theory would lead us
to anticipate that the greater the proportion of water used, the
more extensively will it ionize the acid. Consequently, the addition
of water to a given weight of acid should increase the latter's
efficiency as a conductor. This conclusion has been fully verified by
exact methods of measurement and may be readily demonstrated by the
following series of experiments:

 EXP.[78] An electrolytic cell, having the shape of a
 parallelopipedon and a capacity of about one liter, is fitted with
 electrodes of copper, which reach from the bottom to the top of
 the cell and are connected with a storage cell and an ammeter. The
 cell is first filled with distilled water: no perceptible current
 passes through the water and the latter is therefore practically a
 nonconductor. The cell is then emptied by means of a siphon and 20
 c.c. of 4-molar hydrochloric acid is brought into it. The ammeter
 shows that a definite current passes through the solution (0.17
 ampere in an experiment[79] with a cell 4.6 cm. wide and 11.5 cm.
 long, with copper electrodes 4.6 cm. broad and 21 cm. high). (See
 Fig. 9, p. 48.) [p048]

 [Illustration: FIG. 9.]

The conductivity of a solution, like that of a metal conductor, is
the reciprocal of its resistance. Since, according to Ohm's law,[80]
the current for a ‹given potential› is inversely proportional to
the resistance, the current is also directly proportional to the
conductivity. The resistances of the metal connections and of
the ammeter in the experiment are very small compared with the
resistance of the solution, and they may be considered negligible
for our purpose. Thus, ‹the current indicated by the ammeter is a
closely approximate measure of the conductivity of the solution›.
Now, if a volume of water (20 c.c.) equal to the volume of acid,
were to be added to the latter, the cross section through which the
current flows from plate to plate would be ‹doubled›, and, since the
conductivity of a liquid conductor, like that of a metal, increases
proportionally to the cross section, the current should be doubled by
the change in this one factor. On the other hand, the concentration
of the conducting acid is now ‹one-half› of the original
concentration, and this should in turn reduce the conductivity of the
solution to one-half. Consequently, if there were no further change
in the electrolyte, the original conductivity should be maintained
when the acid is thus diluted. But, according to the theory of
ionization, as has just been shown, the addition of [p049] water to
a given weight of hydrochloric acid ‹should increase the proportion
of ionized acid›, and since the ions are the carriers of the current,
the ‹conductivity› of the solution should be ‹increased› because of
this change in the ‹composition› of the electrolyte. Experiment shows
that such is the case.

 EXP. 20 c.c. of water is added to the 20 c.c. of 4-molar acid in the
 cell, and the mixture is stirred. The current is decidedly increased
 (from 0.17 to 0.22 ampere in the experiment under discussion).
 If 40, 80, 160 and 320 c.c. of water are added in succession
 to the contents of the cell, the conductivity is ‹increased by
 every addition of water›. But, while each addition dilutes the
 acid to one-half the previous concentration, the ‹increase grows
 proportionally smaller and smaller with increasing dilution›. In
 the following table, "Ratios I" are the ratios of the observed
 conductivities ‹to the original conductivity›, "Ratios II" the ratio
 of each observed conductivity to the ‹preceding one›.

  ‹Concentration›      ‹Observed›         Ratios I.  Ratios II.
    ‹of Acid.›      ‹Conductivity.›[A]

       4-molar            0.17             1           1.
       2-molar            0.22             1.30        1.30
       1-molar            0.26             1.53        1.18
     0.5-molar            0.30             1.76        1.15
    0.25-molar            0.31             1.83        1.04
   0.125-molar            0.32             1.88[B]     1.03

  TABLE NOTES:

  A. This is an artificial scale (see text) of conductivities,
  and does not represent reciprocal ohms, the standard units of
  conductivity.

  B. In the exact data on the conductivities of 4-molar and
  1/8-molar HCl (Kohlrausch and Holborn, ‹Leitvermögen der
  Elektrolyte› (1898) p. 160), the ratio 348 / 181.5, or 1.92,
  is found, in place of 1.88 as observed.

We should expect, further, that the increase in conductivity, being
dependent on the increased dissociation of a finite quantity of
electrolyte, should tend towards a ‹limit›, a maximum conductivity
being reached when (practically) all the acid is ionized. As a
matter of experience, the conductivity of a given quantity of an
acid or other ionogen does tend toward a ‹limit›. In the experiment
just made, the conductivity of the acid increases very rapidly at
first, as the 4-molar acid is diluted by water; but the increase
in conductivity with the succeeding dilutions grows ‹smaller› and
‹smaller› and the conductivity is plainly approaching [p050] a limit
(see the ratios I and II in the table). For hydrochloric acid at 18°,
the limit for one mole[81] (36.5 grams HCl) at infinite dilution, as
deduced from the curve of conductivities at finite dilutions, is 384
reciprocal ohms.[82]

«Degree of Ionization of an Electrolyte.»—The conductivity of a
given weight of an electrolyte, for instance of its gram-equivalent
weight, depends, then, at a given temperature on the extent to which
it is ionized, the ions being the only carriers of the current in
a solution of an electrolyte. The conductivity will also depend
on the friction which the ions must overcome in moving through a
solution, but, for sufficiently dilute solutions in a given solvent,
the friction may be assumed to be approximately constant for given
ions. For such solutions, then, the conductivity of a given weight
of a given electrolyte at a given temperature may be said to depend
wholly on the extent to which the electrolyte is ionized. Thus, the
proportion of ionized electrolyte in a solution may be determined by
measuring the conductivity. ‹The extreme limit of its conductivity,
calculated for infinite dilution, represents complete ionization›
of the electrolyte according to a fundamental postulate (§ 3, p.
41) of the theory of Arrhenius, and the ratio of the conductivity
in a given solution to the conductivity of the same weight of
electrolyte at infinite dilution represents then the ‹proportion of
ionized electrolyte to the total electrolyte› used. This proportion
is called its ‹degree of ionization› (commonly designated by α).
If we call Λ_{‹v›} the conductivity of a gram-equivalent weight
of an electrolyte in a given solution, and Λ_{∞} the limit of its
conductivity for infinite dilution, then the degree of ionization is
found from α = Λ_{‹v›} / Λ_{∞}. [p051]

 The method of calculation of α in a specific case may be illustrated
 as follows: the resistance of a cube of 1 cm. edge of a solution
 of hydrochloric acid, which contains 1.825 grams hydrogen chloride
 in a liter, is found to be 55.55 ohms at 18°. Its conductivity
 then is 1 / 55.55 reciprocal ohms. Now, 1.825 grams of hydrogen
 chloride is 1.825 / 36.5 or 1 / 20 gram-equivalent of the acid; a
 whole gram-equivalent of the acid would be contained in 20 liters or
 20,000 c.c. Then Λ_{‹v›} = (1 / 55.55) × 20,000, or 360 reciprocal
 ohms. If we use the value at infinite dilution given above,
 α = 360 / 384, or 93.75%. That is, 93.75% of the hydrochloric acid
 is present in the ionized condition in such a solution, and 6.25% is
 not ionized.

By making the assumption that ‹at infinite dilution electrolytes are
completely ionized›, and by taking the ratio which the equivalent
conductivity of a given solution of an electrolyte bears to the
maximum limit-value (calculated for the conductivity at infinite
dilution) ‹to be the degree of ionization of the electrolyte›, as
just explained, the theory of Arrhenius has thus made it appear
possible ‹to determine experimentally the proportion of ionized
electrolyte present›.

It is a significant fact that the equivalent conductivity of
hydrochloric acid is ‹close to its limit even at finite dilutions›,
and that the same relation holds for the strong acids and the
strong bases, in general, and for most salts. But the equivalent
conductivity of weak acids, like acetic acid, and of weak bases, like
ammonium hydroxide, in finite dilutions is still far removed from
the limits which may be calculated for infinite dilutions. Arrhenius
was led then to the further important conclusion that, in the case
of the first electrolytes mentioned, a ‹very large proportion of the
electrolyte must exist in the ionized form at finite concentrations›,
their equivalent conductivities having almost reached the limit
characteristic of infinite dilution.

«Clausius's Theory of Ionization and the Modern Theory.»—It
is in these conclusions—in particular that the proportion of
ionized electrolyte ‹may be determined experimentally›, and that
frequently a ‹large proportion is found to be ionized at finite
concentrations›,—that the ‹modern theory of ionization differs from
the older theory of Clausius›. The former is an elaboration of the
latter, and some opponents[83] of the modern theory still uphold
the latter as offering an adequate explanation of the phenomena
of conductivity. All facts, then, in particular, which confirm
the validity of the ‹conception of the degree of ionization›, as
introduced by Arrhenius, [p052] must be considered as criteria
favoring his theory, specifically. The development of chemistry in
the last twenty years is replete with such evidence and we shall meet
it in many connections throughout our work.

 Clausius[84] also assumed dissociated molecules or ions to be the
 real carriers of electricity in the passage of a current through the
 solution of an electrolyte, but he assumed only a ‹minute quantity
 of these molecular fragments or ions to be free at any moment›,
 their existence being supposed to be transitory and dependent in
 particular on exchanges of atoms between molecules. As a result of
 the oscillations of the atoms composing a molecule, oscillations
 comparable with the motions of molecules assumed in the kinetic
 theory of gases, molecules were considered by Clausius occasionally
 to reach such a condition of instability, that they dissociated
 into smaller particles; since the atoms were supposed to be held
 in a molecule by attractions of electrical charges on the atoms
 (theory of Berzelius), the fragments of the molecule would carry the
 charges, positive and negative respectively, which they possessed
 in the molecule. Such a breaking up or dissociation of molecules
 was, further, supposed to occur with particular ease during the
 collisions of molecules, the electrical attractions and repulsions
 of the charged atoms favoring, at such moments, an ‹exchange of
 atoms›. During the exchange, the atoms were considered to be free
 molecules, charged with electricity—essentially ions,—capable
 of moving under the influence of electrical forces and of thus
 carrying a current. Finally, such ions were supposed, in part, to
 escape recombination, and to remain free, until each ion either
 collided and combined with an ion of opposite charge, or collided
 with a molecule and displaced an atom of the same charge from that
 molecule, a new ion being thus liberated. The theory, as usually
 interpreted, assumed the existence of only a very small quantity of
 such free ions, that being all that was supposed to be required to
 explain the facts known at the time it was advanced.

 In what follows, we shall confine the discussion strictly to such
 contrasts between the two theories as grow out of a consideration
 of the phenomena of conductivity, and particularly consider some
 evidence which is directly concerned with the conductivity of
 solutions.

 In the first place, if the formation of ions occurs primarily
 during the exchange of atoms in ‹collisions of molecules›, then,
 as Whetham[85] has shown, the specific conductivity (of 1 cm.^3)
 of an electrolyte, like hydrochloric acid, must increase with the
 concentration and must increase, approximately, as a function of
 the ‹third› power of the concentration. The more concentrated the
 solution, the more frequent the collisions between the dissolved
 molecules must be. As a matter of fact, as shown in the following
 table, the conductivity [p053] increases a ‹little less› than
 proportionally to the ‹first› power of the concentration—‹which is
 in conflict with the assumption made in the hypothesis of Clausius›,
 but in perfect agreement with the hypothesis of Arrhenius. The
 small ‹decrease› with increasing concentration, in the simple ratio
 between conductivity and concentration, is due to the decreasing
 degree of ionization in the more concentrated solutions, as demanded
 by the hypothesis of Arrhenius.

 The table gives, in the first column, the specific conductivities
 of hydrochloric acid at 18°, and, in the second column, the
 concentrations; these concentrations are expressed in moles or
 gram-equivalents per cubic centimeter; the last column gives the
 ratio of conductivity to concentration.

  Conductivity                   Conductivity
   of 1 c.c.     Concentration   ─────────────
                                 Concentration.

     0.00370        0.00001           370
     0.00734        0.00002           367
     0.01092        0.00005           364
     0.01800        0.00005           360
     0.03510        0.00010           351

 Furthermore, facts admitted by Clausius to be inexplicable by his
 own assumptions receive, in the theory of Arrhenius, at least a
 quantitative formulation borne out by a mass of corroborative
 evidence. The difference in conductivity between pure water and
 sulphuric acid is such a fact, mentioned by Clausius. Determinations
 of the ionization of sulphuric acid and of water, by the
 conductivity methods which are based on the theory of Arrhenius,
 show that, while sulphuric acid is very considerably ionized (see
 p. 104), water is scarcely ionized at all. The ionization of
 water (see p. 104) has been determined quantitatively by at least
 four independent methods of examination,[86] and, minimal as the
 ionization is, the results agree so well with each other that van 't
 Hoff[87] was led to write: "If one is not previously convinced of
 the correctness of the theory of electrolytic dissociation, hardly
 any result won by means of it is so convincing, as the agreement
 between the conclusions reached in completely different ways as to
 the degree of dissociation of water itself. After such an agreement,
 it is hardly conceivable that the basis on which all these results
 rest should further be altered."

 «Mobilities or Partial Conductivities of Ions: Principle of
 Kohlrausch.»—If ions have a separate existence, each kind of
 ion would be expected to move through a solution under a given
 electrical force at a given temperature with its own specific speed,
 the speed being presumably dependent on the nature of the ion as
 well as on the weight of water combined with it and dragged with it
 through the solution (p. 42). [p054]

 Such relative speeds of ions may be demonstrated by means of
 an experiment: the motion of the hydrogen ions, formed by the
 ionization of hydrochloric and other acids, may be observed by
 their action on a reddened (alkaline) solution of phenolphthaleïn,
 which is decolorized by them; and the motion of the hydroxide ions,
 formed by the ionization of sodium hydroxide and other bases, may be
 followed by their action on colorless phenolphthaleïn, which turns
 red in their presence. The hydrogen and the hydroxide ions are the
 fastest, in aqueous solutions, and their speeds are compared in the
 next experiment with that of blue cupric ions, which have a speed
 roughly the same as that of many common ions. In this experiment the
 hydrogen ions are readily seen to move about twice as fast as the
 hydroxide ions and five to six times as fast as the cupric ions.

 [Illustration: FIG. 10]

 EXP.[88] Five grams of agar-agar are dissolved in 250 c.c. of
 boiling water. To 100 c.c. of the hot solution, 32 c.c. of a
 saturated solution of potassium chloride and about 1 c.c. of
 phenolphthaleïn solution are added, together with enough of a
 solution of potassium hydroxide, added drop by drop, to produce a
 deep red tint in the phenolphthaleïn. Of this mixture 50 c.c. is
 treated with dilute hydrochloric acid, added drop by drop, until the
 red color is just discharged, and then an excess of acid, equal in
 amount to the quantity used to neutralize the 50 c.c., is added to
 the mixture. This colorless solution and 50 c.c. of the red solution
 are poured, while still warm, into the two parts of a wide U-tube,
 slowly and at equal rates, so that the level on the two sides
 remains the same. In this way it is possible without difficulty to
 have the solution on one side red (alkaline) and on the other side
 colorless (acid). The agar-agar is allowed to congeal, and then a
 mixture of 0.5 c.c. of hydrochloric acid, (sp. g. 1.12), 6 c.c. of
 saturated cupric chloride solution and 20 c.c. of water is poured
 over the red half, and a mixture of 20 c.c. of saturated [p055]
 potassium chloride solution and 2 c.c. of 10% potassium hydroxide
 solution is poured over the colorless half. The U-tube is surrounded
 by ice water during the passage of the current, and the cathode is
 placed in the solution on the colorless side. In Fig. 10 the U-tube
 is shown when first charged (on the left), and after the current has
 been running for a short time (on the right).

 The conductivity of a solution must be made up, therefore, of the
 sum of the shares which the positive ions and the negative ions,
 respectively, take in carrying the current. This principle was first
 advanced by Kohlrausch. The share of each kind of ion in conducting
 a current may be determined, for hydrochloric acid for instance,
 in the following way: A porous diaphragm may be used to divide the
 solution in an electrolytic cell into two halves, the concentration
 of the acid being the same in both halves (represented, as indicated
 in Fig. 11, by 15 molecules[89] of ionized acid in each half). A
 measured current is passed through the solution, say, sufficient to
 liberate 3 molecules of hydrogen H_{2}, and 3 of chlorine Cl_{2},
 corresponding to 6 ‹ions› of each, and the concentration of the acid
 in each half is then again determined by analysis. Say it is found
 to correspond to 14 molecules of hydrochloric acid in the half of
 the solution on the side of the cathode and 10 molecules in the half
 on the side of the anode (see Fig. 12). Then the anode half has lost
 5 ions of hydrogen, which must have passed through the diaphragm
 toward the cathode and taken the place of five of the six hydrogen
 ions discharged at the cathode. Similarly, the solution around the
 cathode has lost one chloride ion, which must have passed through
 the diaphragm toward the anode, and the hydrogen-ion corresponding
 to it, remaining on the right side without a compensating negative
 ion, must be the sixth hydrogen-ion discharged at the cathode. In
 other words, five hydrogen ions passed to the right, while one
 chloride ion passed to the left. The hydrogen ions then carried
 five-sixths of the current through the diaphragm, and consequently
 through the solution, and the chloride ions only one-sixth of the
 current. Since the solutions were of equal concentration to start
 with, the hydrogen ions have moved ‹five times as fast› toward the
 cathode as the chloride ions have moved toward the anode.

 [Illustration: FIG. 11.]

 [Illustration: FIG. 12.]

 The equivalent conductivity of 0.1-molar hydrochloric acid is 351
 at 18°, and experiment shows that the hydrogen-ion carries 84% of
 the current, the chloride-ion only 16%. The conductivity may then be
 considered to be the [p056] sum of the share the hydrogen-ion has
 in carrying the current, ‹i.e.› 0.84 × 351, or 295, and of the share
 of the chloride-ion, 0.16 × 352.5, or 56. These values may be called
 the ‹equivalent partial conductivities› or ‹mobilities› of the ions
 in this solution.

 In a similar way, the conductivity of every solution of an
 electrolyte may be shown to represent the sum of the mobilities
 of the ions carrying the current (‹principle of Kohlrausch›). The
 limit of the conductivity of one equivalent of an electrolyte is
 the sum of the mobilities of the ions composing the electrolyte.
 The frictional forces being constant for infinitely dilute
 solutions, at a given temperature, an ion will always show
 the same mobility, irrespective of the nature of the ion of
 opposite charge, with which it forms the electrolyte. We may
 then put Λ_{∞} = (‹l›^{+}_{∞} + ‹l›^{−}_{∞}), if ‹l›^{+}_{∞} and
 ‹l›^{−}_{∞} are used to designate the limits of the mobilities
 of gram-equivalents of the positive and negative ions forming
 the electrolyte. The following table[90] gives the limits of the
 mobilities for gram equivalents of some of the most important ions
 at 18°.

     ‹Limits of Mobilities of Common Ions at› 18°.

         K: 65.3   ½ Ca:  53.0                 I: 66.7
        Na: 44.4      H: 318.0            NO_{3}: 60.8
  (NH_{4}): 64.2     OH: 174.0   C_{2}H_{3}O_{2}: 33.7
        Ag: 55.7     Cl:  65.9          ½ SO_{4}: 69.7

 For quite dilute solutions, in which the friction may be assumed to
 be approximately constant, the conductivity will depend, not only
 on the mobilities of the ions, which may be taken to be the same as
 for solutions of extreme dilution, but also ‹on the proportion of
 electrolyte that is ionized›, ‹i.e.› on the degree of ionization,
 α. Then Λ_{‹v›} = α (‹l›^{+}_{∞} + ‹l›^{−}_{∞}), which is an
 elaboration of the original equation given on page 50.

 Now, Kohlrausch discovered the principle of the summation of the
 mobilities of ions a number of years before the theory of Arrhenius
 was advanced, and the proportion in which the ion is present in a
 given solution being unknown, the effect of what is here known as
 the degree of ionization was included empirically in the value of
 the mobility. It is not surprising, then, that an ion was found
 to have approximately the same mobility ‹only› in solutions of
 the same concentration ‹of strictly analogous and closely related
 salts›, which, according to present methods of investigation, are
 ‹now› found to have approximately the same degree of ionization. For
 instance, the mobility of the gram-equivalent of the chloride-ion
 was found to be approximately the same, 47.3 and 50.5 respectively,
 in molar solutions of sodium and potassium chloride at 18°, no
 account being taken of the degrees of ionization. However, the
 degrees of ionization of the two salts are approximately the same,
 66.9% and 74.9% respectively, and might be ignored in a comparison
 of the conductivities, without affecting the result of the
 comparison in any marked way. [p057]

 When the conductivities of unlike electrolytes are compared, the
 ‹introduction of the conception of the degree of ionization›
 (by Arrhenius,) into Kohlrausch's principle of the independent
 conductivities of specific ions, shows most striking results and
 ‹demonstrates the value of the new conception›. For instance, the
 equivalent conductivity of potassium chloride at 18° in 0.075 molar
 solution is 113.8 reciprocal ohms and the partial conductivity of
 the chloride-ion in the solution is 57.4. But the conductivity of
 an equivalent solution of ‹mercuric chloride› at 18° is only 1.51,
 which is very much less than the conductivity of the chloride-ion
 alone in the potassium chloride solution. Now, mercuric chloride,
 according to investigations of its conductivities and of its effect
 in depressing the freezing-point of water,[91] is one of a very few
 salts that are difficultly ionizable (p. 107); according to the data
 mentioned, it is ionized, at most, to the extent of 2.5 per cent in
 the solution in question, whereas 87.5 per cent of the potassium
 chloride is ionized in such a solution. When the difference in
 the degree of ionization is taken into account, the conductivity
 which mercuric chloride ‹should show› may be calculated, ‹on
 the assumption that the chloride-ion has the same mobility› in
 the two solutions, but that there is less of it in the mercuric
 solutions. We put Λ_{HgCl_{2}} = α (‹l›_{Hg} + ‹l›_{Cl}) = 0.025
 (48 + 65.9) = 2.8. We thus find that the conductivity of the
 mercuric chloride should be, approximately, only 2.8 reciprocal
 ohms, which is of the same order as that found (1.51).[92]

 In the same way, when we compare the conductivity of a strong acid,
 like hydrochloric acid, with that of a weak acid, like acetic
 acid—the conductivity of 0.1 molar hydrochloric acid is 351, of
 0.1 molar acetic acid only 4.6—the principle of the specific,
 characteristic mobility of the hydrogen-ion, which is present in
 both solutions, has significance only if we take into account
 the very different concentrations of the hydrogen-ion in the two
 solutions, ‹resulting from the different degrees of ionization of
 the two acids›—91% for the hydrochloric and only 1.7% for the acetic
 acid. The same relations hold in the comparison of the conductivity
 of a solution of a strong base like sodium hydroxide with that of
 an equivalent solution of a weak, i.e. much less ionized base like
 ammonium hydroxide, or in comparing the conductivity of a ‹weak
 acid› or a ‹weak base› with the conductivities of their ‹much more
 highly ionized salts›.

 ‹In all these cases the use of the conception of the degree of
 ionization of the electrolytes› makes possible a much broader
 and more general application of the principle of the independent
 migration or mobility of the ions than was possible before the
 theory of Arrhenius was proposed, and marks a distinct advance in
 the theory of conductivity, over what was possible on the basis of
 the theory of Clausius. [p058]

«Faraday's Law.»—If a definite quantity of electricity, a
faraday,[93] or 96,600 coulombs, is passed through a solution of
hydrochloric acid, a definite quantity (36.5 grams, one mole) of
the hydrogen chloride is decomposed, and one gram of hydrogen and
35.5 grams of chlorine are liberated by the discharge of one gram
(‹i.e.› one gram-ion) of the hydrogen-ion and 35.5 grams or one
gram-ion of the chloride-ion. In a solution of cupric chloride, the
chloride-ion is identical in every respect with the chloride-ion
found in a solution of hydrochloric acid. In the solution of
cupric chloride, however, a molecule of the salt, when it is
completely ionized, produces two chloride ions for every cupric ion
(CuCl_{2} ⇄ Cu^{2+} + 2 Cl^{−}). Since the solution never shows the
presence of an excess of either form of electricity, and the negative
charge on each chloride ion is the same as on a chloride ion formed
by the dissociation of hydrogen chloride, a cupric ion must hold
‹exactly› double the positive charge that a hydrogen ion does. In
modern terms, each hydrogen atom, present as an ion, has lost one
electron, and each copper atom present in the form of a cupric ion
has lost two electrons. Our unit quantity of electricity, 96,600
coulombs, can discharge therefore ‹only half as many of the cupric›
as of the hydrogen ions, and since each cupric ion is 63.6 times
as heavy as the hydrogen-ion (Cu = 63.6, H = 1), 63.6 / 2 grams of
copper, the ‹equivalent weight›, will be deposited in place of one
gram of hydrogen. Similarly, from a solution of ferrous chloride
FeCl_{2}, 55.9 / 2 grams of iron (Fe = 55.9) will be deposited, the
ferrous ion being Fe^{2+}; while from a solution of ferric chloride
FeCl_{3}, only 55.9 / 3 grams of iron will be deposited by 96,600
coulombs, the ferric ion, Fe^{3+}, holding three times the charge
that a hydrogen ion does. In other words, a given quantity of current
will decompose ‹equivalent› quantities of electrolytes and deposit
‹equivalent quantities› of metals. This is the well-known law of
Faraday. The theory of Arrhenius agrees with it, as did the theory
of Clausius. It cannot be considered as evidence bearing on the
question of the preference to be given to either of the theories of
ionization, since the degree of ionization of electrolytes is not
involved in the relations covered by the law. But any other relation
would have been incompatible with the theory of Arrhenius. The law
is of particular importance in giving us [p059] the best clew that
we have in regard to the ultimate nature of "valence" (as shown for
instance in the difference between the ferrous, Fe^{2+}, and the
ferric ions, Fe^{3+}). On the basis of this law, valence may be
said to consist simply in the capacity of atoms to hold different
multiples of the unit electrical charge (positive or negative). This
conception will be of especial value to us when we come to consider
the relation of the theory of ionization to oxidation and reduction
(Chapters XIV and XV).

«Diffusion of Ions and Concentration Cells.»—When the, apparently,
abnormally low molecular weight of ammonium chloride was explained as
being due to the dissociation of each molecule of ammonium chloride
into a molecule of ammonia and one of hydrogen chloride, the evidence
of the correctness of this interpretation was at once forthcoming—the
vapor of ammonium chloride, by the unequal rates of diffusion of its
components, was proved to be a mixture of the two gases (p. 35).
Now, if an electrolyte like hydrochloric acid in aqueous solution is
dissociated more or less into separate ions, H^{+} and Cl^{−}, then
one may well ask, whether the dissociation cannot be demonstrated
by the same kind of experiment, as, for instance, by showing that
hydrogen and chloride ions ‹are molecules with unequal powers of
diffusion› and ‹by separating them by virtue of such inequality›.
Ions being, according to the theory under consideration, independent
molecules, except for the attractive and repulsive forces of the
electrical charges, they should have, like cane sugar, copper
nitrate and other solutes, the capacity for diffusion from regions
of higher to those of lower concentration. Further, if ions show
different degrees of mobility (p. 53), one would expect the more
mobile or faster moving one to diffuse more rapidly than a less
mobile ion. Such a relation should hold for the ions in a solution of
hydrochloric acid, the hydrogen-ion, according to the calculations
of Kohlrausch[94] and the observation of Lodge,[95] moving at a
rate about five times as great as that of the chloride-ion, at
18°. Thus, if a rather concentrated solution of hydrochloric acid
were covered with a layer of water, or with a very dilute solution
of the acid, one might expect the hydrogen ions to migrate faster
than the chloride ions from the [p060] point of higher to that of
lower concentration, ‹i.e.› from the more concentrated to the dilute
acid. When the experiment is tried in this way, no separation of the
hydrogen from the chloride ions seems to occur. The reason for the
failure of the experiment is as follows: If any such separation did
occur, even to the extent of say one milligram-equivalent of hydrogen
and chloride ions, we would have a separation of electrostatic
charges of 96 coulombs. These charges, on the small areas involved,
would inevitably produce enormous potentials, that would operate
against the separation. The hydrogen ions, which would tend to move
from the concentrated to the dilute acid, would therefore be held
back by the powerful attraction between their positive charges and
the negative charges left in the concentrated acid (on the Cl^{−}
ions). The separation of the electrical charges, incidental to a
faster diffusion of hydrogen ions, if it occurred, would result,
therefore, in the development of electrical forces of attraction,
which would prevent a separation of the oppositely charged particles
beyond any but distances too small to be measured. It would follow,
however, that no difficulty whatever should be experienced in
‹observing such a separation›, as a result of unequal rates of
migration of the ions in question, ‹if provision were made to
preserve electrical neutrality in all zones› of the two solutions,
‹i.e.› if provision is made for the immediate discharge of the ions,
as they separate by the unequal rates of diffusion. For instance, the
part of the liquid into which the positive hydrogen ions move more
rapidly, charging it with positive electricity, may be connected, by
means of a wire, with the part of the liquid to which the chloride
ions, left behind by their slower movements, are imparting a negative
charge. In such a circuit, a current of electricity should be
produced, the positive current flowing through the wire from the
dilute to the concentrated acid. As a matter of fact, we find that a
current is produced, when these conditions are observed.

 EXP. The lower plate in an Arrhenius cell is covered with
 concentrated hydrochloric acid. Very dilute acid is allowed to flow
 slowly on to the surface of the concentrated acid, from a pipette
 with a curved, narrow point, until the upper plate is submerged. The
 two plates are connected with a sensitive galvanometer. The current
 flows in the direction demanded by the observed mobilities of the
 ions, the positive current entering the galvanometer from the plate
 covered by the dilute solution, which is charged positively by the
 faster moving hydrogen ions coming from the concentrated solution.
 If the cell is [p061] connected with the electrodes of a very
 small cell containing copper sulphate, in the course of twenty-four
 hours quite a deposit of metallic copper is formed on the electrode
 connected with the concentrated solution of hydrochloric acid.

The existence of the products of the electrolytic dissociation, of
hydrochloric acid may therefore be demonstrated,[96] by the aid
of the individual diffusion of the products of the dissociation,
in the same way as was the coëxistence of the products of the
gaseous dissociation of ammonium chloride, when the conditions
for the experiment are adapted to the nature of the dissociation
products. Cells of this type, depending for their current on unequal
concentrations of given ions, are called "concentration cells."

 If it can be shown that the flow of electricity, resulting from
 such unequal diffusibility of ions, is a function not only of the
 difference in the total concentration of the electrolyte in the
 two solutions brought into contact with each other, but is also a
 function of the relative degrees of ionization of the electrolyte
 in the two solutions, as defined by the theory of Arrhenius, then
 this method of experimentation may be used as a further test of
 the validity of this theory as against that of Clausius. It is
 obvious that if such currents are the results of the diffusion of
 ‹ions› from higher to lower concentrations, then the essential
 concentrations do not embrace all of the electrolyte, but only the
 ionized part. W. K. Lewis[97] has rather recently shown that the
 degrees of dissociation of electrolytes may be measured by the use
 of concentration cells, and that the results agree well with the
 determinations of the degree of dissociation from conductivity
 measurements (p. 50). From calculations, based on Jahn's accurate
 measurements of the electromotive forces of concentration cells,
 A. A. Noyes[98] finds that "when the conductivity ratio is assumed
 to represent the degree of ionization of the salt, the calculated
 values of the electromotive force of concentration cells exceed the
 measured ones by only about one per cent, in the case of potassium
 and sodium chloride between the concentrations of 1 / 600 and 1 / 20
 molar."

«The Rôle of the Solvent in Ionization.»—A question that has
profoundly interested chemists, particularly during the last few
years, has been that of the rôle which the solvent plays in the
[p062] dissociation of electrolytes into ions. The most important
ionizing solvent is water and, of the common solvents which cause
ionization, it is the most powerful in this particular. Alcohols have
also ionizing power; methyl or wood alcohol, which stands nearest
to water, has a higher ionizing power than ordinary ethyl alcohol.
The exact work[99] of Franklin and Kraus, on the conductivity of
solutions of salts in liquid ammonia, showed that the same general
relations obtain for such solutions as for solutions in water, the
differences being differences of degree rather than of kind. Salts
are found to be less ionized in liquid ammonia than in equivalent
aqueous solutions, but their conductivities are higher, the result of
smaller friction in ammonia. Liquid hydrogen cyanide is also a very
good ionizing medium.

Solvents which cause ionization only to a minimal extent are benzene
(C_{6}H_{6}), carbon bisulphide, ether, chloroform, petroleum ether
(gasoline) and similar solvents. Hydrogen chloride dissolved in
benzene has an extremely small conductivity, indicating only a trace
of ionization.[100]

The question may be raised, why the first solvents mentioned
should have the power to cause ionization, while the second series
of solvents named do not have this power, or have it only to a
very slight extent. Without attempting to enter into an elaborate
discussion of this important question, it may be said that J. J.
Thomson[101] and Nernst[102] suggested that the ionizing powers
of solvents must be intimately connected with their ‹dielectric
behavior›, and this view has now been well established. It may be
said, in simple terms, that the so-called dielectric constant of
a solvent determines the force with which electrical charges will
attract and repel each other; the higher the dielectric coefficient
of a medium, the ‹smaller will be the attraction between opposite
electrical charges›, other conditions being the same. In solvents,
then, of high dielectric powers, the coëxistence of oppositely
charged particles must be more favored than in solvents of low
dielectric powers. The dielectric constants of a number of solvents
are given in the following table: [p063]

  Hydrogen cyanide, HNC                   95
  Hydrogen peroxide, H_{2}O_{2}           93
  Water, H_{2}O                           81
  Methyl (wood) alcohol, CH_{4}O          32
  Ethyl (ordinary) alcohol, C_{2}H_{6}O   22
  Ammonia, H_{3}N                         22
  Chloroform, CHCl_{3}                     5
  Ether, (C_{2}H_{5})_{2}O                 4
  Benzene, C_{6}H_{6}                      2

It is quite apparent that the good ionizing media have, as a matter
of fact, the highest constants; those which cause ionization, at most
minimally (‹e.g.› benzene), the lowest.

 Recent extended and exact investigations by Walden[103] have
 succeeded in bringing the ionizing power of solvents into definite
 quantitative relations to their dielectric constants, with the
 result that order has been brought out of a condition of chaos
 that, for a number of years, existed in this field, as the result
 of conclusions based on incomplete data. Conductivity being a
 function both of the proportion of dissociated electrolyte and of
 the mobility of the ions in a given solution, Walden determined, for
 a certain salt (an organic derivative of ammonium iodide, namely,
 tetraethyl ammonium iodide N(C_{2}H_{5})_{4}I), for all solvents
 used, not only the conductivities for finite dilutions but also, by
 extrapolation, the limiting values for infinite dilution. He was
 thus able to determine the degree of ionization of the salt. Some of
 his results are particularly interesting; for instance, a ‹poorly
 conducting› solution, such as that of the salt in glycol, a solvent
 resembling glycerine in general character, may contain the dissolved
 electrolyte in a ‹highly ionized› state, while in a much better
 conducting solution the degree of ionization may be much smaller—the
 low conductivity of the first solution being the result of a
 very high friction and of the slow motion of the ions, while the
 well-conducting solution might show a very high degree of mobility
 of the ions. The mobility changes with the nature of the solvent,
 and the limit, Λ_{∞}, of the equivalent conductivity of the salt, as
 found by Walden, ranges from 8 in glycol, which is a thick, viscous
 oil like glycerine, to 200 in acetonitrile, a thin mobile solvent.
 In the one solution, an observed conductivity of 4 represents 50%
 ionization of the salt, in the other only 2%.

 Now, for solutions of a given electrolyte—tetraethyl ammonium iodide
 was used—Walden[104] found the following exceedingly interesting
 relation between the ionizations in, and the dielectric constants
 of, various solvents:

 ‹e›_{1} : ∛‹c›_{1} = ‹e›_{2} : ∛‹c›_{2} = a constant,

 where ‹e›_{1} and ‹e›_{2} represent the dielectric constants
 of different solvents, and ‹c›_{1} and ‹c›_{2} represent the
 concentrations of the salt in the solvents when the salt is ‹ionized
 to the same degree[105] in the two solutions›.

 The bearing of the relation is apparent from the data in the
 following [p064] table.[106] The upper half of the table gives
 the dielectric constants (column two) of the solvents named in
 column one; the concentrations which show identical degrees of
 ionization—47%—are given in the third column, and the last column
 gives the value of the relation ‹e› : ∛‹c›. The lower half of the
 table presents the same kind of data, for the same salt, when its
 degree of ionization is 91%, in the different solutions examined. It
 is clear that the numbers in the third column of each part represent
 approximately constants.

 All solutions, including aqueous solutions, are thus brought into
 one general relation.

    Solvent.       ‹e›     ‹c›    ‹e› : ∛‹c›
  Methyl alcohol   32.5   0.125      65
  Ethyl alcohol    21.7   0.020      80
  Acetyl bromide   16.2   0.010      75
  Benzaldehyde     16.9   0.016      78
  Acetonitril      35.8   0.100      77

  Water            80     0.00910   383
  Furfurol         39.4   0.00125   365
  Nitromethane     40     0.00125   371
  Acetonitril      36     0.00100   358
  Methyl alcohol   32.5   0.00050   365

«The Ionizing Power of Solvents Related to the Unsaturated Condition
of their Simple Molecules and to their Power of Association.»—A
careful scrutiny of the group of highly-ionizing solvents (p. 62)
brings out another interesting relation, to which attention is called
because it is a chemical one, and which should always be considered
in connection with reactions in such solvents. It is well known
that ammonia is an ‹unsaturated› body, combining readily with all
acids, and with many salts, such as copper sulphate. The fact may
be recalled, that this unsaturated condition is ascribed to the
unsaturated nitrogen atom in the molecule of ammonia, the nitrogen
showing a valence of only 3 in ammonia, whereas in the derivatives it
forms when it saturates itself with the compounds mentioned, ‹e.g.›
in H_{4}NCl, it has five saturated valences. Assuming that a valence
consists in a unit charge, positive or negative, on the atom (pp. 42,
59), a view which has almost become a certainty, we should decide
that the two free valences in ammonia must consist of a negative
and a positive charge, as expressed in H_{3}N^{±}. (We may imagine
such a double [p065] charge to be produced by the movement of one
electron of the nitrogen atom to a position in that atom which would
make one point of the atom negative and the other positive.) As a
matter of fact, we find ammonia uniting with hydrogen chloride, by
absorbing a positive and a negative fragment of it—producing H_{4}NCl
from H_{3}N^{±} + H^{+} + Cl^{−}. It is also evident that, through
these charges, ammonia could combine with itself to form larger
complexes, ^{+}NH_{3}-NH_{3}^{−}, in which we would still have two
opposite charges, presumably removed further from each other than in
the simple molecule. The new molecule could, in turn, by virtue of
its charges, combine with a further molecule to form a still larger
or more ‹associated› molecule, ^{+}NH_{3}-NH_{3}-NH_{3}^{−}, and
such ‹association› could evidently go still further. One can readily
see that such molecules would be ‹electrically polarized›, and their
charges might easily have the ‹power to cause[107] electrolytic
dissociation or ionization›. The larger the associated molecule, the
further apart might be the positive and negative charges upon it:
the further apart the charges, the smaller would be their mutual
attraction: and the smaller the mutual attraction, the stronger,
presumably, would the dissociating power of such a molecule be. The
dissociation may be effected, possibly, by the ‹action of these
intensified charges› upon ‹charges already existing›[108] within the
molecule of the dissolved ionogen.

 In liquid ammonia we might well have, for instance, the action
 ^{+}NH_{3}-NH_{3}^{−} + HCl ⇄ ^{+}(NH_{3}-NH_{3})H + Cl^{−}, or
 ^{+}NH_{3}-NH_{3}^{−} + H^{+}Cl^{−} ⇄ ^{+}(NH_{3}-NH_{3})H + Cl^{−}.
 Now, in liquid ammonia, the salts NH_{4}Cl, NH_{4}NO_{3} [or, more
 probably, (NH_{3})_{‹x›}HCl, (NH_{3})_{‹x›},HNO_{3}] have the
 functions of the aqueous acids[109]; that is, the ‹hydrogen-ion›
 of the acids is found ‹combined with the solvent› ammonia. The ion
 ^{+}(NH_{3}-NH_{3})H, and similar ions in liquid ammonia, would
 correspond then to what is considered the hydrogen-ion in aqueous
 solutions[110] (formed according to HCl ⇄ H^{+} + Cl^{−}, as
 ordinarily written), and the ‹polarized charges on molecules› like
 ^{+}NH_{3}-NH_{3}^{−} appear thus as ‹possible active agents› in
 this dissociation of the hydrogen chloride molecules. [p066]

Now, it is a significant fact that all the best ionizing solvents
are compounds whose simple ‹molecules are unsaturated› exactly like
those of ammonia; this is true for water H_{2}O, the unsaturated
character of whose oxygen atom is now universally recognized. It
is now a familiar fact that liquid water is not represented by the
formula H_{2}O but consists of more complex molecules (H_{2}O)_{n}.
According to the most recent investigations,[111] while steam is
H_{2}O, or monohydrol, ice is trihydrol (H_{2}O)_{3}, and liquid
water, at ordinary temperatures, a mixture consisting chiefly of
dihydrol (H_{2}O)_{2}, some trihydrol, and very little monohydrol.
The proportion of the last appears to increase with a rise of
temperature; the proportion of trihydrol seems to increase with a
fall in temperature. One can easily see how such aggregates would
result from the saturation of the free charges on oxygen, by further
molecules of water. One can also see that such an association of
water molecules could leave a positive and a negative charge on the
associated molecules, which would be ‹polarized› and more effective
than the simple molecule would be.

That the molecule of hydrogen cyanide contains a similarly
unsaturated atom was demonstrated by Nef.[112] He proved that the
behavior of hydrocyanic acid agrees with the structure expressed
by the formula HN=C=, which we may well write HN=C^{±}. In sulphur
dioxide, another good ionizing solvent, we have, similarly,
unsaturated sulphur, the sulphur atom being here quadrivalent,
whereas its maximum valence is six.

Now, the ionizing power of solvents like water, ammonia, etc., has
been ascribed, by various chemists, not only to their dielectric
properties, but also to the ‹unsaturated condition of their
molecules, and particularly to their powers of association into
large molecules›. The relations developed suggest that ‹all three
properties are most intimately related›, the dielectric properties
and the powers of association being consequences, possibly, of the
fundamental condition of unsaturation, and of the great tendency
toward self-saturation,[113] of the simple molecules of the best
ionizing solvents. From Walden's work it appears that the dielectric
constant finally determines the quantitative ionizing effect of a
solvent.


  FOOTNOTES:

  [49] From the molecular weights of elements and compounds, the
  atomic weights of elements may be determined, with the aid of
  analysis. (‹Cf.› Smith, ‹Inorganic Chemistry› (1909), p. 196, or
  ‹General Chemistry for Colleges› (1908), p. 130 («Stud.»), or
  Remsen, ‹Inorganic Chemistry, Advanced Course› (1904), pp. 71–80
  («Stud.»).)

  [50] The weight of a small volume of a gas or vapor, at any
  definite temperature and pressure, is determined. With the aid of
  Boyle's and Gay-Lussac's laws, this observed volume is then reduced
  to standard conditions. Finally, the weight of 22.4 liters, under
  standard conditions, is obtained by calculation.

  [51] For the deduction of formulæ see Smith, ‹Inorganic Chemistry›,
  196, 203; ‹College Chemistry›, 40; or Remsen, ‹ibid.›, p. 79
  («Stud.»).

  [52] Kopp, ‹Liebig's Ann.›, «105», 390 (1858); Kékulé, ‹ibid.›,
  «106», 143 (1858) («Stud.»).

  [53] ‹Liebig's Ann.›, «123», 199 (1862) («Stud.»).

  [54] Wanklyn and Robison, ‹Compt. rend.›, «52», 549 (1863)
  («Stud.»).

  [55] For instance in a test tube held in a horizontal position.

  [56] By applying the corrections demanded by the kinetic theory
  (van der Waals's equation) to gases even under ordinary pressures,
  Guye and D. Berthollet have obtained, with the aid of Avogadro's
  hypothesis, values for the molecular weights of gases and for the
  atomic weights of their components, which compare in accuracy with
  the best analytical work on solutions and solids.

  [57] The usual experimental methods consist in determining
  the elevation of the boiling-point, or the lowering of the
  freezing-point, or the lowering of the vapor tension of a solvent
  by a solute, methods which were discovered by Raoult and used
  empirically until van 't Hoff developed their relations to the
  Avogadro principle. The calculation of a molecular weight is
  much simplified by the use of the different specific constants
  expressing the lowering or elevation produced by one gram-molecule
  or mole, dissolved either in one liter or in 100 grams of each
  specific solvent.

  [58] See Arrhenius, ‹Z. phys. Chem.›, «1», 631 (1887).

  [59] Or, on the basis of the accepted molecular weights, abnormally
  high osmotic pressures, abnormally great lowerings of the
  freezing-point, raisings of the boiling-point, etc., were obtained.
  Van 't Hoff, originally, on account of these discrepancies,
  considered this extension of the Avogadro Hypothesis to hold
  only for the "majority" of substances in solution, not for all
  (Arrhenius, ‹loc. cit.›). It was considered to have ‹universal›
  application (for dilute solutions) only after Arrhenius had
  explained the exceptions with the aid of his theory of electrolytic
  dissociation.

  [60] That is, hydrogen chloride, in aqueous solution, depresses the
  vapor tension and the freezing-point and elevates the boiling-point
  considerably more than an ‹equimolecular› quantity, for instance,
  of glucose does, and gives a considerably higher osmotic pressure.
  The differences are relatively greater, the more dilute the
  solutions used.

  [61] A fourth interpretation advanced at one time in opposition to
  the theory of ionization is that salts like sodium chloride and
  zinc chloride are ‹hydrolyzed› and thereby produce more solute
  molecules, ‹e.g.› NaCl + H_{2}O → NaOH + HCl. Aside from the fact
  that such hydrolysis of salts, when it does occur (Chapter X.), is
  easily detected, and that it can be proved not to occur appreciably
  in the case of sodium chloride (‹loc. cit.›), this interpretation
  fails utterly to account for the results obtained with ‹acids,
  e.g.› HCl, HNO_{3}, H_{2}SO_{4}, and with ‹bases›, ‹e.g.› NaOH,
  Ba(OH)_{2}, which in aqueous solutions show an increase in the
  number of molecules as great as shown by salts. This explanation is
  therefore untenable.

  [62] ‹Z. phys. Chem.›, «1», 631, (1887). Previous papers were
  published in the transactions of the Royal Academy of Sweden
  (Stockholm). For a history of the theory see Ostwald, ‹Z. phys.
  Chem.›, «69», p. 1 (1909), and Arrhenius, ‹The Willard Gibbs
  Address›, ‹J. Am. Chem. Soc.›, 1911 («Stud.»).

  [63] In the case of double salts, such as sodium-ammonium
  phosphate, and similar compounds, the dissociation leads to
  the formation of more than two products. The molecules of two
  or more different products may then be charged positively and,
  conversely, there may be two or more different products of
  dissociation carrying negative charges. We have, for instance,
  Na(NH_{4})HPO_{4} ⇄ Na^{+} + NH_{4}^{+} + H^{+} + PO_{4}^{3−}
  and Na(NH_{4})HPO_{4} ⇄ Na^{+} + NH_{4}^{+} + HPO_{4}^{2−}. In
  all cases the rule concerning the sum of all the charges, as
  expressed in (2), must be fulfilled, the charge on the phosphate
  ion, PO_{4}^{3−}, being three times as great as that on a sodium,
  ammonium, or hydrogen ion; that on the acid phosphate ion,
  HPO_{4}^{2−}, being twice as great.

  [64] Ion = the going or the migrating particle.

  [65] See Washburn, ‹J. Am. Chem. Soc.›, «31», 322 (1909), in regard
  to the values of ‹x› and ‹y›, the quantities of water carried by
  certain ions.

  [66] ‹Vide› J. J. Thomson, ‹Electricity and Matter› (1905) and
  ‹Corpuscular Theory of Matter› (1907) («Stud.»). ‹Vide› R.
  A. Millikan, ‹Science›, «32», 436 (1910), on the discrete or
  "granular" nature of electricity («Stud.»).

  [67] See ‹Millikan›, ‹loc. cit.›, as to the exact value of this
  "unit charge."

  [68] ‹Cf.› McCoy, ‹J. Am. Chem. Soc.›, «33», March, 1911, in regard
  to electropositive, composite (‹i.e.› nonelementary) "metals."

  [69] The symbol ε is used to designate an electron. The loss of one
  electron by an atom leaves a ‹unit positive charge› on the particle.

  [70] In Chapter XV (‹q. v.›) the affinity of the elements for
  electrons and the reactions, of the nature of oxidation and
  reduction, depending on this affinity, are discussed in detail.

  [71] J. J. Thomson, ‹Corpuscular Theory of Matter›, p. 120.

  [72] A. A. Noyes (‹Carnegie Institution Publications›, No. «63», p.
  351 (1907)), believes that we may have two ‹kinds of molecules›,
  HCl and H^{+}Cl^{−}, as well as the ions H^{+} and Cl^{−}.

  [73] Modern theory thus is reverting to the Berzelius theory
  of chemical affinity [‹Vide› Meyer's ‹History of Chemistry›
  (translated by M'Gowan) 1891, 220–265, or Ladenburg's ‹History of
  Chemistry› (translated by Dobbin) 1900, 86, 88, etc.]

  [74] To a saturated solution of cupric nitrate may be added a
  small amount of a saturated solution of potassium permanganate,
  sufficient to give a decided purple color to the mixture. Potassium
  chromate, as recommended by A. A. Noyes, may be used in place of
  the permanganate. (‹Cf.› Noyes and Blanchard, ‹J. Am. Chem. Soc.›,
  «22», 726 (1900).)

  [75] ‹Exp.›; ‹cf.› Eckstein, ‹J. Am. Chem. Soc.›, «27», 759 (1905)
  («Stud.»).

  [76] W. A. Noyes, ‹J. Am. Chem. Soc.›, «23», 460 (1901); Stieglitz,
  ‹ibid.›, «23», 796 (1901); Walden, ‹Z. phys. Chem.›, «43», 385
  (1903).

  [77] ‹Corpuscular Theory of Matter›, p. 130 (1907).

  [78] The experiment is an adaptation of a similar one described by
  A. A. Noyes and Blanchard, ‹J. Am. Chem. Soc.›, «22», 726 (1900).

  [79] The copper electrodes are polarized by the formation of
  hydrogen on the cathode, but, in the course of a few seconds, the
  current becomes rather constant and is then read. The polarization
  may be considered as simply reducing the potential of the cell, and
  since, within the range of concentrations of acid used,—4-molar
  to 1/8-molar—the polarization current does not vary markedly,
  as compared with the potential of the storage cell, the total
  potential used through the series of dilutions may be considered
  sufficiently constant for the purposes of the experiment. Readings
  are made three or four seconds after each dilution, when the
  polarization has been fully established. Polarization may be
  entirely avoided by the use of a silver nitrate solution and silver
  electrodes or of a cupric salt solution and copper electrodes
  (Noyes and Blanchard). Hydrochloric acid is used here in order
  to carry the discussion in the text as far as possible with this
  typical ionogen. If one takes care to make readings as described,
  the result is quite satisfactory, as is shown by the comparison
  of the ratios of the readings with the ratios calculated from the
  known conductivities of the various dilutions (see table below).

  [80] Current = (Potential Difference) / Resistance, or
  Current = (Potential Difference) × Conductivity. For a ‹constant
  potential difference›, then, Current ~ Conductivity.

  [81] The ‹specific conductivity› of a solution (commonly designated
  by κ) is the conductivity of a cube of 1 cm. edge; the ‹molecular
  conductivity› is the conductivity of a mole of the electrolyte; the
  ‹equivalent conductivity› (designated by Λ) is the conductivity
  of a ‹gram-equivalent› of the electrolyte. Λ = κ × ‹v›, where
  ‹v› is the volume, expressed in cubic centimeters, containing
  the gram-equivalent. For instance, the resistance of 0.1 molar
  hydrochloric acid in a cube of 1 cm. edge is 28.5 ohms and its
  conductivity (κ) therefore 1 / 28.5 or 0.0351 reciprocal ohms.
  Since 10 liters or 10,000 c.c. of 0.1-molar hydrochloric acid is
  the volume (‹v›) containing one mole of the acid (the molar and the
  equivalent conductivities, for a monobasic acid being the same)
  Λ = 0.0351 × 10,000, or 351.

  [82] Kohlrausch and Holborn, p. 200.

  [83] Cf. Kahlenberg, ‹Transactions of the Faraday Society›, «1», 42
  (1905).

  [84] Clausius, ‹Poggendorf's Ann.›, «101», 347 (1857) («Stud.»).
  His theory replaced the older one of Grotthuss.

  [85] ‹Phil. Mag.›, «5», 729 (1903), and‹ Transactions of the
  Faraday Society›, «1», 55, (1905).

  [86] ‹Vide›, Hudson, ‹J. Am. Chem. Soc.›, «31», 1136 (1909), for a
  recent summary of results.

  [87] ‹Lectures on Physical Chemistry›, «1», p. 131.

  [88] ‹Vide› A. A. Noyes and Blanchard, ‹J. Am. Chem. Soc.›, «22»,
  726 (1900).

  [89] The concentrations are figurative, but may be taken to
  represent actual concentrations, such as 0.015 molar, etc.

  [90] Kohlrausch and Holborn, ‹loc. cit.›, p. 200.

  [91] Raoult, ‹Ann. de Chim. et de Phys.› (6), «2», 84 (1884).

  [92] The degree of ionization of mercuric chloride is based on
  Raoult's freezing-point measurements and is subject to revision,
  and the limit of the mobility of the mercuric-ion (½ Hg) is assumed
  to be 48, close to the values found for the ions of zinc and
  cadmium, elements in the same family as mercury.

  [93] Lehfeldt's ‹Electrochemistry›, 1904, p. 3.

  [94] See table, p. 56.

  [95] Report of the British Association for the Advancement of
  Science, 1886, p. 389.

  [96] With the aid of more elaborate apparatus rigorous
  demonstrations and measurements of such diffusion currents of
  so-called "concentration cells" are made.

  [97] ‹Z. phys. Chem.›, «63», 174 (1908). The work was carried out
  in Abegg's laboratory.

  [98] ‹Report of the St. Louis Congress of Arts and Sciences›, «IV»,
  314 (1904).

  [99] ‹Am. Chem. J.›, «20», «21», «23» (1898–1900).

  [100] Kablukoff, ‹Z. phys. Chem.›, «4», 429 (1889).

  [101] ‹Phil. Mag.› (5), «36», 320 (1893).

  [102] ‹Z. phys. Chem.›, «13», 531 (1893).

  [103] Walden, ‹Z. phys. Chem.›, «54», 129 (1906); McCoy, ‹J. Am.
  Chem. Soc.›, «30», 1074 (1908).

  [104] ‹Z. phys. Chem.›, «54», 229 (1906).

  [105] The degrees of ionization were always determined from the
  relation α = Λ_{‹v›} / Λ_{∞} according to the method discussed on
  page 50.

  [106] Walden, ‹loc. cit.›

  [107] ‹Cf.› Arrhenius, ‹Theories of Chemistry›, p. 83 (1907).

  [108] In hydrogen chloride, the hydrogen and the chlorine atoms may
  be held in the molecules H^{+}Cl^{−} by the electric attraction of
  a positive charge on the hydrogen, and a negative charge on the
  chlorine atom (see p. 43).

  [109] Franklin and Kraus, ‹Am. Chem. J.›, «23», 305 (1900) (Stud.)

  [110] It is very likely that in aqueous acids, a large proportion,
  at least, of the hydrogen-ion is similarly combined with water.
  (Lapworth, ‹J. Chem. Soc.›, (London) «93», 2187 (1908). See Chapter
  XII.)

  [111] ‹Vide› the discussion on the "Constitution of Water," ‹and
  the summary› by J. Walker, ‹Transactions of the Faraday Society›,
  «VI», 71–123 (1910).

  [112] ‹Proc. Am. Acad.›, 1892; Liebig's Ann. «287», 263 (1895).

  [113] ‹Cf.› Walden, ‹Z. phys. Chem.›, «55», 683 (1906).

[p067]




 CHAPTER V

 «THE THEORY OF IONIZATION. II»

 IONIZATION AND OSMOTIC PRESSURE. IONIZATION AND CHEMICAL ACTIVITY


We will turn now to the consideration of evidence bearing on the
theory of ionization, found in the data on osmotic pressure.
The apparent molecular weight of hydrogen chloride is found to
be smaller than 36.5, when determined in aqueous solution (p.
37), and it is found to approach the limit 18.25 as a more and
more dilute acid is used.[114] The value found represents the
average molecular weight of all the molecules in any solution,
the osmotic pressure, freezing-point or boiling-point of which
has been taken. It is evident that, if there is dissociation
of hydrogen chloride into hydrogen and chloride ions, the
average values found for the molecular weight must be lower
than 36.5, ‹must be variable›, and must ‹approach› the ‹limit›
18.25, as the dissociation into the smaller molecules becomes
more and more complete. Such a result is, therefore, what we
would anticipate on the basis of the theory of ionization. For
a salt like potassium chloride KCl, a similar tendency toward
a minimum, average molecular weight of (K^{+} + Cl^{−}) / 2 or
(39.1 + 35.5) / 2 = 37.3 would be anticipated, and, as a matter of
fact, molecular weight determinations with potassium chloride in
aqueous solution give results agreeing with such a tendency.[115]
For a salt like calcium chloride, on the other hand, we would
expect that its ionization into ‹three› ions, according to the
equation CaCl_{2} ⇄ Ca^{2+} + 2 Cl^{−}, would give a minimum,
not of one-half the formula weight, but of one-third, viz.,
(Ca^{2+} + 2 Cl^{−}) / 3 or (40 + 71) / 3 = 37, when the molecular
weight determination is carried out in aqueous solution. As a matter
of fact, with salts of this type, the determinations, by osmotic
pressure methods, indicate a dissociation into ‹three› smaller
components, as required by the theory. It may be added that, for
[p068] a salt, sodium mellitate, Na_{6}(C_{12}O_{12}), the salt of
a hexabasic acid, Taylor found average molecular weights tending
to a minimum of ‹one-seventh› of the formula weight, as we should
expect from the ionization of the salt into seven smaller molecules,
(C_{12}O_{12})Na_{6} ⇄ 6 Na^{+} + (C_{12}O_{12})^{6−}.

«Quantitative Evidence.»—Some of the most exact quantitative evidence
bearing on these relations, such as the results of investigations,
by Griffith and by Taylor, on the freezing-point depressions of
solutions of electrolytes, may be briefly considered. The depression
of the freezing-point of a given solvent by a solute is proportional
to the concentration of the solute or proportional to its osmotic
pressure. Further, according to the Van 't Hoff Hypothesis (p. 15),
the osmotic pressure at a constant temperature is dependent only on
the number of molecules present in unit volume, and not on the nature
or composition of the molecules: the freezing-point of the solvent
is depressed, likewise, proportionally to the total concentration of
the solute, irrespective of the fact whether the solution contains
only one, or more than one molecular species. ‹The ratio, observed
depression / concentration›,[116] or ‹Δ› / ‹C›, ‹should be
constant›,[117] therefore, in a given solvent, for dilute solutions
of all kinds of solutes, simple or mixed. Griffith[118] found, for
a solution of cane sugar, a non-electrolyte, in water, the ratio of
the freezing-point depression to the concentration to be 1.858°. For
instance, the freezing-point of a 0.01 molar solution of cane sugar
(3.42 grams of cane sugar per liter; C_{12}H_{22}O_{11} = 342) is
found to be −0.01858°, and 0.01858 / 0.01 = 1.858. This ratio should
be the same, as stated above, according to van 't Hoff's theory of
solutions, for dilute aqueous solutions of all solutes. But the
ratio ‹Δ› / ‹C› for an aqueous solution of potassium chloride, an
electrolyte, ‹was found to increase slowly› and ‹continuously› until
in 0.0003 molar solution the ratio 3.72 was found, which is exactly
twice the value obtained with cane sugar. The result indicates,
therefore, a ‹gradual dissociation› of the potassium chloride with
‹increasing› dilution, and a ‹dissociation, ultimately, of each
molecule› of the salt into ‹two› new molecules, in all respects
exactly as demanded by the theory of Arrhenius.

Loomis[119] found in a similar way a ratio of 3.61 for HCl, 3.71
[p069] for KOH, 3.60 for KCl, 3.67 for NaCl, 3.73 for HNO_{3}, etc.,
when 0.01 molar aqueous solutions were used. For similar solutions of
calcium chloride CaCl_{2}, magnesium chloride MgCl_{2}, and sodium
sulphate Na_{2}SO_{4}, the value 5.07 was found as the ratio between
the depressions of the freezing-point and the concentration of the
salts in extremely dilute solutions—a result showing, plainly, a
dissociation of each salt into ‹three smaller molecules›. The limit
5.67 for such a dissociation is not quite reached in these cases,
because salts of the types Me″X_{2} and Me_{2}′Y″ ionize less
readily than do the electrolytes Me′X′, a fact also shown by their
conductivities.

We thus find that the most exact work on molecular weight
determinations in ‹dilute› aqueous solutions agrees excellently,
as does the conductivity of such solutions, with the demands of
the theory of ionization, a fact which is particularly impressive
because osmotic pressure and electrical conductivity are in no wise
fundamentally related phenomena, and yet each, as a measure of
ionization or electrolytic dissociation, leads independently to the
same conclusion.[120]

«The Chemical Composition of the Ions of Electrolytes.»—Accepting the
theory of Arrhenius, we may now inquire more closely than heretofore,
first, what compounds are subject to electrolytic dissociation, and
then, what the chemical composition of their ions is and how it is
determined.

The compounds which are dissociated into ions, by solvents which
cause ionization (p. 62), comprise the ‹salts›, the ‹acids› and the
‹bases›; chemists are, in fact, more inclined now to invert the
statement and say that those substances which have long been known
as salts, acids and bases, owe the essential characteristics, which
led to their classification, to the fact that they are ionizable (see
pp. 72–82). The composition of the ions, formed from the simpler
of these compounds,[121] may be expressed by saying that the metal
component or metal-like component (hydrogen, ammonium) forms the
positive ion (cation, metal ion) and all the rest of the [p070]
molecule forms the negative ion (anion, acid ion[122]). Thus,
sodium chloride, nitrate, sulphate, phosphate yield the sodium-ion,
Na^{+}, and the chloride (Cl^{−}), nitrate (NO_{3}^{−}), sulphate
(SO_{4}^{2−}), or phosphate (PO_{4}^{3−}) ions; cupric nitrate
Cu(NO_{3})_{2} dissociates into the cupric ion (Cu^{2+}) and the
nitrate ion, calcium sulphate CaSO_{4} into the calcium-ion (Ca^{2+})
and the sulphate-ion, aluminium sulphate Al_{2}(SO_{4})_{3} into the
aluminium-ion (Al^{3+}) and the sulphate-ion.

But the question arises, as to how we know that the salts mentioned
produce ions of the given composition; why, for instance, should
sodium nitrate be considered to dissociate into sodium, Na^{+}, and
nitrate ions, NO_{3}^{−}, the nitrogen atom carrying all of the
oxygen atoms with it in the negative ion?

 [Illustration: FIG. 13.]

The composition of the ions of a salt can be determined
experimentally[123] by devices of which the U-tube experiment (p.
45) may be considered to be a simple type. For instance, if we wish
to determine the composition of the ions of sodium nitrate, we
could cover a solution of sodium nitrate with a solution, say, of
hydrochloric acid, pass a current through the liquids, and determine
the composition of the components that have moved to the negative
and positive poles, respectively. In practice, the device could be
elaborated for the sake of convenience. Stopcocks, for instance,
might be placed in the U-tube, at the points of separation of the
nitrate solution and the hydrochloric acid (see Fig. 13), the
stopcocks being opened only during the passage of the current. Or
porous plates or cells might be used, in place of stopcocks, at these
[p071] points. Now, if we assume sodium nitrate to be dissociated,
not into Na^{+} and NO_{3}^{−}, but let us say into positive ions
NaO^{+} and negative ions NO_{2}^{−}, the changes which would result
from the passage of a current would be as follows: starting with the
action at the positive pole, we should find chloride ions discharged
and chlorine evolved at the pole (the evolution of chlorine could
be avoided, if considered desirable, by the use of a silver anode,
which would absorb the liberated chloride-ion to form insoluble
silver chloride on the electrode). At the same time, hydrogen ions
would move out of the space ‹P›, being repelled by the positive
pole, and attracted by the negative. At the boundary between the
sodium nitrate solution and the hydrochloric acid, the negative ions
of sodium nitrate, which we are supposing to have the composition
NO_{2}^{−}, would move up from ‹B› toward the positive pole (‹cf.›
exp., p. 45), being attracted by its charge; at any moment we
should have in any part of ‹P› as many negative ions (Cl^{−} and
NO_{2}^{−}), as there are hydrogen ions, the solution showing no
excess of free electricity at any point. Now, if NO_{2}^{−} were the
ion that moved up into the space ‹P›, then we should presently find
‹nitrous› acid ‹around› the ‹positive pole› in space ‹P›, H^{+} and
NO_{2}^{−} combining to form nitrous acid, HNO_{2}. But, as a matter
of experiment, although the tests for nitrous acid belong to the most
sensitive ones in chemistry, no trace of this acid is found there;
what we do find is ‹nitric acid›, HNO_{3}, resulting obviously from
the presence in space ‹P› of both hydrogen ions and ‹nitrate ions›,
NO_{3}^{−}, which have moved up from space ‹B›. It is clear, that
the presence of nitric acid in the region around the positive pole
means that the nitrogen atoms must have carried with them all three
of the oxygen atoms of the nitrate—in a word, that the composition
of the negative ion of sodium nitrate is NO_{3}^{−} and not, say,
NO_{2}^{−}. Similarly, considering what happens in space ‹N›, round
the negative pole, we have here an evolution of hydrogen, a migration
of some chloride ions out of ‹N› into the space ‹C›, and, at the same
time, a migration of the positive ions of space ‹C› into the division
‹N›. On examining the solution in ‹N›, we now find sodium chloride,
with unchanged hydrochloric acid, exactly what we should expect from
the migration of the ion Na^{+} toward the negative electrode.[124]
If the positive ion were, say, [p072] NaO^{+}, we should expect to
obtain either some of the hypochlorite NaOCl (NaO^{+} + Cl^{−}), or,
at least, an evolution of oxygen in this place, since sodium chloride
is formed. As a matter of experiment, no oxygen is evolved here, and
no trace of hypochlorite is found in ‹N› round the negative pole,
although the tests for hypochlorites are extremely sensitive.

Comparatively simple methods, in principle of the nature outlined,
enable us, then, to ‹determine experimentally› the composition of
the ions into which ionizable compounds, salts, acids and bases,
dissociate. Whenever any doubt may exist about the composition of the
ions of a given electrolyte, this device may be employed to settle
the matter, and there will presently be occasion to employ the U-tube
for such a purpose.

‹Ionization and Chemical Activity.›—The fact that the theory of
ionization gives us adequate explanations of the conductivity shown
by dissolved electrolytes and of their abnormally high osmotic
pressures, would have been in itself of interest to chemists; but,
if its applications were limited to these phenomena, we should not
be considering it in connection with qualitative chemical analysis,
nor would the theory, presumably, have greatly affected the
development of chemistry, as it has done. It is the fact that the
electrolytic dissociation of an electrolyte into its ions involves
‹chemical› changes of the most profound nature, and most intimately
affects ‹chemical› reactivity, that has made it play, in the last
two decades, such a leading rôle in the development of chemistry,
and that makes it necessary to include its consequences in the
consideration of analytical problems, if one would understand, as
far as present knowledge permits, the reactions involved in chemical
analysis.

Hydrogen chloride, as a perfectly dry gas, is a non-conductor of
electricity and, at the same time, it is found to be chemically
‹inactive›—it does not combine, for instance, with dry ammonia[125]
or act upon dry calcium carbonate[126] or on dry litmus. Hydrogen
chloride, subjected to great pressure at a low temperature, is
liquefied. The liquid is also a very poor conductor of [p073]
electricity[127] and does not show the chemical activity of
ordinary, aqueous hydrochloric acid; it does not combine with calcium
oxide or attack marble, zinc, iron or even magnesium.[127]

A solution of hydrogen chloride in a poorly ionizing medium,
like benzene or toluene, is an extremely poor conductor. There
is an extremely small conductivity indicating only a trace of
ionization.[128]

 EXP. A solution of hydrogen chloride, prepared by passing the dried
 gas into benzene or toluene (thiophene-free benzene will not become
 discolored), and kept anhydrous by means of fused calcium chloride,
 is tested for its conductivity, by dipping into it electrodes
 connected with a lighting circuit and a galvanometer.

Such a solution behaves chemically, also, quite differently from
the aqueous solutions of hydrogen chloride with which we are
familiar: dry steel nails,[129] dropped into it, will remain almost
unchanged—there is no marked evolution of hydrogen (‹exp.›).
Perfectly dried marble, added to it, will not give rise to the
evolution of carbon dioxide[129] (‹exp.›). We find thus, in all the
cases discussed—the nonconducting dry gas, the anhydrous liquefied
hydrogen chloride and the anhydrous benzene solution—an absence of
ionization,[130] as indicated by the lack of conductivity, and, along
with this, a lack of the familiar action of hydrochloric acid as an
acid. If we dissolve the gas in water, we obtain a well-conducting
solution (‹exp.›), in which, according to molecular weight
determinations, the [p074] hydrogen chloride is more or less largely
ionized, and this same solution has all the well-known chemical
properties of hydrochloric acid—it evolves hydrogen liberally when
given an opportunity to act upon zinc or iron (‹exp.›), it evolves
carbon dioxide copiously when marble is brought into contact with it
(‹exp.›). In such an aqueous solution we have both the ions of the
acid and the more or less non-ionized hydrogen chloride, the action
(HCl ⇄ H^{+} + Cl^{−}) being reversible.

Now, since in those cases in which we have admittedly only
non-ionized hydrogen chloride, there is no vigorous chemical action,
we are bound to conclude that, in the aqueous solution where we have
both the non-ionized and the ionized substance, it must be the new
components, the ions of the acid, which give this solution its new
qualities, the well-known properties of a pronounced acid.[131] This
conclusion, that the acid properties of hydrogen chloride in aqueous
solution are due to the ionized hydrogen chloride, rather than to the
hydrogen chloride itself, is one of fundamental importance.

«Dry Salts and their Aqueous Solutions.»—If the study of the relation
of ionization to chemical activity be extended, it is found that a
dry salt, such as, for example, silver nitrate, in crystals or finely
pulverized, is not perceptibly ionized, for it is a non-conductor
(‹exp.›). The same result is obtained with potassium chromate. If the
dry powders are intimately mixed, there is no chemical action between
them, no perceptible change occurs. The aqueous solutions of the
salts are excellent conductors (‹exp.›), as are the aqueous solutions
of almost all salts; the dissolved salts are therefore largely
ionized. As soon as the ionizing medium, water, is added to the dry,
yellow mixture of silver nitrate and potassium chromate, instantly
a chemical change results—red silver chromate, Ag_{2}CrO_{4}, is
precipitated (‹exp.›). Now, in the aqueous solution of these salts we
have both non-ionized molecules and their ions:

 AgNO_{3} ⇄ Ag^{+} + NO_{3}^{−},

 K_{2}CrO_{4} ⇄ 2 K^{+} + CrO_{4}^{2−}.

Since there is no interaction when the dry salts, containing only the
non-ionized substances, are mixed, and since there is interaction
[p075] when the solutions are mixed, in which both the non-ionized
and the ionized salts are present, one must conclude again that the
formation of silver chromate is the result of the action of the
silver ions on the chromate ions in the solution. In point of fact,
there could hardly fail to be an action, since the positive silver
ions and the negative chromate ions, moving in all directions through
the solution, must collide and be discharged, or combine, to form
molecular silver chromate. This salt happens to be very difficultly
soluble, and to be colored red, as well, so that silver chromate is
precipitated and is immediately recognizable.

The two dry powders in the experiment were allowed to be in contact
for only a few moments. It is important to note, therefore, that
dry sodium acid carbonate and dry potassium acid tartrate are also
nonconductors (‹exp.›), and that the intimate mixture of these
two powders is kept for years in the well-known form of baking
powders without appreciable decomposition—yet best in tin vessels,
to exclude moisture. The aqueous solutions, however, are good
conductors (‹exp.›), and, when dissolved, these salts are more or
less ionized. The addition of water to the mixed salts (‹exp.›) leads
at once to the well-known action, carbon dioxide being liberated and
sodium-potassium tartrate or Rochelle salt being formed.

«Behavior of Fused Salts.»—It may be objected that there are common
cases, where dry salts are known to act upon each other; barium
sulphate is fused with sodium carbonate to convert the former into
the carbonate, BaSO_{4} + Na_{2}CO_{3} ⇄ Na_{2}SO_{4} + BaCO_{3}.
Before one decides that this must be an instance of the action of
non-ionized salts on each other, the conductivity of dry salts under
the conditions of the experiment, namely at an elevated temperature,
must be examined. There is no difficulty in recognizing that while
dry sodium carbonate or potassium nitrate at ordinary temperatures
does not conduct a current, and is not perceptibly ionized, each
salt, when fused, becomes an excellent conductor (‹exp.›,[132]
with potassium nitrate). It is, in fact, well known that, in many
electrolytic operations, fused salts[133] are used in place [p076]
of solutions. It must be added that the heat, not the change of
state, causes the ionization, careful work having shown that
conductivity begins to be appreciable below the point of fusion.

 EXP. Two platinum wires, fused, one inch apart, into a glass rod,
 are connected with a sensitive galvanometer and the lighting
 circuit. When the glass is warmed, a current is found to pass.

The action between barium sulphate and sodium carbonate at a high
temperature does not mean, then, that the non-ionized salts interact;
on the contrary, we find that, under such conditions, coincident with
the evidence of reactivity, we have also decided conductivity—again
indicating decided ionization.

 «Dry Salts at Ordinary Temperatures.»—Inasmuch as ordinary
 temperatures are still far removed from the absolute zero, one
 must suppose that dry salts must be ionized, minimally at least,
 even at room temperature, and should therefore react with each
 other. Presumably they do, only so slowly, as a result of the
 minimal degrees of ionization, and of the few chances of collision
 between ions of opposite charges, owing to the restricted range
 of the molecular motions, that the total change is imperceptible.
 Critical work on the question is most desirable. In this connection
 it maybe said that Spring[134] found that dry salts do interact
 at ordinary temperature, when ‹subjected to great pressures›,
 provided the volume of the products is smaller than the volume of
 the initial substances. Whether this action is due to the ionization
 of the salts, minimal as it is, or whether we have here a case
 of interaction of non-ionized molecules, has not, it seems, been
 determined; it would require difficult quantitative work to settle
 the question.

 «Influence of Light and Heat.»—It is apparent that heat, a form
 of energy, contributes to the dissociation of ionogens, and it is
 natural that we should consider other forms of energy, ‹e.g.› light,
 to have the same power. One may speculate about the possibility of
 light inducing chemical action (‹e.g.› in starting the combination
 of hydrogen and chlorine, or in photography) by its ionizing power,
 and about the possibility that rapid combination of oxygen and
 hydrogen follows the application of a flame to the mixture, as the
 result of increased ionization of the components at the elevated
 temperature of the flame and of the burning gases. The experimental
 evidence shows that, in some actions of this nature, ionization
 is an important factor, while in other instances it appears to be
 negligible.[135] [p077]

«Conclusions.»—It appears that we must accept the conclusion, that
the ‹reactions of salts›, ‹acids› and ‹bases› (ionogens) ‹in aqueous
solution› (the so-called "salt reactions") ‹are the reactions of the
ions and not of the non-ionized molecules.› This conclusion is of
the greatest and most practical importance in our science. It is the
natural inference from the results of the qualitative experiments
described in the three preceding sections. Its final adoption,
however, is based on the existence of a great mass of ‹quantitative
evidence›, and to the consideration of some of this we now turn.

«Quantitative Relations.»—If the active components in aqueous
solutions of acids, bases and salts are the ions, rather than the
undissociated compounds, then quantitative data supporting such a
conclusion should be found. Such quantitative confirmation, from the
point of view of chemical activity, is not lacking. Only a small part
of the data can be considered here.

Conductivity measurements, and the lowering of freezing-points
and the elevation of boiling-points, show that there are very
decided differences ‹in the degrees of ionization of different
acids and bases› in solutions of equivalent concentration. For
instance, potassium hydroxide is somewhat more ionized than is
barium hydroxide, and decidedly more so than ammonium hydroxide, a
fact that can readily be demonstrated by the conductivities of the
solutions[136]:

 EXP. Equivalent solutions (1 / 10 normal) of the three bases
 are introduced into three vertical tubes, containing electrodes
 connected, in parallel, with a lighting circuit and with small
 electric lamps. When the two electrodes in each of the three tubes
 are at equal distances from each other, the lamp connected with the
 potassium hydroxide solution glows most brightly, that connected
 with the barium hydroxide solution a little less brightly, and the
 lamp connected with the ammonium hydroxide solution does not glow
 at all—not enough current is carried through the ammonium hydroxide
 solution to heat the filament in the corresponding lamp sufficiently
 to make it red. Now, the current, for a given fall of potential, is
 proportional to the conductivity of a solution (p. 48) and, in the
 equivalent solutions[137] the conductivity depends on the proportion
 of charged particles (the degree of ionization) of the base. It is
 clear then, that ammonium hydroxide is very much less ionized than
 are the two other bases. [p078]

 The resistance in a tube may be reduced, and the conductivity
 increased, by reducing the distance through which the current must
 be carried, ‹i.e.› by bringing the electrodes closer together.
 In the solution of barium hydroxide, we find that we must reduce
 the distance between the electrodes to about five-sixths the
 corresponding distance in the potassium hydroxide solution before
 we obtain, approximately, as bright a lamp from the current passing
 through it, and in the case of ammonium hydroxide, we must bring the
 electrodes so close together that they almost touch, the distance
 being only one or two hundredths of the distance between the
 electrodes in the potassium hydroxide solution.

 For the degrees of ionization of the three bases we have,
 approximately, the relation α_{K} : α_{Ba} : α_{NH_{4}}::
 ‹d›_{K} : ‹d›_{Ba} : ‹d›_{NH_{4}}, if we indicate by ‹d›_{K},
 ‹d›_{Ba}, ‹d›_{NH_{4}} the distances between the electrodes in the
 three solutions when the lamps are of uniform brightness, ‹i.e.›
 when the same quantity of current passes through each solution. In
 this deduction, the conductivities of the bases at infinite dilution
 (Λ_{∞}) are taken to be the same, which is roughly true.

The experiment gives us a rough measure of the relative
conductivities and the relative degrees of ionization of the three
bases. It shows that potassium hydroxide is somewhat more ionized
than is barium hydroxide, in equivalent solution, and decidedly more
than is ammonium hydroxide.

Limiting the further discussion, at this moment, to potassium
hydroxide and ammonium hydroxide, we should find that, since in
equimolar solutions, a larger portion of the former is ionized than
of the latter, ‹the potassium hydroxide solution must contain the
larger proportion or concentration of hydroxide-ion, HO^{−}, which
is the characteristic ion of bases›. It should, therefore, show
the ‹chemical› characteristics of a base much more decidedly than
the ammonium hydroxide solution. That such is the case can be very
simply shown by adding equal quantities (0.1 c.c.) of the 0.1 molar
solutions to equal volumes (50 c.c.) of water[138] containing some
phenolphthaleïn. This is an indicator for bases and acids, like
litmus, but it is less sensitive to hydroxide-ion than is litmus.
We find that the potassium hydroxide causes a very decided change,
producing a deep red color with the phenolphthaleïn, whereas the
ammonium hydroxide only produces a pink hue.[139] [p079]

In all the chemical changes produced by these alkalies, the
same difference in intensity of action is shown, that is here
exhibited towards indicators. If, for example, we measure the rate
of change in an action, which is slow enough to be measured and
which proceeds quantitatively in proportion to the concentration of
hydroxide-ion, we find that the measured rates of change indicate
the same ratio in the concentrations of hydroxide-ion in potassium
and ammonium hydroxide solutions, as is indicated by quantitative
conductivity measurements. An action suitable for the purpose is
the saponification of an ester, such as ethyl acetate. Under the
influence of an alkali, like potassium hydroxide, ethyl acetate is
decomposed, more or less rapidly, into an acetate and alcohol: we
have, for instance,

 CH_{3}CO_{2}C_{2}H_{5} + KOH → CH_{3}CO_{2}K + C_{2}H_{5}OH.

The rate of saponification is found to be proportional to the
‹concentration of hydroxide-ion›, and not to the total concentration
of the base, and the action may be formulated more accurately as
follows:

 CH_{3}CO_{2}C_{2}H_{5} + K^{+} + HO^{−} → CH_{3}CO_{2}^{−} + K^{+} +
   C_{2}H_{5}OH

 or CH_{3}CO_{2}C_{2}H_{5} + HO^{−} → CH_{3}CO_{2}^{−} + C_{2}H_{5}OH.

For ammonium hydroxide we have similarly,

 CH_{3}CO_{2}C_{2}H_{5} + NH_{4}^{+} + HO^{−} → CH_{3}CO_{2}^{−} +
   NH_{4}^{+} + C_{2}H_{5}OH.

Now, Arrhenius[140] proved that the rate of saponification of ethyl
acetate by ammonium hydroxide, which is ‹very much slower› than
the rate of saponification by potassium hydroxide of equivalent
concentration, ‹does agree quantitatively, indeed, with the rate
demanded by the theory of ionization›, when the hydroxide-ion
is considered the active component of the bases, to which the
saponification is due.

 EXP. A rough idea of the difference in the chemical actions of the
 two bases may be obtained by observing their effects on the ester,
 methyl acetate, which is decomposed into an acetate and methyl
 alcohol rather rapidly. To 50 c.c. of (CO_{2} free) water containing
 some phenolphthaleïn, 10 c.c. of 0.1 molar potassium hydroxide
 is added; a similar mixture with 10 c.c. of 0.1 molar ammonium
 hydroxide solution is prepared. To each of the solutions, 2 c.c.
 (an excess) of methyl acetate is added (to the ammonium hydroxide
 solution first), and the mixtures are shaken for a moment. At room
 temperature, the mixture containing potassium hydroxide will become
 pale pink in a few minutes, and colorless soon thereafter, while the
 mixture [p081] containing ammonium hydroxide will still be deep red
 at the end of 45 minutes.[141]

 In the following tables are summarized some of the results
 which have been obtained in comparing the ‹activity of bases›,
 in saponifying methyl acetate, and ‹the concentrations of the
 hydroxide-ion›, in the solutions of the bases, as determined by
 conductivity measurements. The comparisons are made by representing
 the activity of the hydroxide-ion in a solution of lithium hydroxide
 by 100 and by expressing the ratio of the activity of a given base
 to that of the lithium hydroxide in percentages of the activity of
 the latter. All the bases were used in 0.025 molar concentration,
 and their degrees of ionization are given in the last column of the
 table.

  CHEMICAL ACTIVITY OF BASES AND THEIR IONIZATION[A]

                                         Relative
          Base.            Activity.   Concentration
                                         of HO^{−}.
  Lithium hydroxide          100           97
  Potassium hydroxide         98           97
  Sodium hydroxide            98           97
  Ammonium hydroxide           2            2.5
  Ethyl ammonium hydroxide    12           16.

  TABLE NOTE:

  A. Whetham, ‹Theory of Solutions›, p. 338 (1902). (‹Cf.›
  Walker, ‹Introduction to Physical Chemistry›, p. 277 (1899).)

 An ester is decomposed also ‹under the influence of acids›,
 in aqueous solution, into an organic acid and an alcohol,
 and cane sugar is similarly decomposed into glucose and
 fructose (grape sugar and fruit sugar): C_{12}H_{22}O_{11} +
 H_{2}O → C_{6}H_{12}O_{6} + C_{6}H_{12}O_{6}. Both actions are
 found to be caused by the influence of the ‹hydrogen ions› of
 the acids used and to proceed, at a given temperature, ‹with a
 velocity proportional to the concentration of the hydrogen ions›.
 Now, in 0.1 molar solution, acetic acid is very little ionized
 (1.3%), as compared with hydrochloric acid (91%), the degrees
 of ionization being determined by conductivity measurements (p.
 50); the relation may easily be demonstrated with the aid of the
 conductivity apparatus used to show the difference in ionization
 between potassium hydroxide and ammonium hydroxide. In the presence
 of 0.1 molar hydrochloric acid, the decomposition of cane sugar
 actually proceeds at 79 times the rate that it does in the presence
 of 0.1 molar acetic acid. The ratio of the concentrations of the
 hydrogen-ion in the two [p082] solutions is, in fact, 70 : 1.
 There is, therefore, close agreement[142] between the ‹relative
 chemical activity› of the two acids and the relation demanded, if
 we assume, on the basis of the theory of ionization (p. 77), ‹that
 the chemically active components of the acids are their ions and
 particularly their hydrogen ions›.

 In the following table, the relative activities of acids, in
 accelerating the decomposition of methyl acetate by water,
 are contrasted, in a similar fashion, with their relative
 conductivities. The conductivities of acids depend to such an extent
 on the concentration of hydrogen-ion, which moves five times, or
 more, faster than the anions and carries therefore the greater part
 of the current, that the conductivities of acids, in equivalent
 concentrations, may be considered an approximate measure of their
 relative degrees of ionization and ‹of the concentrations of
 hydrogen-ion›. For the purpose of comparison the activity and the
 conductivity of molar hydrochloric acid are both represented by 100.
 All the acids were used in normal solutions.

  CHEMICAL ACTIVITY OF ACIDS AND THEIR IONIZATION.[A]

       Acid.          Activity.   Conductivity.
  Hydrochloric acid     100          100
  Nitric acid            92          100
  Sulphuric acid         74           65
  Acetic acid             0.3          0.4
  Formic acid             1.3          1.7
  Chloracetic acid        4.3          4.9
  Tartaric acid           2.3          2.3

  TABLE NOTE:

  A. Whetham, ‹Theory of Solutions›, p. 338.

In the following chapters and, indeed, throughout our further work,
we shall continually meet additional instances of the quantitative
relation between chemical activity and ionization. In fact, the
results obtained in the field of quantitative measurement of chemical
action, of which the above are single instances, have demonstrated,
more than anything else, the value of the theory of ionization to
chemistry and the necessity of taking it into account in expressing
the results of chemical action in mathematical terms. [p083]

«Summary.»—Measurements made, then, in three great and independent
fields of investigation, ‹electrical conductivity›, ‹osmotic
pressure› and the allied relations, and ‹chemical activity›,
bring independent testimony to the correctness of the fundamental
assumptions of Arrhenius's theory of ionization. In the quantitative
study of solutions of electrolytes, wherever secondary disturbing
influences are eliminated or are taken into account as far as
possible, the three lines of investigation give results which
agree satisfactorily[143] as to the degree of ionization of the
electrolytes under examination. With the aid of this theory,
‹predictions› of the course of chemical action may now be made more
definitely and with more assurance than ever before in the history of
chemistry.

«Chemical Activity of Non-ionized Molecules.»—The conclusion
reached, on the basis both of qualitative and, particularly, of
quantitative evidence, that the reactions of salts, acids and bases
(ionogens) in aqueous solutions (the so-called salt reactions) are
the actions of the ions and not of the non-ionized molecules, does
not necessarily mean that the non-ionized molecules are altogether
inactive chemically. Some chemists believe that ions have only the
advantage of an ‹enormously greater degree of reactivity›.[144]
If the atoms in a molecule carry electric charges even prior to
their separation (ionization), as expressed for instance by the
formula H^{+}Cl^{−} for hydrogen chloride (p. 43), it can be
readily seen that an action[145] resulting from the collision
of a molecule of hydrogen chloride with a molecule of potassium
hydroxide H^{+}Cl^{−} + HO^{−}K^{+} ⇄ K^{+}Cl^{−} + HO^{−}H^{+}
would, in some respects, resemble the ionic action H^{+} + Cl^{−} +
K^{+} + HO^{−} ⇄ K^{+} + Cl^{−} + HOH. The latter would probably
have the advantage of a considerably smaller resistance to the
action, and consequently of a far greater speed. ‹But the question of
supreme importance and interest to chemistry is the question as to
which actions are found experimentally to be of moment in any given
case.› Now, a great mass of corroborative evidence shows that for
the interactions of ionogens in aqueous solutions the ionic actions,
probably on account of their enormous speeds, ‹are the important
ones›. [p084]

On the other hand, there are large numbers of compounds, especially
among organic substances, which do not appear to ionize to a
measurable extent and whose actions, in large part at least, appear
to be the actions of ‹non-ionized molecules›. It is characteristic
that most of these actions take place at ‹slow›, very frequently
easily measurable, rates of speed. Critical study shows that even
for such actions ionization often plays a very important rôle, at
least in some of their stages, and throughout the field of organic
chemistry the ‹intimate relations› between ‹electrical phenomena
and chemical activity can be readily recognized›.[146] But these
relations are not obvious ones and do not, as yet, play a dominant
rôle. It is because analytical chemistry deals predominantly with the
reactions of ‹ionogens›, that the study of the ‹reactions of ions›
will demand our extended attention.

 «Reactions in Non-aqueous Solutions.»—Kahlenberg[147] has made some
 interesting and important, although not conclusive, contributions
 to the problem of chemical activity of ionogens in non-aqueous
 solutions. He has found, for instance, that zinc, left in contact
 with a benzene solution of hydrogen chloride carefully freed from
 moisture, displaces hydrogen.[148] Cadmium, aluminium and magnesium,
 on the other hand, do not evolve hydrogen in such a solution.[149]
 The solution shows an enormous resistance to the passage of an
 electric current, and the conclusion is drawn by Kahlenberg that the
 liberation of hydrogen is due to the action of non-ionized hydrogen
 chloride on the zinc.

 It is evident,[150] from Walden's equation showing the relation
 between the ionizing power and the dielectric constant of a
 solvent (p. 63), that the presumption is that hydrogen chloride in
 benzene solution is not absolutely non-ionized, but rather that it
 is ionized in traces.[151] No exact measurements of the [p085]
 ‹degrees of ionization of hydrogen chloride in benzene solution›
 have been made; that the solution shows an enormous resistance
 to the passage of the electric current and can be, at best, very
 little ionized, is all that has been established. In default of
 exact data, the semiquantitative determination by Kablukoff, showing
 that a 0.25 molar solution of hydrogen chloride in benzene has a
 resistance of 120 × 10^6 ohms, is of interest. From the meager data
 concerning the dimensions of the electrodes used, one may calculate
 (with the aid of a not unreasonable assumption as to the limiting
 value of the conductivity, at infinite solution) that the degree
 of ionization of the acid in the solution is perhaps of the order
 5E−9, and the concentration of hydrogen-ion,[152] consequently,
 roughly 10^{−9}. Now, the evolution of hydrogen by means of zinc,
 in aqueous solutions, takes place according to the equation
 Zn ↓, + 2 H^{+} ⇄ Zn^{2+} + H_{2} ↑, and depends on a ‹ratio of
 the concentrations› of zinc-ion and hydrogen-ion[153] (Chapters
 XIV and XV, ‹q.v.›). Even if the concentration of hydrogen-ion is
 very small, zinc will liberate hydrogen, provided the conditions
 are such that the concentration of zinc-ion cannot reach a large
 enough value to satisfy the equilibrium ratio, and stop the
 action. Now, in an alkaline solution, zinc-ion is converted into
 zincate-ion (Zn^{2+} + 4 HO^{−} ⇄ ZnO_{2}^{2−} + 2 HOH) and a large
 concentration of zinc-ion cannot accumulate. The consequence is
 that zinc liberates hydrogen freely even from alkaline solutions,
 for instance from molar solutions of potassium hydroxide, in which
 the concentration of hydrogen-ion, roughly 10^{−14}, is ‹very
 much smaller› than that calculated for the benzene solution of
 hydrogen chloride (namely, 10^{−9}). Now, although the values of
 the solution-tension constants of elements change most decidedly
 with a change of solvent, it seems likely[154] that their ‹ratios›,
 on which their mutual displacement depends, will not be found
 materially altered. Zinc chloride being insoluble in benzene, the
 ratio for equilibrium may not be fulfilled for zinc in contact with
 a benzene solution of hydrogen chloride. Hence, with that solvent,
 ‹the evolution of hydrogen may, so far as it goes, very well be
 due to precisely the same machinery as that operating in aqueous
 solution›. The liberation goes on until the metal is protected
 against any further action by a film of the solid chloride. It
 seems, therefore, at least possible, that the evolution of hydrogen
 observed by Kahlenberg and his collaborators[155] is a purely ionic
 action, the same as the similar [p086] action in aqueous solution
 has been proved to be by quantitative measurements.[156] Only exact
 measurements, comparable with those made in aqueous solutions, can
 settle the question at issue, and until such quantitative evidence
 is forthcoming, a definite conclusion that the action of hydrogen
 chloride in benzene solution is or is not an ionic action is not
 warranted by the facts.

 Equally interesting are Kahlenberg's observations of interaction
 between hydrogen chloride in benzene solution and a similar solution
 of copper oleate. Each solution shows absence of appreciable
 conductivity, yet, when the solutions are mixed, precipitation
 of copper chloride occurs instantly. Whether we have here an
 instantaneous action between non-ionized molecules, as claimed by
 the observer, or whether the minimal ionization[157] of the hydrogen
 chloride and copper oleate, the existence of which we have a right
 to assume, is sufficient to account for this rapid action, both
 components being in solution and intimately mixed, is a question
 of the greatest interest. But until quantitative measurements of
 all the factors involved in chemical actions in benzene solution
 are obtained, a very difficult, but necessary task, which the
 discoverer of the action omitted to perform, no definite conclusion
 whatever can be based on such results, interesting as they are.
 Water, although it is only minimally ionized (tables, Chapter VI),
 hydrolyzes salts like potassium cyanide and aluminium chloride
 almost instantly, and it has been rigorously proved that the
 resulting condition of equilibrium involves the ‹ions of water›[158]
 (Chapter X). With the possibility that the well-known enormous
 speeds of action of ions may completely offset the tremendous
 reduction in concentration of the hydrogen-ion, in a benzene
 solution of hydrogen chloride as compared with an aqueous solution,
 further analysis of the relations is imperative.[159] Until such
 investigations have been carried out, we must consider [p087] it
 possible that the reactions of hydrogen chloride in benzene solution
 may be reactions of its non-ionized molecules or reactions of its
 ions. In view of the undoubted minute concentrations of the latter,
 as compared with aqueous solutions, and in view of the inertness of
 non-ionized hydrogen chloride in aqueous solutions as compared with
 the activity of its ions, a benzene solution of hydrogen chloride
 should show far less ionic activity than an aqueous solution,
 and that such is the case is brought out clearly by Kahlenberg's
 interesting experiments.

«Some Applications of the Chemical Activity of Ions to Qualitative
Analysis.»—The knowledge that aqueous solutions of ionogens show
the reactions of the ions contained in them, gives us a clear,
sharply defined interpretation of many of the simpler facts of
qualitative analysis. The elementary observation that a large number
of hydrogen derivatives show acid properties and a considerable
number of others do not (at least not to a sufficient extent to be
appreciable), finds its simplest explanation in the fact that all
solutions showing acid properties have these properties as the result
of the presence of a common component, namely the hydrogen-ion. The
acid properties are, in fact, the properties of this one substance
and no other. Thus hydrochloric, nitric, sulphuric, carbonic acids
are acids because they are dissociated more or less, liberating
hydrogen ions; and compounds like marsh-gas CH_{4}, ammonia NH_{3},
benzene C_{6}H_{6}, in spite of the presence of a great deal of
hydrogen in their molecules, are not acids, because they do not,
to an appreciable extent,[160] ionize as do the first compounds
mentioned. In the same way, glycerine C_{3}H_{5}(OH)_{3}, although
it is a trihydroxide, does not show the characteristic actions
of the hydroxides of potassium, barium, aluminium, of the metal
hydroxides in general—the latter are more or less ionized, forming
the characteristic ion of bases, the hydroxide-ion HO^{−}; but
glycerine does not appear to ionize into C_{3}H_{5}^{3+} and HO^{−}.
The well-known observation of qualitative analysis, that potassium
chlorate solutions do not precipitate silver chloride from silver
nitrate, while potassium chloride and other chlorides do so at once,
is now understood as being the result of the fact that the chlorates
produce the chlorate-ion ClO_{3}^{−} (see page 70 for the method
of determining its composition), while the chloride-ion [p088] is
required for the precipitation of silver chloride. Chlorplatinic acid
H_{2}PtCl_{6}, in spite of the large proportion of chlorine in its
composition, does not precipitate silver chloride, but rather silver
chlorplatinate,[161] a yellow salt, insoluble in ammonia, and it does
so because its ions[162] are H^{+} and (PtCl_{6}^{2−}).

Perhaps the most instructive case of this kind, that we can study,
is that of iron in ferrous and ferric salts. Exceedingly sensitive
tests are known for the ferrous and the ferric ions. Thiocyanates
produce an intensely red salt, Fe(SCN)_{3}, when added, for instance,
to ‹ferric› chloride; potassium ferrocyanide, K_{4}Fe(CN)_{6},
precipitates ferric ferrocyanide, Fe_{4}[Fe(CN)_{6}]_{3}, Prussian
blue, from ferric chloride solutions; ammonium hydroxide precipitates
quantitatively the insoluble red ferric hydroxide (exps.). With
‹ferrous› salts, potassium ferricyanide K_{3}Fe(CN)_{6} precipitates
ferro-ferricyanide Fe_{3}[Fe(CN)_{6}]_{2}, Turnbull's blue; ammonium
sulphide precipitates black ferrous sulphide (‹exps.›). Now, in
two of the reagents used, potassium ferro- and ferricyanide, iron
is present according to the formulæ given. If one should attempt
to demonstrate its presence by means of these tests—among the
most sensitive and most reliable tests known in analysis—one
would fail utterly. Thiocyanates do not produce even the faintest
tinge of pink in potassium ferricyanide solution[163]; ammonium
hydroxide does not precipitate any ferric hydroxide (‹exps.›).
Ammonium sulphide does not precipitate the least trace of a black
sulphide from a ferrocyanide solution, and when the latter is
mixed with the ferricyanide solution, no trace, either of Prussian
or Turnbull's blue, is shown (‹exps.›). The contrast between
the behavior of these salts and ferrous and ferric salts is now
sharply and definitely interpreted, as being the result of the
contrast in their ionization,—the color tests we use are extremely
sensitive tests only for the ‹ferric› and ‹ferrous ions›, Fe^{3+}
and Fe^{2+}, respectively,—but potassium ferrocyanide ionizes into
potassium ions and the negative ferrocyanide ions Fe(CN)_{6}^{4−},
and shows the actions of ferrous ions as little as chlorate ions
ClO_{3}^{−} exhibit the reactions of chloride ions Cl^{−}. Potassium
ferricyanide, in turn, gives rise to trivalent, negative ferricyanide
ions Fe(CN)_{6}^{3−} and not to ferric [p089] ions.[164] If any
doubts arise on this point, one can decide the question readily by
experiment. When a concentrated solution of potassium ferricyanide is
placed in a U-tube under a solution of some colorless electrolyte,
such as sodium sulphate, and plates connected with a battery are
inserted, there is no difficulty (‹exp.›) in seeing that the yellow
ion,[165] containing the iron, moves to the ‹positive› pole and ‹not›
to the ‹negative›. The iron is, therefore, as a matter of experiment,
‹part of a negatively charged substance›.

That iron is really present in these compounds can be shown most
effectively if we destroy the salts:

 EXP. Dry, pulverized potassium ferrocyanide is intimately mixed with
 dry potassium carbonate and the mixture heated in a hard glass test
 tube. When the whole mass has become red-hot, insuring complete
 decomposition, the hot (not red-hot) tube is plunged into water;
 the salts are extracted and particles of metallic iron are left
 undissolved. The action is

 K_{4}Fe(CN)_{6} + K_{2}CO_{3} → 6 KCN + FeCO_{3}

 FeCO_{3} → FeO + CO_{2}

 and FeO + KCN → KCNO + Fe.

 If the iron is dissolved in a little dilute hydrochloric acid and
 oxidized to the ferric condition, by the addition of a few drops of
 bromine water, the intensely red solution characteristic of ferric
 salts may be readily obtained, when a thiocyanate is added to the
 solution.


  FOOTNOTES:

  [114] Loomis. (‹Cf.› Whetham, ‹Theory of Solution›, p. 320 (1902).)

  [115] Loomis; and E. H. Griffith. (‹Cf.› Whetham, ‹loc. cit.›)

  [116] Expressed in moles per liter.

  [117] Δ_{1} : Δ_{2}... = ‹C›_{1} : ‹C›_{2}... or  Δ_{1} / ‹C›_{1} =
  Δ_{2} / ‹C›_{2} = a constant.

  [118] ‹Cf.› Whetham, ‹loc. cit.›, pp. 147, 158.

  [119] ‹Ibid.›, p. 320.

  [120] In regard to the degrees of ionization, as shown by
  freezing-point depressions and conductivities of salts, see also A.
  A. Noyes, ‹Report of the Congress of Arts and Sciences›, St. Louis,
  1904, Vol. «IV», p. 313.

  [121] See Chapter XII, in regard to so-called "complex ions" and
  their salts.

  [122] The term "acid ion" is used to designate the "acid radical,"
  when it exists, in solution, as an independent charged particle or
  ion. "Acid ion" is thus a convenient synonym for anion, just as
  "metal ion," designating the metal or metal-like radical of a salt,
  is used as a synonym for cation. The term, acid ion, has been found
  to convey more quickly and definitely to the student's mind, than
  does the term anion, which component of an acid or salt is referred
  to. While it is not, in some respects, an ideal term, yet its
  use seems justified by its very close relation to the term "acid
  radical" and by its practical advantages.

  [123] The principle was first applied by Hittorf.

  [124] This does not preclude the possibility that the ion is
  combined with more or less water and is Na(H_{2}O)_{‹x›}^{+}; see
  pp. 42, 65.

  [125] Baker, ‹J. Chem. Soc.› (London), «65», 611 (1894), «73»,
  422 (1898). On page 623 of the first article is given a list of
  chemical actions for which the effect of the presence of moisture
  has been investigated (‹Stud.›).

  [126] Hughes, ‹Phil. Mag.›, «34», 117 (1892) (‹Stud.›).

  [127] Gore, ‹Proc. Royal Soc.›, «14», 204 (1841). Gore found that
  aluminium was dissolved and that sodium and potassium were attacked
  by the gas, even before its liquefaction. It is uncertain whether
  these positive reactions are reactions of absolutely anhydrous
  hydrogen chloride or the result of the presence of moisture in
  the experiments in question, since Cohen [‹Chem. News›, «54», 305
  (1896)], drying the gas more carefully than did Gore, found, in
  contrast to the latter, that metallic sodium may be exposed for
  several weeks to dry hydrogen chloride gas and retain its lustre.
  In all experiments demanding the rigorous exclusion of moisture,
  more weight must be attached to negative results (showing lack of
  activity) than to positive results. [‹Cf.› the controversy between
  Baker, ‹loc. cit.›, and Gutmann, ‹Liebig's Ann.›, «299», 3 (1898)].

  [128] Nernst's ‹Theoretical Chemistry›, p. 375. Kablukoff, ‹Z.
  phys. Chem.›, «4», 430 (1889).

  [129] In regard to the behavior of zinc, see below, p. 84. (‹Cf.›
  Kahlenberg, ‹J. Phys. Chem.›, «6», 13 (1902) (‹Stud.›).)

  [130] For a fuller discussion of the benzene solution see p. 84.

  [131] The ‹acid› character, in particular, is due to the
  hydrogen-ion, H^{+}; see below.

  [132] The fusion is conveniently made in a platinum dish; the dish
  and a platinum cathode are connected with the lighting circuit and
  an electric lamp.

  [133] See Smith, ‹Inorganic Chemistry›, pp. 550, 569, 578, 588,
  608, 610, 683: ‹College Chemistry›, 361, 373, 380, 389, 404, 405,
  443 («Stud.»).

  [134] ‹J. Chem. Soc.› (Abstracts) (London), «40», 504 (1881).

  [135] For positive evidence of the ionizing power of light, see
  Haber, ‹Z. Elektrochem.›, «11», 847 (1905). For evidence as to the
  negligible rôle of ionization in the combination of chlorine and
  hydrogen, see Mellor, ‹Chemical Statics and Dynamics› (1904), p.
  290.

  [136] The apparatus described by A. A. Noyes and Blanchard for
  comparing acids is used [‹J. Am. Chem. Soc.›, «22», 737 (1900)].

  [137] The conductivity depends in this case chiefly on the
  migration of the ‹fast moving hydroxide ions› (p. 56), common to
  the three bases. There is little difference in the rates at which
  the cations move.

  [138] The water should be free from carbonic acid.

  [139] The various indicators show different, specific ‹degrees
  of sensitiveness to acids (to hydrogen ions) and to bases
  (to hydroxide ions)›. That is, different concentrations of
  hydrogen-ion or of hydroxide-ion are required to change their
  colors. As they are particularly useful in demonstrating ‹varying›
  concentrations of these ions, they will frequently be used in
  illustrating conclusions reached in the course of our work, just
  as they are used extensively in practical analysis. The following
  tables are intended to give some definite information on this
  valuable quality. The fourth column of the first table shows the
  concentration of ‹hydrogen-ion›, required to change the color of
  the indicator from the tint given in the second column to the tint
  given in the third column. The second table gives, similarly, the
  concentrations of hydroxide-ion required to produce the changes of
  tint indicated. The tables refer to results obtained when 0.1 c.c.
  (about two drops) of a 0.1 to 0.15% solution of the indicator is
  added to 10 c.c. of the solution examined.

  TABLE OF SENSITIVENESS TO ACIDS (TO HYDROGEN-ION)

  Indicator.              From     to              Concentration
                                                      H^{+}.
  Phenolphthaleïn         Pink     Colorless        10E−9
  Azolitmin[A] (litmus)   Violet   Violet ‹pink›     1E−6
  Methyl orange           Yellow   Reddish orange    1E−3 – 0.1E−3

  TABLE NOTE:

  A. Azolitmin is an important component of litmus.

  TABLE OF SENSITIVENESS TO BASES (TO HYDROXIDE-ION)

  Indicator.        From        to              Concentration
                                                   HO^{−}.
  Phenolphthaleïn   Colorless   Pink            10E−6
  Azolitmin         Violet      Violet ‹blue›    1E−6 – 0.1E−6
  Methyl orange     Orange      Yellow           1E−9

  It is clear that of the three indicators given in the table,
  phenolphthaleïn is the most sensitive to acids, methyl orange the
  most sensitive to bases. An extended table of the sensitiveness
  of many indicators, on which the above tables are based, is given
  by Salm, ‹Z. phys. Chem.›, «57», 471 (1907). The ‹theories› (of
  Ostwald, Bernthsen, and others) regarding the ‹color changes›,
  and the ‹theory› (of Ostwald) concerning the ‹sensitiveness of
  indicators›, are discussed (with references to the literature)
  by Stieglitz, ‹J. Am. Chem. Soc.›, «25», 1117 (1903). Later
  modifications of the views on color changes are discussed in
  papers by Stieglitz, ‹Am. Chem. J.› «39», (1908), and by Acree,
  ‹ibid.›, «37», «39», «42», and in these papers references to the
  literature will be found. For investigations on the sensitiveness
  of indicators, see McCoy, ‹ibid.›, «31», 508 (1904), Salm, ‹loc.
  cit.›, and A. A. Noyes, ‹J. Am. Chem. Soc.›, «32», 815 (1910).

  [140] ‹Z. phys. Chem.›, «2», 289 (1888). Note the remarks in the
  footnote following.

  [141] The formation of an ammonium salt in the latter action still
  further reduces the concentration of the hydroxide-ion (Chapter VI)
  and retards the action; but the solution, in equal measure, becomes
  less active toward the indicator, phenolphthaleïn (p. 114). The
  experiment shows, therefore, rather fairly, the relative activities
  of the bases. The exact work of Arrhenius included consideration of
  the effect of the ammonium salt, and the clearing up of the mystery
  of this effect (p. 114) formed one of the greatest triumphs of his
  theory.

  [142] Arrhenius, ‹Electro-chemistry›, p. 184 (1902). A second
  accelerative factor, the so-called "salt effect" (Chap. VI, ‹q.
  v.›), is more pronounced in the case of 0.1 molar hydrochloric acid
  than in that of 0.1 molar acetic acid, as the result of which the
  activity of the hydrochloric acid should be increased about ten
  per cent; the ratio, therefore, of the speeds of reaction, both
  the degrees of ionization of the acids and the "salt effect" being
  considered, should be approximately 83 : 1, whereas the ratio found
  by experiment is 79 : 1.

  [143] ‹Vide› also A. A. Noyes, ‹Report of the Congress of Arts and
  Science›, Vol. «IV», p. 311 (1904).

  [144] Haber, ‹Z. für Elektrochem.›, «10», 775 (1904); see Chapter
  XII.

  [145] This is, essentially, the old Berzelius view of chemical
  action.

  [146] ‹Vide›, for instance, Stieglitz, ‹Report of the Congress
  of Arts and Sciences›, St. Louis, «IV», 276 (1904); W. A. Noyes,
  ‹Ibid.›, 285; Nef, ‹J. Am. Chem. Soc.›, «30», 645 (1908). For the
  application of the electron theory to organic compounds, see Falk
  and Nelson, ‹School of Mines Quarterly›, «30», 179, and ‹J. Am.
  Chem. Soc.›, «32», 1637 (1910). (‹Cf.› also Chapter XV.)

  [147] ‹J. Phys. Chem.›, «6», 1 (1902), and other papers in the same
  Journal.

  [148] ‹Cf.› Patten, ‹ibid.›, «7», 168 (1903), and Falk and
  Waters, ‹Am. Chem. J.›, «31», 398 (1903). According to the latter
  investigators, the evolution of hydrogen is slow and weak.

  [149] Patten, ‹loc. cit.›

  [150] Students will not be capable of following the argument given
  in the succeeding passages and would better omit this part until
  Chapter XV has been studied.

  [151] Kablukoff, Z. ‹phys. Chem.›, «4», 430 (1889). See also
  Nernst, ‹Theoretical Chemistry›, p. 373.

  [152] In view of the low order of accuracy of the data, and of the
  approximate method of calculation, this result is only qualitative,
  but even with an error of 10^2 to 10^4 the argument in the text
  would hold.

  [153] For hydrogen under atmospheric pressure, the equilibrium
  ratio, [Zn^{2+}] / [H^{+}]^2, is, approximately, 10^{27}.

  [154] ‹Vide› Sackur, ‹Z. Elektrochem.›, «11», 387 (1905).
  Kahlenberg holds a different view; ‹ibid›.

  [155] The ‹negative› results obtained with aluminium and magnesium
  are possibly more interesting than the positive action observed
  with zinc, but their inactivity ‹may› be due to thin films of
  protective chloride or oxide or to a passive condition (‹vide›
  Smith's ‹Inorganic Chemistry›, pp. 723, 753; ‹College Chemistry›,
  p. 475).

  [156] The work of Ostwald, Arrhenius, Nernst and many others shows
  conclusively that the liberation of hydrogen by metals and the
  precipitation of metals by one another is a function of ‹ion›
  concentrations (Chapter XIV). ‹Vide› Nernst, ‹Theoretische Chemie›
  (1905), p. 245.

  [157] See above.

  [158] In a 0.1 molar solution of potassium cyanide, the potassium
  hydroxide formed by the decomposition of the cyanide by water is
  approximately 0.0013 molar and the concentration of hydrogen-ion
  is reduced to 10^{−11} (Chapter X), a value roughly of the same
  order as that calculated above as a possible concentration of
  hydrogen-ion in a benzene solution of hydrogen chloride. In
  spite of this small concentration of hydrogen-ion in the cyanide
  solution, the reactions in which it is involved are, as far
  as known, completed in a few moments. Only for much smaller
  concentrations of ions have any doubts as to their ‹direct action›
  been aroused; in Chapter XII this question, as raised by Haber,
  is discussed for concentrations of ions of the order of 10^{−23}.
  Haber considers that ionic concentrations of 10^{−14} can still
  account for very fast actions.

  [159] ‹Cf.› Abegg., ‹Theorie der Elektrolytischen Dissociation›
  (1903), 255; Lehfeldt, ‹Electro-chemistry› (1904), 87.

  [160] There is probably ‹minimal› ionization in all these cases,
  especially in the case of ammonia (NH_{3} ⇄ NH_{2}^{−} + H^{+}),
  but not enough to yield a sufficient supply of hydrogen-ion to show
  its common properties.

  [161] ‹Vide› Jorgensen, ‹J. prakt. Chem.›, «16», 349 (1877).

  [162] See Chapter XII in regard to the stability of (PtCl_{6}^{2−})
  as a complex ion.

  [163] Freshly prepared solutions must be used.

  [164] See Chapter XII as to the decomposition of the "complex ions."

  [165] K^{+} and CN^{−} are ‹colorless› ions. The yellow color of
  the ion moving to the positive electrode shows the presence of the
  iron in it—a fact that can be confirmed by testing the solution
  round the anode for ferricyanide by the method discussed further on
  in the text.

[p090]




 CHAPTER VI

 «CHEMICAL EQUILIBRIUM. THE LAW OF MASS ACTION»


The theory of ionization, as studied so far, gives us simple, rational
explanations of many of our qualitative reactions—explanations which
agree with phenomena taken from separate fields of investigation.
But, if our study of the theory ceased at the present stage without
further elaboration, we should fail to find in it a satisfactory
explanation of a number of other important facts of analysis—notably,
why certain reactions, the occurrence of which we might anticipate,
‹do not take place›. For instance, the addition of a soluble
carbonate to a barium chloride solution precipitates almost all the
barium as barium carbonate (‹exp.›); we have 2 Na^{+} + CO_{3}^{2−} +
Ba^{2+} + 2 Cl^{−} → BaCO_{3} ↓ + 2 Na^{+} + 2 Cl^{−}. But the
addition of carbonic acid to barium chloride solutions fails to
produce the slightest precipitate (‹exp.›), although carbonic acid
also gives rise to the carbonate-ion, CO_{3}^{2−}. In the same way
silver nitrate readily precipitates silver phosphate from sodium
phosphate solutions (‹exp.›), but not from a solution of phosphoric
acid (‹exp.›). Hydrogen sulphide precipitates zinc sulphide
from a zinc sulphate solution (‹exp.›), Zn^{2+} + SO_{4}^{2−} +
2 H^{+} + S^{2−} → ZnS ↓ + 2 H^{+} + SO_{4}^{2−}; but the addition of
hydrochloric acid effectually prevents the precipitation (‹exp.›),
although the hydrogen sulphide is still ionized, as is apparent from
the precipitation of copper sulphide when copper sulphate is added
to the mixture (‹exp.›). In the negative results, we have instances
of a very large number of cases which require closer study, and a
further development of the theory, if we wish to interpret them
satisfactorily. The line of development to be followed is indicated
perhaps most sharply by the following experiment.

 EXP. Some sodium tetraborate (borax) is dissolved in a little water
 and silver nitrate is added to a small part of the solution. A pure
 ‹white› precipitate (silver borate) results. Another portion of the
 borate solution is diluted with a ‹large quantity of water›, and
 then silver nitrate is added; quite a different result is obtained—a
 ‹brown› precipitate (silver oxide) is formed. [p091]

The change in the quantity of water brought about the difference
in result—the ‹quantitative› relations were altered thereby. In
order to follow intelligently this and the other actions referred
to, the study of reactions in solutions must be taken up from the
‹quantitative side›—the development heretofore has been essentially
qualitative in character. On several occasions we have found that all
electrolytes do not ionize equally well, and that the intensity of
their action, demonstrated, for instance, for potassium and ammonium
hydroxides, varies accordingly. We shall now have to study these
relations in greater detail.

For our purpose, the study of two of the fundamental quantitative
laws governing action in solution and of their application to
analytical phenomena, will be sufficient: these are, ‹the law of
chemical or homogeneous equilibrium›, in which the ‹law of mass
action› is included, and the law of ‹physical› or ‹heterogeneous
equilibrium›.

«The Law of Chemical Equilibrium.»—The law of chemical equilibrium
may be expressed, for a simple case, by saying that if two substances
‹A› and ‹B› interact at a constant temperature to give two compounds
‹C› and ‹D› and, vice versa, ‹C› and ‹D› interact with each other to
produce ‹A› and ‹B›, then equilibrium will be reached ‹when the ratio
of the product of the concentrations of› ‹A› ‹and of› ‹B› ‹to the
product of the concentrations of› ‹C› ‹and of› ‹D› ‹has a definite,
constant value›, which is a value characteristic of the equilibrium
between the compounds involved, at the given temperature. The action
may be expressed in the chemical equation

 ‹A› + ‹B› ⇄ ‹C› + ‹D›,

in which ‹A›, ‹B›, ‹C› and ‹D› represent four different substances
reacting in the molecular proportions indicated by their symbols,
which as usual represent molecular weights. And the condition for
equilibrium may be expressed in the mathematical equation

 [‹A›] × [‹B›] / ([‹C›] × [‹D›]) = ‹k›.

[‹A›], [‹B›], [‹C›] and [‹D›] are used to represent the
concentrations[166] of [p092] the four reacting substances and ‹k›
is some definite number, called the equilibrium constant.

The law was discovered by Guldberg and Waage in 1867, and, with
certain limiting conditions (see below) it has been fully established
by extensive experimental work.[167] The significance of the law
may be interpreted on the basis of the following considerations.
If we start with the two substances ‹A› and ‹B› alone and have
one mole of each in one liter (as gas or in solution) at a given
temperature, then, all the conditions being given,—the temperature,
the concentrations, and the nature of the substances,—the reaction
‹A› + ‹B› → ‹C› + ‹D›, leading to the formation of ‹C› and ‹D›,
‹will proceed with a perfectly definite velocity›. The molecules of
‹A› and of ‹B› move in all directions (kinetic theory of gases and
solutions), and molecules of ‹A› will collide with molecules of ‹B›
a definite number of times in unit time and will form a definite
number[168] of molecules of ‹C› and ‹D› per minute. The velocity of
chemical change of a given substance (‹chemical velocity›) is also
measured in terms of moles, and is represented by the number of moles
or the fraction of a mole changed per minute. If ‹v′›_{1} stands
for the velocity of the action between ‹A› and ‹B›, under the given
conditions, then

 ‹v′›_{1} = ‹k›_{1},

where ‹k›_{1} is some number. Now, if the concentration of one of
the components, ‹e.g.› ‹A›, should be doubled, then the chances
for collision and for action between molecules of ‹A› and ‹B› will
be twice as great as before and the velocity of the action will be
doubled. If only one-tenth of the concentration of ‹A› (one-tenth
mole) is used, the velocity will only be one-tenth as great as
originally, and, in general terms, if [‹A›] moles of ‹A› are used per
liter, the ‹velocity of the change will be proportional to› [‹A›],
‹and equal to› ‹k›_{1} × [‹A›]. If the concentration of the other
reacting component, ‹B›, is now doubled, the chances for action are
again doubled, and, in general, the velocity of the action will be
proportional also to the concentration [p093] [‹B›] of the second
reacting substance. For the velocity, ‹v›_{1} of the action for any
concentrations, [‹A›] and [‹B›], of ‹A› and ‹B› at any moment at a
given temperature, we have

 ‹v›_{1} = ‹k›_{1} × [‹A›] × [‹B›].

Hence, if by the symbols [‹A›] and [‹B›] the concentrations at any
given moment are represented, we may say that the velocity of the
formation of ‹C› and ‹D› at that moment[169] ‹is proportional to
the product of the concentrations of› ‹A› ‹and› ‹B›, ‹and to some
constant›, which is characteristic of the interaction of ‹A› and ‹B›.

The validity of this conclusion has been fully verified by
‹experiment›.[170] The case is an instance of the ‹law of mass
action, which states that in chemical changes the velocity
of the action is proportional at any moment to the molecular
concentrations›[171] ‹of the reacting components, and to a constant,
which is characteristic of the chemical nature of the reacting
components› (and of the temperature).

If we start with the reversed action

 ‹A› + ‹B› ← ‹C› + ‹D›,

the relation may be developed in the same way. Thus the two
substances ‹C› and ‹D› will react upon each other, at the given
temperature, with a velocity proportional to a constant, ‹k›_{2},
and, at any given moment, proportional also to their respective
concentrations at that moment:

 ‹v›_{2} = ‹k›_{2} × [‹C›] × [‹D›].

Equilibrium will be reached when the substances ‹A› and ‹B› are
formed at any moment from ‹C› and ‹D› just as rapidly as they are
used up to produce ‹C› and ‹D›, and ‹vice versa›. Such is the case,
[p094] when ‹the velocities of the two opposite reactions are equal
to each other›. For the condition of equilibrium, then, ‹v›_{1} must
be equal to ‹v›_{2} and therefore

 ‹k›_{1} × [‹A›] × [‹B›] = ‹k›_{2} × [‹C›] × [‹D›]

or

 [‹A›] × [‹B›] / ([‹C›] × [‹D›]) = ‹k›_{2} / ‹k›_{1} =
   ‹k›_{equilibrium}.

In this way the meaning of the fundamental law of chemical
equilibrium may be developed from the consideration of the velocities
of the reversible actions, such as are involved in all conditions
of equilibrium, and the ‹equilibrium constant represents the ratio
of the velocity constants of the two opposite reactions›. This
conclusion has been fully verified by experiment, the equilibrium
constant being, as a matter of fact, found equal to the ratio of the
velocity constants.[172]

The relations, so far considered, have been those of the simplest
type of reversible reaction. We may now discuss the modifications
required for other types of reaction by the law of equilibrium.

When two molecules of any reacting component take part in a
reaction—for instance, in ‹A› + 2 ‹B› ⇄ ‹C› + ‹D›—‹the concentration
of this component is raised to the second power in the mathematical
expression of the law of equilibrium;› when three molecules of a
component take part, its concentration is raised to the third power,
etc.

For instance, hydrogen iodide is decomposed, reversibly, into
hydrogen and iodine, according to 2 HI ⇄ H_{2} + I_{2}. A condition
of equilibrium is reached, at a given temperature when

 [H_{2}] × [I_{2}] / [HI]^2 = K.

At 440°, the results given in the following table were obtained by
Bodenstein. The concentrations are expressed in moles per liter.[173]
The constant is calcuated according to the equation just given.
Analytical errors affect the value of the constant most in the first
and last experiments, as a result of the very small concentrations of
one component, I_{2} or H_{2}.

[p095]

  [H_{2}]    [I_{2}]     [HI]       K
  0.0268     0.000190   0.0177   (0.016)
  0.00986    0.00203    0.0328    0.019
  0.00308    0.00783    0.0337    0.021
  0.00175    0.0114     0.0315    0.020
  0.000653   0.0204     0.0236    0.024
  0.000265   0.0242     0.0202   (0.016)

The mechanical significance of the raised powers of the
concentrations of components, two or more molecules of which take
part in a reaction as indicated, will be discussed further on, in
connection with a case of equilibrium between an electrolyte and its
ions (Chapter VI, p. 102).

 «Limitations to the Law of Chemical Equilibrium.»—Quite in agreement
 with the interpretation of the law of chemical equilibrium from
 the view-point of the kinetic theory, it is found that, in its
 applications, one must take into consideration the possibility,
 that molecular attractions (p. 27) or other important forces
 of attraction or repulsion (‹e.g.› electrical) of a more than
 ‹negligible› magnitude exist between the molecules of the
 components in a reversible reaction. If such forces are involved,
 suitable allowance must be made for them, so that the mathematical
 formulation of the law may express the facts of observation.[174]
 For these reasons, the law, in its simplest terms, which, alone,
 can be considered here, holds for the relations ‹obtaining in
 dilute systems›[175] (dilute solutions or gases that are not too
 strongly compressed), and in ‹systems involving only nonelectrolytes
 or only weak ionogens›, more generally than for the relations in
 concentrated solutions (or strongly compressed gases) or in systems,
 in which electrically charged particles (ions) are present in large
 proportions (see below, p. 108).

«The Factors of the Law of Chemical Equilibrium.»—Inspection of the
mathematical expression of the law of chemical equilibrium (p. 91)
shows that there are two significant kinds of factors in it: first,
the equilibrium ‹constant›, whose value depends only on the nature
of the substances involved and on the temperature.[176] In [p096]
the second place, we have concentration factors, which, to a large
extent,[177] may be varied at will.

The following experiments may be used to illustrate the significance
of the two classes of factors: Phosphorus pentabromide is partially
decomposed by heat into the tribromide and bromine (a case of gaseous
dissociation):

 PBr_{5} ⇄ PBr_{3} + Br_{2}.

Phosphorus trichlordibromide is decomposed more or less, in a similar
fashion, into the components phosphorus trichloride and bromine,
according to the equation

 PCl_{3}Br_{2} ⇄ PCl_{3} + Br_{2}.

For the condition of equilibrium in the two cases we have

 [PBr_{3}] × [Br_{2}]′ / [PBr_{5}] = ‹k›_{1} and
   [PCl_{3}] × [Br_{2}]″ / [PCl_{3}Br_{2}] = ‹k›_{2}.

 EXP. Two tubes containing equivalent quantities of the two bromides
 are placed side by side in warm water.[178] The tube containing the
 trichlordibromide is found to be much more intensely colored by free
 bromine than that containing the pentabromide.

The intensity of the color of the bromine vapor shows that the
concentration of bromine, [Br_{2}]″, in the PCl_{3}Br_{2} tube,
is ‹greater than the corresponding concentration›, [Br_{2}]′, in
the PBr_{5} tube. As a molecule of pentahalide PX_{5} dissociates
into one molecule of PX_{3} and one molecule of X_{2}, [PCl_{3}]
equals [Br_{2}]″ and is ‹greater› than [PBr_{3}], which is equal
to [Br_{2}]′. Further, more of the pentabromide than of the
trichlordibromide must be left undecomposed, ‹i.e.› [PCl_{3}Br_{2}]
is ‹smaller› than PBr_{5}. Since the factors in the ‹numerator›
of the second equation are ‹both larger›, and the factor in the
‹denominator smaller, than the corresponding factors› in the first
equation, ‹k›_{2} ‹must be greater than› ‹k›_{1}. These ‹constants›
are thus seen to be a ‹measure› of the ‹chemical stability› of these
pentahalides. It is evident, too, that in reactions which depend on
the presence of free bromine, such as the bromination of many organic
compounds, the trichlordibromide should be more ‹effective› than the
equivalent quantity of the pentabromide.

[p097]

In the second place, if we were to introduce into either tube, for
instance into the tube containing the phosphorus trichlordibromide,
an ‹excess of one of the dissociation products›, say an excess of
phosphorus trichloride, then the condition of equilibrium would
necessarily be disturbed:

 ‹y› [PCl_{3}] × [Br_{2}]′ / [PCl_{3}Br_{2}] > ‹k›_{2},

in which the bracketed symbols represent the concentrations of the
first experiment. The velocities of the two opposite reactions would
be no longer equal, the combination of trichloride with bromine would
be accelerated by the increased concentration of the former. Here,
equilibrium would only be reëstablished when the trichloride and
bromine had combined to a sufficient extent to make

 (‹y› [PCl_{3}] − ‹x›) × ([Br_{2}]′ − ‹x›) / ([PCl_{3}Br_{2}] + ‹x›) =
    ‹k›_{2},

in which x represents the number of moles of additional phosphorus
trichlordibromide formed in unit volume by the combination of bromine
with phosphorus trichloride. The ‹net result› is seen to be that an
‹increase in the concentration of the one dissociation product eo
ipso reduces the concentration of the other dissociation product›.

 EXP. A third tube charged with the same quantity of phosphorus
 trichlordibromide as the tube mentioned above, and with an added
 excess of phosphorus trichloride, is placed in the warm water next
 to the tube containing the trichlordibromide. Its color is much
 paler than that of the latter, owing to the suppression of free
 bromine.[179]

The concentration of the free bromine, ([Br_{2}]′ − ‹x›), under
the new conditions of equilibrium, is smaller than the original
concentration [Br_{2}]′—a result confirmed by experience. ‹It is
in our power, therefore, arbitrarily to change the concentration
of a reacting component›, in a case of equilibrium, ‹and thus to
affect the reactivity of the system;› for instance, for brominating
purposes, the new system would be less effective than the original
one, and it might be of especial service where bromination is to be
avoided.

In the cases studied, are found the two fundamentally important
relations expressed by the law of equilibrium: ‹the equilibrium
constant is a measure of the stability of a certain system› and, in
a way, of its ‹reactivity› at a given temperature; and the [p098]
‹concentration factors are variables›, which we may change to a
very considerable extent, so as, to a certain degree, to subject the
system to our own purposes. We shall repeatedly have occasion to
refer to these two fundamental relations and we shall use them again
and again in our analytical work.

«Chemical Equilibrium of Electrolytes.»—Ionization of an
electrolyte is a reversible chemical action and its relation to
the law of chemical equilibrium will now be discussed. For acetic
acid, ionization into hydrogen and acetate ions occurs thus:
CH_{3}CO_{2}H ⇄ CH_{3}CO_{2}^{−} + H^{+}, and, in accordance with the
law of equilibrium, at a given temperature, the following relation
would hold:

 [H^{+}] × [CH_{3}CO_{2}^{−}] / [CH_{3}CO_{2}H] = K_{ionization}.

If the total concentration of the acid is known, the concentrations
of the ions and of the non-ionized acid may be calculated from the
conductivity of the solution. For instance, if 60 grams of acetic
acid (1 mole) is dissolved in sufficient water to make 10 liters,
the equivalent conductivity of the solution (p. 50) is found to be
4.67 reciprocal ohms at 18°. The maximum conductivity of one mole
of acetic acid, at infinite dilution, when all the acid would be
ionized, would be 347. Therefore, in the acid under examination,
4.67 / 347, or 1.34 per cent, is ionized (p. 50). Since the total
concentration of the acid is 0.1 mole ‹per liter› and 1.34 per
cent is ionized, the concentration of the hydrogen-ion, [H^{+}],
is 0.1 × 0.0134, and that of the acetate-ion, [CH_{3}CO_{2}^{−}],
is the same. The concentration of the non-ionized acetic acid,
[CH_{3}CO_{2}H], is 0.1 × 0.9866. If these values are inserted in the
equation for the condition of equilibrium, we have

 (0.1 × 0.0134)^2 / (0.1 × 0.9866) = K_{ionization} = 18.2E−6.

From this experimental result, the equilibrium constant, which is
called the ‹ionization constant› of the acid, is found to have the
value 18.2E−6. If the ratio [H^{+}] × [CH_{3}CO_{2}^{−}] /
[CH_{3}CO_{2}H] really is a constant, the same value, within
the limits of experimental errors, should be obtained from
acetic acid in other concentrations. Now, if the above solution
is diluted to ten times its volume, the concentration of the
acid is made 0.01 mole ‹per liter›, the conductivity [p099] is
found to have increased to 14.5 reciprocal ohms, and the percentage
of ionized acid is then 14.5 / 347, or 4.17. Here, [H^{+}]
and [CH_{3}CO_{2}^{−}] = 0.01 × 0.0417 and [CH_{3}CO_{2}H] =
0.01 × 0.9583. Inserting these values in our general equation
and calculating the result, we obtain 18.1E−6 as the value
of the constant. In the following table[180] are given the
molar conductivities, Λ (column 2), of acetic acid of varying
concentrations, ‹m› (column 1). The degrees of ionization, α, and
the ionization constant, calculated according to the equilibrium
equation, are given in columns 3 and 4.

  IONIZATION OF ACETIC ACID. Λ_{∞} = 347.

   m.      Λ.     100 α.     K.
  0.1      4.67   1.34    18.2E−6
  0.08    5.22    1.50    18.3E−6
  0.03    8.50    2.45    18.5E−6
  0.01   14.50    4.17    18.1E−6

It is evident, that a constant value is found for the ratio
[H^{+}] × [CH_{3}CO_{2}^{−}] / [CH_{3}CO_{2}H] and that the
ionization of acetic acid, in these dilute solutions, obeys the law
of chemical equilibrium.[181] The equilibrium constant expresses in
definite, quantitative terms the tendency of acetic acid to ionize in
dilute solution. Examination of other acids shows that there is an
enormous range in the values found for their respective ionization
constants. The constants are the best ‹measure› of the ‹strength›
of the ‹acids› as acids. Obviously, the more readily acids in
equivalent solutions ionize, the greater will be the concentration
of the hydrogen-ion to which the characteristic acid properties are
due, and the more pronounced (stronger) will be the exhibition of
these properties. From the ionization constants one may calculate,
for instance, the proportion in which two competing acids will
neutralize a base, when the latter is used in quantity insufficient
to neutralize both acids. [p100]

Inspection of the equation for acetic acid, which is the typical
equilibrium equation for all ‹monobasic› acids, shows that the
greater the degrees of ionization of acids are in equivalent
solutions, ‹i.e.› the greater the concentrations of the hydrogen-ion
which their ionization produces in equivalent solutions, the larger
will be the values of their ionization constants. The acids with the
‹larger› constants are, then, the ‹stronger› acids.

«The Ionization of Various Acids.»—The table given on page 104
shows the ionization constants for a number of acids of interest
in analysis. Before proceeding to give the table, we must consider
further two important points.

In the first place, for the strongest acids, such as hydrochloric,
nitric, hydrobromic and similar acids, chemists have been unable to
determine ionization constants on the basis of the law of chemical
equilibrium. Strong acids, strong bases and most salts (see pp.
106–8, below), the three classes comprising ‹all› the ‹very readily
ionizable electrolytes, do not give constants› when the values of
the equilibrium ratio,[182] [Cation] × [Anion] / [Molecules], are
calculated for different concentrations, and ‹they therefore do not
ionize simply in accordance with the law of chemical equilibrium›.
The reasons for this abnormal behavior will be discussed presently
(p. 108), when other necessary facts are before us. In order to have,
at least, a rough basis for comparison of these strong acids with
the weak ones, which do obey the law of chemical equilibrium, the
table will give for the strong acids ‹the value of the above ratio as
calculated from their ionization in 0.1 molar solutions›.

«The Ionization of Polybasic Acids.»—In the second place, the
meaning of the ‹constants for polybasic acids›, such as sulphuric,
phosphoric, carbonic and similar acids, requires explanation. The
relations for carbonic acid will be first developed, as representing
a typical case. Carbonic acid, in ionizing, forms the carbonate-ion
CO_{3}^{2−}, and the hydrogen-ion, as expressed in the [p101]
equation[183] H_{2}CO_{3} ⇄ 2 H^{+} + CO_{3}^{2−}. According to the
law of chemical equilibrium for the case where a product (here the
hydrogen-ion) appears twice on one side of the reaction equation, we
have, for the condition of equilibrium (p. 94)

 [H^{+}]^2 × [CO_{3}^{2−}] / [H_{2}CO_{3}] = K.                  (1)

We may ask, however, whether both the hydrogen atoms of carbonic
acid show the ‹same tendency to ionize›, or, since there is
a vast difference in the ease of ionization of different
acids, whether there is not also a difference in the ease of
ionization of the different hydrogen atoms in a polybasic acid.
As a matter of experiment, we find that a molecule of carbonic
acid does ionize, first, and more readily, into one hydrogen
ion and an ‹acid carbonate› ion HCO_{3}^{−}, according to
H_{2}CO_{3} ⇄ H^{+} + HCO_{3}^{−}.

For this reversible reaction we have[184]

 [H^{+}] × [HCO_{3}^{−}] / [H_{2}CO_{3}] = K_{1}.                (2)

The value of this constant,[185] called the ‹primary ionization
constant› of carbonic acid, is 0.3E−6.

The acid carbonate-ion HCO_{3}^{−}, in turn, is ionized to a certain
extent, producing another hydrogen ion and the carbonate-ion,
CO_{3}^{2−}. We have HCO_{3}^{−} ⇄ H^{+} + CO_{3}^{2−}, and

 [H^{+}] × [CO_{3}^{2−}] / [HCO_{3}^{−}] = K_{2}.                (3)

The value of this constant[186], called the ‹constant› of the [p102]
‹secondary ionization› of carbonic acid, is 0.07E−9, which has about
one four-thousandth of the value of the constant for the primary
ionization.

If we combine equations (2) and (3) we have

 [H^{+}] × [HCO_{3}^{−}] × [H^{+}] × [CO_{3}^{2−}] /
   ([H_{2}CO_{3}] × [HCO_{3}^{−}]) = K_{1} × K_{2}                 (4)

or

 [H^{+}]^2 × [CO_{3}^{2−}] / [H_{2}CO_{3}] = K.

This is equation (1), derived originally by the application of
the law of mass action to the relation between the carbonate-ion,
CO_{3}^{2−}, the hydrogen-ion, and carbonic acid, H_{2}CO_{3}.

This relation, and, in particular, the ‹significant squaring› of
the concentration of the hydrogen-ion, an ion which appears ‹twice›
in the equation for the formation of carbonic acid from carbonate
and hydrogen ions, (2 H^{+} + CO_{3}^{2−} ⇄ H_{2}CO_{3}), may now
be interpreted mechanically (p. 92) as follows: For the formation
of carbonic acid from a carbonate ion and ‹two› hydrogen ions, a
carbonate ion must collide and combine first with one hydrogen ion,
and the velocity for the formation of this intermediate product,
HCO_{3}^{−}, will be proportional to the (total) concentration of
the hydrogen ions; the product, HCO_{3}^{−}, to form H_{2}CO_{3},
must collide and combine with a hydrogen ion once more, and this
combination will proceed with a velocity ‹again proportional› to the
(total) concentration of the hydrogen ions. So the velocity for the
transformation of CO_{3}^{2−} into H_{2}CO_{3} will be proportional
‹twice over› to the (total) concentration of the hydrogen ions—as
well as, in the usual fashion, to the concentration of the carbonate
ions present at any moment.

‹It is a general principle that the primary ionization of polyvalent
acids occurs more readily than the secondary›, and this in turn more
readily than the tertiary (if a third ionizable hydrogen atom is
present in the acid).

 In the case of phosphoric acid, for instance, the primary
 ionization into the hydrogen-ion and the dihydrogen-phosphate-ion,
 H_{2}PO_{4}^{−}, takes place so readily that phosphoric acid reacts
 strongly acid[187] to methyl orange,[188] the [p103] concentration
 of hydrogen-ion being sufficiently great to affect this indicator
 (see EXP. below).

 When phosphoric acid is neutralized by one equivalent of a base, say
 of sodium hydroxide, the salt formed, sodium dihydrogen-phosphate,
 NaH_{2}PO_{4}, yields sodium-ion and dihydrogen-phosphate-ion,
 H_{2}PO_{4}^{−}. The latter is ionized ‹somewhat› into H^{+} and
 the bivalent hydrogen-phosphate-ion, HPO_{4}^{2−}. The ionization
 of the ion H_{2}PO_{4}^{−} is now the chief source of supply of
 hydrogen-ion (the further ionization of HPO_{4}^{2−} is practically
 negligible here) and it is ionized so little that the solution
 of NaH_{2}PO_{4} no longer changes the color of methyl orange
 (see EXP. below). The solution is, however, acid to the indicator
 phenolphthaleïn, which is much more sensitive to the hydrogen-ion
 and will show the presence of much smaller concentrations of it than
 will methyl orange. The addition of a second equivalent of sodium
 hydroxide to the solution converts NaH_{2}PO_{4} into Na_{2}HPO_{4}.
 This salt gives sodium-ion and the hydrogen-phosphate-ion
 HPO_{4}^{2−}, which, in turn, is ionized only very slightly,
 producing phosphate-ion PO_{4}^{3−}, and again hydrogen-ion.
 The ionization of HPO_{4}^{2−} is so slight, however, and the
 concentration of the hydrogen-ion, therefore, so minute, that
 the solution does not react acid even to the sensitive indicator
 phenolphthaleïn.

 EXP. Methyl orange (very little) is added to 10 c.c. of a 0.1
 molar solution of phosphoric acid and 10 c.c. of 0.1 molar sodium
 hydroxide solution is added to the mixture; the color will be found
 to change from the acid to the neutral tint just as the last drop or
 two of the alkali are added. Phenolphthaleïn is then added to the
 mixture and 10 c.c. more of the 0.1 molar sodium hydroxide solution
 are required to change the color of the mixture to a pronounced pink
 (alkaline) tint.

 Even sulphuric acid, although its two hydrogen atoms are ionized
 very easily, making sulphuric acid a strong acid, shows a difference
 in the ease of ionization of the two hydrogen atoms. Since
 ionization, in general, is favored by dilution, we find that in
 the case of such a strong acid the difference is most marked in
 more concentrated solutions, the smaller amount of water starting
 the ionization in the more favored direction and producing first,
 chiefly, hydrogen-sulphate ions, HSO_{4}^{−}. When the solution
 is diluted, the hydrogen-sulphate ions are to a very considerable
 extent dissociated into sulphate ions and hydrogen ions. The
 described change in ionization can be roughly followed with the aid
 of an insoluble sulphate like barium sulphate. Barium sulphate,
 while very insoluble in water, dissolves in rather strong sulphuric
 acid to form the acid sulphate, Ba(HSO_{4})_{2}, the SO_{4}^{2−}
 ion of the sulphate being more or less suppressed by uniting with
 hydrogen-ion. We have the action

 BaSO_{4} ⇄ Ba^{2+} + SO_{4}^{2−} and

 Ba^{2+} + SO_{4}^{2−} + H^{+} + HSO_{4}^{−} ⇄ Ba^{2+} + 2 HSO_{4}^{−}.

 If the solution of the acid sulphate is poured into a large volume
 of water, barium sulphate is immediately reprecipitated, the
 hydrogen-sulphate-ion being dissociated, in the dilute solution,
 into hydrogen-ion and sulphate-ion, SO_{4}^{2−}, whose barium salt
 is so difficultly soluble:

 Ba^{2+} + 2 HSO_{4}^{−} → Ba^{2+} + 2 H^{+} + 2 SO_{4}^{2−} →
   BaSO_{4} ↓ + 2 H^{+} + SO_{4}^{2−}.

 [p104]

 EXP. Finely divided barium sulphate is warmed for a moment with a
 few cubic centimeters of concentrated sulphuric acid in a test tube,
 the mixture is allowed to settle, and some of the clear acid is
 carefully decanted into a large beaker full of water.

 It may be added, that while the primary ionization of sulphuric
 acid does not yield an equilibrium constant for the ratio
 [H^{+}] × [HSO_{4}] / [H_{2}SO_{4}], even such a strong acid as
 is sulphuric acid is found to give a fairly good constant[189]
 for [H^{+}] × [SO_{4}^{2−}] / [HSO_{4}^{−}]. The value of this
 constant[189] is 0.03.

  «The Ionization Constants[A] of Acids»

   Acid.              Equilibrium Ratio.                          K.
 Hydrochloric     [H^{+}]×[Cl^{−}]/[HCl]                         (1)
 Hydrobromic      [H^{+}]×[Br^{−}]/[HBr]                         (1)
 Hydroiodic       [H^{+}]×[I^{−}]/[HI]                           (1)
 Nitric           [H^{+}]×[NO_{3}^{−}]/[HNO_{3}]                 (1)
 Chromic[B]       [H^{+}]×[HCrO_{4}^{−}]/[H_{2}CrO_{4}]          (1)
                  [H^{+}]×[CrO_{4}^{2−}]/[HCrO_{4}^{−}]         0.6E−6
 Sulphuric[C][D]  [H^{+}]×[HSO_{4}^{−}]/[H_{2}SO_{4}]            (1)
                  [H^{+}]×[SO_{4}^{2−}]/[HSO_{4}^{−}]           0.3E−1
 Oxalic[E]        [H^{+}]×[C_{2}O_{4}^{−}]/[H_{2}C_{2}O_{4}]    3.8E−2
                  [H^{+}]×[C_{2}O_{4}^{2−}]/[HC_{2}O_{4}^{−}]   0.5E−4
 Phosphoric[F]    [H^{+}]×[H_{2}PO_{4}^{−}]/[H_{3}PO_{4}]       0.1E−1
                  [H^{+}]×[HPO_{4}^{2−}]/[H_{2}PO_{4}^{−}]      0.2E−6
                  [H^{+}]×[PO_{4}^{3−}]/[HPO_{4}^{2−}]          0.4E−12
 Arsenic[D]       [H^{+}]×[H_{2}AsO_{4}^{−}]/[H_{3}AsO_{4}]     0.5E−2
 Nitrous[B]       [H^{+}]×[NO_{2}^{−}]/[HNO_{2}]                0.5E−3
 Acetic[G]        [H^{+}]×[CH_{3}CO_{2}^{−}]/[CH_{3}CO_{2}H]    1.8E−5
 Carbonic[H][I]   [H^{+}]×[HCO_{3}^{−}]/([H_{2}CO_{3}]
                                                 + [CO_{2}])    0.3E−6
                  [H^{+}]×[CO_{3}^{2−}]/[HCO_{3}^{−}]           0.7E−10
 H_{2}S[J][K]     [H^{+}]×[SH^{−}]/[H_{2}S]                     0.9E−7
                  [H^{+}]×[S^{2−}]/[SH^{−}]                     0.1E−14
 Boric[B]         [H^{+}]×[H_{2}BO_{3}^{−}]/[H_{3}BO_{3}]       0.7E−9
 Hydrocyanic      [H^{+}]×[CN^{−}]/[HCN]                        0.7E−9
 Arsenious        [H^{+}]×[H_{2}AsO_{3}^{−}]/[H_{3}AsO_{3}]     0.6E−9
 Water[L][C]      [H^{+}]×[HO^{−}]/[H_{2}O] at 25°              0.2E−15
                                            at 100°             0.9E−14
                  [H^{+}]×[HO^{−}] at 25°                       1.2E−14
                                   at 100°                      0.5E−11

  TABLE NOTES:

  A. As explained on p. 100, the bracketed values given for
  the strong acids ‹are not constants›, but express the values
  of the ratios [H^{+}] × [Anion] / [Acid] for 0.1 ‹molar
  solutions›.

  B. See references, Noyes, ‹ibid.›, «32», 860 (1910).

  C. Noyes and Eastman, ‹Carnegie Institution Publications›,
  «63», 274 (1907).

  D. Luther, ‹Z. Elektroch›, «13», 296 (1907).

  E. Chandler (McCoy), ‹J. Am. Chem. Soc.›, «30», 713 (1908).

  F. Abbot and Bray, ‹ibid.›, «31», 760 (1909).

  G. See above, p. 99.

  H. Walker, ‹J. Chem. Soc.›, (London), «77», 5 (1900).

  I. McCoy, ‹Am. Chem. J.›, «29», 455 (1903); Stieglitz,
  ‹Carnegie Institution Publications›, «107», 243 (1909).

  J. Auerbach, ‹Z. phys. Chem.›, «49», 220 (1904).

  K. Knox, in Abegg's laboratory, ‹Trans. Faraday Soc.›, «4», 43
  (1908).

  L. ‹Vide› p. 66.

[p105]

The difference in the tendencies of acids to ionize, as expressed in
the table, may be recognized in equivalent solutions by any of the
properties dependent on the ionization, such as the conductivity, the
chemical activity, the osmotic pressure and allied effects, and so
forth. If the conductivities of equal volumes of equivalent (‹e.g.›
normal) solutions of hydrochloric, phosphoric and acetic acids
are compared (‹exp.›)[190], it is readily seen that hydrochloric
acid is the best conductor, phosphoric acid a much poorer one, and
acetic acid an exceedingly poor one (the conductivity of normal
acetic acid is about 1 / 200 that of normal hydrochloric acid, and
the conductivity of normal phosphoric acid is about 1 / 14 that of
normal hydrochloric acid). Since the conductivity is approximately
proportional to the concentration of the hydrogen-ion[191] in each of
the solutions, it is evident that the hydrochloric acid is ionized
to a considerably greater extent than either of the other acids—than
acetic acid, in particular. Similarly, if a drop (0.05 c.c.) of
molar hydrochloric acid and a drop of molar acetic acid are added to
equal volumes (50 c.c.) of a very dilute solution of methyl orange
(‹exp.›), the color will be changed decidedly by the hydrochloric
acid to a bright pink, but by the acetic acid only to an orange hue.
Again, if a precipitate of barium chromate or calcium oxalate is
treated with some strong acid, hydrochloric or nitric, for instance,
it dissolves readily, while a considerable excess of acetic acid
(‹exp.›) only dissolves traces of either precipitate.[192] In this
way, the chemical behavior of these acids differs in degree, as a
result of the different tendencies to ionize, which are expressed in
the constants of the table. Advantage is taken, in analysis, of such
differences. Acetic acid, for instance, is used when only a slight
degree of acidity is desired—as in recognizing barium-ion by its
chromate, or oxalic acid by means of its calcium salt. Hydrochloric
or nitric acid is used when decided acidity is required—as in the
separation of groups by hydrogen sulphide (Chap. XI).

«The Ionization of Bases.»—The same relations hold for bases as for
acids: the weaker bases give ionization constants as [p106] do
the weaker acids; the strong bases, again, as was mentioned above,
do not give constants. The values for strong bases, stated in the
following table, are bracketed, and refer to the ionization in 0.1
molar solutions of the bases. Polyvalent bases, like polybasic acids,
ionize in stages, and the primary ionization is usually stronger
than the secondary ionization, and so forth. For instance, a study
of ferric chloride solution shows that the third hydroxide group
of ferric hydroxide, Fe(OH)_{3}, must have the smallest ionization
constant.[193]

  «The Ionization Constants[A] of Bases»

       Base.                         Ratio.                        K.
 Potassium hydroxide        [K^{+}]×[HO^{−}]/[KOH]                (1)
 Sodium hydroxide           [Na^{+}]×[HO^{−}]/[NaOH]              (1)
 Barium hydroxide           [Ba^{2+}]×[HO^{−}]^2/[Ba(OH)_{2}]   (0.03)
 Strontium hydroxide        [Sr^{2+}]×[HO^{−}]^2/[Sr(OH)_{2}]   (0.03)
 Calcium hydroxide[B]       [Ca^{2+}]×[HO^{−}]^2/[Ca(OH)_{2}]   (0.03)
 Ammonium hydroxide[C][D]   [NH_{4}^{+}]×[HO^{−}]/
                                        ([NH_{4}OH]+[NH_{3}])    1.8E−5
 Hydrazine[E]               [N_{2}H_{5}^{+}]×[HO^{−}]/
                                ([N_{2}H_{5}OH]+[N_{2}H_{4}])    0.3E−5
 Aniline[F]                 [C_{6}H_{5}NH_{3}^{+}]×[HO^{−}]/
                                       ([C_{6}H_{5}NH_{3}OH]+
                                          [C_{6}H_{5}NH_{2}])    0.5E−9
 Water                      [H^{+}]×[HO^{−}]/[H_{2}O] at 25°     0.2E−15
                                                      at 100°    0.9E−14
                            [H^{+}]×[HO^{−}] at 25°              1.2E−14
                                             at 100°             0.5E−11

  TABLE NOTES:

  A. As explained above, the bracketed values under K for strong
  bases are not constants, but express the values of the ratios
  for 0.1 molar solutions only. (For the alkaline earths 0.05
  molar solutions are referred to.)

  B. Estimated value.

  C. ‹Vide› page 160.

  D. Corrected value, from Bredig's data, ‹Z. phys. Chem.›,
  «13», 322 (1894). A. A. Noyes, ‹Carnegie Institution,
  Publication› No. 63, p. 178, finds the value 17.3E−6 for 18°.

  E. Uncorrected value, Bredig, ‹ibid.›

  F. Bredig, ‹ibid.›; Stieglitz and Derby, ‹Am. Chem. J.›, «31»,
  457 (1904).

While the constants of a large number of organic bases[194] have
been determined few constants of inorganic bases are as yet known.
The fact that the majority of ‹inorganic bases› are polyvalent and
difficultly soluble has made their examination in this respect more
difficult. From the study of the decomposition of salts by water (see
Chapter X), the trivalent bases, such as [p107] ferric hydroxide
and aluminium hydroxide, are found to be much weaker than bivalent
bases like cadmium, zinc and lead hydroxides,[195] but the data
are not sufficient for the calculation of any constants, or for
distinguishing between the ionization of the first, second and third
hydroxide groups.

The difference in ionization and in chemical activity between a
strong base, like sodium or potassium hydroxide, and a weak base,
like ammonium hydroxide, has already been discussed and illustrated
(see p. 77). In analysis, advantage is frequently taken of these
relations.[196]

«The Ionization of Salts.»—While we read and hear a good deal about
strong and weak acids, and strong and weak bases, the expression
"strong" or "weak" salt is never heard; as a matter of fact, all
salts, with very few exceptions, ionize exceedingly readily—about
as readily as the strongest acids and bases. There are minor
differences, but none of great moment—none of the kind indicated
by the wide range of constants for the acids and bases. There are
only a few important exceptions to this general rule—the most
important ones, among the common salts, being mercuric chloride
and mercuric cyanide: their exceptional behavior in regard to
ionization, as indicated by their conductivities (see below), is
found side by side with an exceptional chemical behavior, exactly
as the theory of ionization would lead us to anticipate, and it
renders necessary certain precautions, particularly in analytical
work, which will be discussed later (Chap. VI). Ordinary salts are
all ionized readily: for instance, whereas acetic acid in molar
solution is ionized only to the extent of 0.37 per cent, its salts
are highly ionized, the degree of ionization of sodium acetate, for
example, being 52.8% in molar solution. As in the case of the strong
acids and bases, salts of the type MeX, which ionize according to
the equation MeX ⇄ Me^{+} + X^{−} and which, according to the law
of chemical equilibrium, might be ‹expected› to give a constant
ratio [Me^{+}][X^{−}] / [MeX], do ‹not› give a ‹constant ratio›.
That is, when the values obtained for the concentrations of the
ions and of the nondissociated molecules, in solutions of various
[p108] strengths, are substituted in this formula, different values
are obtained.[197] For potassium chloride, we have the following
relations:

      Molar                        Per cent   Ratio.
  Concentration.   Conductivity.   Ionized.
      0.               131.2        100        —
      0.001            127.6        97.3      0.035
      0.01             122.5        93.4      0.130
      0.05             115.9        88.4      0.335
      0.10             111.9        85.1      0.485
      0.20             107.7        82.1      0.754
      0.50             102.3        77.9      1.38
      1.00              98.2        74.9      2.23

«The Ionization of Strong Electrolytes and the Law of Chemical
Equilibrium.»—The fact that the ionization of good electrolytes
does not seem to conform to the law of chemical equilibrium is an
exceedingly important one—it is, perhaps, the most important problem
demanding rigorous investigation, which is before chemists at the
present time. It has been used as an argument against the whole
theory of ionization, and is the most important objection that has
been urged against it. But, to the impartial observer, this single
discrepancy, between observation and what we might have anticipated,
will only prove a stronger stimulus to keener investigation and
to more rigorous analysis of relations, since the latter are more
complex than was at first expected. Without considering the mass
of evidence in favor of the theory, found in other fields of
chemistry and in physics, a part of which has been given above, we
must remember that this fundamental law of chemical equilibrium has
already decided unequivocally in favor of the theory in hundreds of
cases of the ionization of weak acids and weak bases[198] and that
these are the cases where the conditions are most simple.[199] [p109]

 It would lead too far from our subject to enter into a full
 discussion of this important question. It will be sufficient here
 to indicate two directions of inquiry, which promise to lead to
 an explanation of the apparent contradiction between the demands
 of the law of chemical equilibrium and the ionization of strong
 electrolytes.

 In the first place, the law of chemical equilibrium is based
 thermodynamically, ‹i.e.› from the point of view of the ultimate
 energy relations involved, on the assumption that none but
 negligible forces of attraction or repulsion exist between the
 molecules, whose concentrations are factors in the equilibrium
 equations (‹cf.› p. 95).[200] Now, in solutions of electrolytes
 this condition is not strictly fulfilled under any circumstances;
 the attractions between ions of opposite charge and the repulsions
 of ions of like charge, as well as the effect of charged particles
 on neutral molecules, come into play. For strong electrolytes,
 where the proportion of charged particles is always a large one,
 the deviations from the simpler conditions to which alone the
 law is really applicable must be very much greater than for weak
 electrolytes. It is, therefore, probable that these electrical
 forces[201] are the source of the deviation of the ionization of
 strong electrolytes from the law of chemical equilibrium: although
 ionization is a reversible reaction, forces come into play which
 make the ‹simple law inapplicable›, and it is altogether likely,
 therefore, that we shall find, when all the factors have been
 investigated, that strong electrolytes should not and cannot obey
 ‹this law alone›.[202] In confirmation of this conclusion, recent
 careful calculations[203] have shown that entirely analogous
 deviations from the equilibrium law become perceptible in rather
 ‹concentrated› solutions of weak electrolytes, such as acetic acid,
 in which there is an accumulation of charged particles, more nearly
 akin to that present in ‹dilute› solutions of strong electrolytes.
 So it appears more and more certain that the deviations are a result
 of the presence of electrically charged components in the solutions,
 the amount of deviation depending on their concentration.

 «The "Salt Effect".»—In the second place,[204] it seems possible
 that the presence of strong electrolytes in a solution may modify
 the ‹ionizing power of the solvent› in such a way as to increase
 it, and to increase it the more, the more concentrated the ions are
 in the solution.[205] The ionizing power of solvents, as has been
 explained, is intimately connected with their dielectric properties.
 [p110]

 Now, solid ‹salts› have higher dielectric constants than has[206]
 solid water, and the dielectric constant of a compound is usually
 much higher in the liquid than in the solid form.[207] It is
 possible, therefore, that the presence of salts in the solution
 increases the dielectric or, at any rate, the ionizing power of
 the solvent and there are many facts which would be explained by
 such a behavior. Unfortunately for any decision of the question,
 determinations of the dielectric constants of salt solutions
 have given contradictory results; the more recent, and possibly
 more reliable results of Drude[208] indicate that salt solutions
 show approximately the same dielectric behavior as water itself.
 Smale, in Nernst's laboratory, on the other hand, obtained results
 indicating that salt solutions have decidedly higher dielectric
 constants than pure water.[209] A final decision in the matter would
 be of great importance.[210] But, as explained before (p. 64),
 there are other properties of a solvent which seem to be intimately
 related to its ionizing power and which may be modified by the
 presence of salts, ‹i.e.› of strong electrolytes. The value obtained
 for the proportion [Me^{+}] × [X^{−}] / [MeX] grows rapidly
 with increasing concentration, ‹indicating a disproportionately
 large ionization in the more concentrated solutions›—which is
 what one would expect, if ‹electrolytes or their ions in some way
 increased› the ionizing power of the medium. In agreement with such
 a conclusion, Arrhenius found[211] that ‹the ionization of weak
 acids›, like acetic acid, is increased by the presence of ‹foreign
 neutral› salts, such as sodium chloride. This means, of course, that
 the strength of acetic acid, as an acid, is increased likewise.

 EXP. 0.5 c.c. of 0.1 molar acetic acid is added to 100 c.c. of a
 dilute solution of methyl orange in each of three test glasses.
 When some solid sodium chloride (3 grams, and then 3 grams
 more—altogether 0.1 mole) is added to the one solution, a plain
 increase in the intensity of the acid tint is observed.[212] The
 addition of cane sugar to a second solution has no such effect.
 The addition of sodium chloride to a fourth portion of the methyl
 orange, to which no acetic acid has been added, shows that its
 color remains unchanged: the effect on the indicator in the first
 case, then, is the result of the action of the salt on the acetic
 acid.[213] [p111]

 The so-called "salt-effect" on the ionization of ammonium hydroxide
 may be illustrated in a similar way.

 EXP. 0.5 cc of 0.1 molar ammonium hydroxide is added to each of
 two portions (100 c.c.) of a dilute solution of phenolphthaleïn.
 When some sodium chloride solution is then added to one of
 the two portions, the basicity of the solution is distinctly
 increased. The addition of sodium chloride to a third portion of
 the phenolphthaleïn solution shows that its own reaction to the
 indicator is neutral.

 If the ionizing power of a solvent is changed by the presence of an
 electrolyte, then the law of chemical equilibrium, in its simple
 form, would not apply to the ionization of such electrolytes in
 varying concentrations—as little as we should expect to obtain the
 same constant for acetic acid in aqueous solution and in alcoholic
 solution, the ionizing power of alcohol being much smaller than
 that of water. The deviation from the law, naturally, would be most
 marked in the case of those electrolytes which ionize so easily as
 readily to produce high concentrations of ions.

It may be said that ‹laws based on the electrical properties of salt
solutions› seem to be the predominating laws governing the ionization
of electrolytes and modifying, in certain cases, the chemical laws
based on the study of non-electrolytes.[214]

For the purposes of qualitative analysis, it will suffice to bear in
mind the fact that the ionization[215] of salts, strong acids and
strong bases does not conform to the laws of mass action, and the
fact that practically all salts (with the notable exceptions, among
common salts, given on p. 107) ‹are very readily ionized› in aqueous
solution, namely to the extent of 40 to 85% in solutions of such
moderate concentration as 0.1 molar.[216]

«Some Applications of the Law of Chemical Equilibrium.»—According
to the discussions given above, for the ionization of acetic acid,
CH_{3}CO_{2}H ⇄ CH_{3}CO_{2}^{−} + H^{+} we have the relation

 [CH_{3}CO_{2}^{−}] × [H^{+}] / [CH_{3}CO_{2}H] = K_{ionization}.

[p112]

If the concentrations of the components are modified in any
way, the condition of equilibrium is disturbed and change will
result, always toward the restoration of equilibrium. The changes,
in the case of purely ionic actions, are found to take place with an
enormous velocity, equilibrium being restored almost instantly.

(1) If the solution of acetic acid, represented in the above
equation, is diluted by an equal volume of water, the condition of
equilibrium is disturbed:

 ½ [CH_{3}CO_{2}^{−}] × ½ [H^{+}] / (½ [CH_{3}CO_{2}H]) <
   K_{ionization.}

The ratio is smaller than that required for equilibrium, and there
will be a change towards increasing the ratio. The acid will ionize
more rapidly than it will be formed from the acetate and hydrogen
ions (which collide less frequently in the diluted solution) and a
new condition of equilibrium will be reached, when more of the acid
is ionized. We found, as a matter of fact, that the more a solution
of acetic acid is diluted, the larger is the proportion of ionized
acid (see p. 99).

(2) If the concentration of the acetate-ion is increased in the
solution by the addition of a salt of acetic acid, say sodium
acetate, we have

 ‹x› [CH_{3}CO_{2}^{−}] × [H^{+}] / [CH_{3}CO_{2}H] > K_{ionization.}

The ratio is larger than allowed by the equilibrium law, and the
acetate ions will combine with the hydrogen ions to form acetic acid
more rapidly than the ions are formed from it, until equilibrium is
reëstablished. In a molar solution of acetic acid, 0.42% of the acid
is ionized, and we have

 [CH_{3}CO_{2}^{−}] × [H^{+}] / [CH_{3}CO_{2}H] =
   0.0042 × 0.0042 / 0.9958 = 1.8E−5.

If an equivalent quantity of sodium acetate should be added, ‹i.e.›
one mole or 82 grams of the salt per liter, the salt being ionized to
the extent of 53%, we would have

 0.534 × 0.0042 / 0.9958 > 1.8E−5.

The equilibrium constant will be satisfied (and the velocity of
ionization of the acetic acid will become equal to the velocity of its
[p113] formation from its ions) when[217] [CH_{3}CO_{2}^{−}] = 0.53,
[H^{+}] = 0.000,034 and [CH_{3}CO_{2}H] = 0.999,966. If we use two
characteristic places in the decimals, we have

 (0.53 × 0.000034) / 1 = 1.8E−5.

The most significant fact in the new condition of equilibrium is the
‹extremely small concentration of hydrogen-ion› in the solution.
Since the acid properties of acetic acid are due to its forming
hydrogen-ion, we would conclude that such properties of acetic
acid are ‹very much weakened› by the presence of its own salts.
This conclusion has been fully verified by careful quantitative
measurements and can be demonstrated as follows[218]:

 EXP. To two of three portions of a dilute solution of methyl
 orange equal quantities of acetic acid are added (‹e.g.› 0.5 c.c.
 molar acid), the third portion being reserved to show the color
 of the neutral solution of the indicator. Now, if into one of the
 solutions, to which acetic acid has been added, a few crystals of
 sodium acetate are gradually dropped, the color reverts gradually
 to the color of the original neutral solution; the concentration of
 hydrogen-ion becomes so small, that it does not visibly affect this
 indicator, which is not very sensitive to acids, (H^{+}).[219]

The solution, according to the views expressed, ‹should still be
very slightly acid›, and by the use of an indicator (litmus paper)
which is much more sensitive to the hydrogen-ion than is methyl
orange, no difficulty is found in recognizing this fact also. As a
matter of experiment, then, an acid like acetic acid ‹is very much
weaker in the presence of its own salts than in their absence›, and
the equilibrium constant and the concentrations of the components
used determine the extent to which the hydrogen-ion is suppressed.
The same must be true for all weak acids and similar relations must
[p114] hold for all weak bases[220]—in general, ‹weak acids and weak
bases are very much weakened by the addition of their own salts›.

The importance of recognizing such changes, in considering analytical
reactions, may be illustrated as follows:

 EXP. A solution of ferrous acetate (ferrous chloride with an
 equivalent quantity of sodium acetate) is treated with hydrogen
 sulphide; a precipitate of black ferrous sulphide is formed. A
 second portion of the solution is first decidedly acidified with
 acetic acid: hydrogen sulphide does not precipitate any ferrous
 sulphide. Some crystals of sodium or ammonium acetate are added to
 the mixture and a black precipitate of iron sulphide immediately
 appears around the salt as it dissolves, and on mixing the contents
 a heavy precipitate of the sulphide throughout the vessel is formed.

It is evident that the addition of a neutral salt, containing the
same negative ion as the added acid, may completely reverse the net
result of a test with hydrogen sulphide.

(3) If the concentration of the hydrogen ions in the solution of
acetic acid is increased by the addition of hydrochloric, or some
other strong acid, equilibrium between the acetic acid and its ions
will likewise be disturbed and the new condition of equilibrium will
show a suppression of the acetate-ion. Instances of such ‹action
of a strong acid in suppressing the characteristic ions of weaker
acids› will be discussed in detail in connection with the analytical
applications of hydrogen sulphide (Chap. XI), where the action is of
peculiar importance. Strong bases have a similar effect on weak bases.

(4) If one of the ions of acetic acid is ‹suppressed› by the addition
of some agent, equilibrium is again destroyed and the resulting
change is always in the direction of reëstablishing a condition of
equilibrium on the basis of the law of equilibrium. Instances of this
common case, such as the ‹neutralization› of acetic or any other acid
by a base, or the ‹driving out› of a ‹weak› acid, from its salts, by
a strong acid, or of a ‹weak› base by a ‹strong› base, considered
from the point of view of the equilibrium law, should be worked out
by the student.[221] [p115]

(5) The displacement of an acid (or base) in salts by another acid
(or base) is subject always to the law that equilibrium is reached,
when all the equilibrium constants are satisfied in the system. Very
frequently, the application of the law will lead, apparently, to the
incorrect conclusion that the stronger acid (or base) will ‹always›
displace, more or less completely, the weaker[222]—an inference, out
of which grew, indeed, the characterization of acids and bases as
strong and weak. Yet, when the laws of equilibrium, as the result
of the peculiar values of constants, demand that, on the contrary,
a strong acid or base should be displaced by a weak, or even a
feeble one, we find that the change in this direction occurs with
equal ease. Numerous instances will be given where a weak acid (or
a weak base) does this to a certain extent (Chap. X), and others
where precipitation of salts facilitates the action of weaker acids
greatly by the introduction of new, physical constants. The following
case of the liberation of hydrochloric acid by the exceedingly weak
acid, hydrocyanic acid, is important because it shows a reversal
of the common action without the formation of any precipitate, and
especially because it brings out most strikingly the relations
between ionization and chemical activity in a case of special
importance to analytical chemists.

«The Exceptional Ionization of Mercuric Cyanide and Its
Consequences.»—We have found that practically all salts are very
readily ionized. But it was mentioned that there are a few exceptions
to this rule, and mercuric chloride and especially mercuric cyanide
were named as the most important exceptions from the point of view
of analytical chemistry. The difference in ionization between these
two salts and ordinary salts may be shown readily by the apparatus
previously used to demonstrate the difference in the ionization of
various bases and acids.

 EXP. Into the parallel tubes of the conductivity apparatus (p. 77)
 equivalent quantities[223] of solutions of mercuric cyanide[224]
 Hg(CN)_{2}, mercuric chloride [p116] HgCl_{2}, and barium chloride
 BaCl_{2}, are introduced. The barium chloride represents an ordinary
 salt of the same type as the mercury salts, and the current passing
 through its solution makes the little lamp glow. The electrodes
 in the mercuric chloride solution must be brought ‹quite close›
 together before sufficient current will pass through the solution to
 bring its little lamp to redness. In the case of the cyanide we can,
 at most, get a faint, dull glow by bringing the electrodes together
 as closely as we can, without allowing them to touch each other and
 short-circuit the current.

It is evident that these mercury salts are not as readily ionizable
as are ordinary salts. This difference, as may be anticipated,
shows itself also in the ‹chemical behavior› of their solutions and
makes ‹necessary special precautions on the part of the analyst in
examining mercury compounds›. For instance, whereas mercuric oxide is
readily precipitated by the addition of sodium hydroxide to solutions
of the nitrate and even of the moderately ionized chloride, one fails
to get a precipitate of oxide from the cyanide solution (‹exp.›), and
if we relied on this test, we should overlook the mercury entirely.
That traces of the mercuric-ion are present, as indicated by the
minimal conductivity of the cyanide, is confirmed by the fact that
from the cyanide solution the sulphide, which is much less soluble
than is the oxide, may be precipitated by the addition of ammonium
sulphide (‹exp.›). That the sulphide is in fact less soluble[225]
than the oxide is shown by the conversion of the latter into the
former by the action of ammonium sulphide (‹exp.›).

As a further result of the abnormally slight ionization of these
mercury salts, the analyst, unless he is on his guard, may also have
difficulty in discovering the presence of their negative ions. Thus,
while sodium chloride readily gives hydrogen chloride when treated
with concentrated sulphuric acid, mercuric chloride, although it is
a soluble salt, does not (‹exp.›), and reliance on this test alone
might lead to a gross error.[226] In the case of the cyanide, it
is correspondingly difficult to recognize the [p117] cyanide-ion
(see the laboratory experiment, Part III). The ordinary tests fail
to show its presence until the mercury has been removed from the
solution by precipitation as a sulphide. Mercuric cyanide being a
deadly poison which analysts are liable to meet and have met with in
criminal cases, it is clear that a knowledge of these facts is vital
to analytical accuracy.

Now, the very slight ionization of mercuric cyanide enables us to
realize, in the following experiment, the case where an exceedingly
weak acid without the formation of any precipitate involving physical
constants, may displace a much stronger acid from its salts.
Hydrocyanic acid is one of the weakest acids (table, p. 104), the
constant for the ratio [H^{+}] × [CN^{−}] / [HNC] being 0.7E−9.
It is so weak an acid that the addition of a dilute solution to
methyl orange will not redden the indicator, but will have only a
barely perceptible effect on it (‹exp.›). Mercuric chloride solutions
also are almost neutral to methyl orange (‹exp.›) (very slight
decomposition of the salt by water makes the solution very slightly
acid, not enough to produce more than an orange color with methyl
orange). Now, mercuric chloride, while it is not very easily ionized,
is, we found, very much more readily ionized than is mercuric
cyanide. The consequence is that when we add hydrocyanic acid to a
mercuric chloride solution, the equilibrium between mercuric chloride
and its ions and between hydrocyanic acid and its ions will be
decidedly displaced, ‹the mercuric-ion combining with the cyanide-ion
to form the scarcely ionizable mercuric cyanide›. As a result, more
and more of the molecular mercuric chloride and hydrocyanic acid will
be ionized; and since the other ions, the chloride and the hydrogen
ions, form a readily ionizable electrolyte, hydrochloric acid, ‹these
ions› (H^{+} and Cl^{−}) ‹will accumulate in the solution› and we
shall have sufficient ‹ionized hydrochloric acid› liberated to make
the solution decidedly acid.

 EXP. When the two solutions described above are mixed, a strongly
 acid solution, colored a bright pink, results.

In the following equations the dark arrows indicate the direction in
which the action goes when the solutions are mixed:

 HgCl_{2} ⥂ Hg^{2+} + 2 Cl^{−}

 2 HCN ⥂ 2 CN^{−} + 2 H^{+}

 2 CN^{−} + Hg^{2+} ⥂ Hg(CN)_{2}

 2 Cl^{−} + 2 H^{+} ⇄ 2 HCl


  FOOTNOTES:

  [166] ‹Concentrations are usually measured in moles or
  gram-molecular weights per liter, and a gram-molecular or molar
  weight of a compound is its molecular weight expressed in grams.›
  Hence the number of grams of a given substance in a liter divided
  by its molecular weight represents its concentration.

  [167] Nernst, ‹Theoretical Chemistry›, 423, 433; Ostwald,
  ‹Lehrbuch›, II_{2}, 104, etc., 296; Walker, ‹Introduction to
  Physical Chemistry› (1909), 259, etc.

  [168] Not every collision of a molecule of ‹A› with one of ‹B›
  is supposed to result in a chemical interaction, but the number
  of collisions with such a result is considered to be directly
  proportional to the total number of collisions. Van 't Hoff,
  ‹Lectures on Physical Chemistry›, I, 104.

  [169] Since in any chemical action, which has not reached a
  condition of equilibrium, the concentrations of the reacting
  substances change continuously, the relation between the velocity
  of the action and the concentrations, for any moment, is found by
  the application of the calculus to the experimental data. (‹Cf.
  Elements of Calculus›, by Young and Linebarger (1900), 168, 181,
  240; Mellor, ‹Higher Mathematics for Students of Chemistry and
  Physics› (1902), 197.)

  [170] Nernst, ‹loc. cit.›, 541, etc.; Ostwald, ‹loc. cit.›, 107,
  etc.; Walker, ‹loc. cit.›, 257; Smith, ‹loc. cit.›, 250, and 180
  (‹Stud.›).

  [171] If a component takes part more than once in the action,
  its concentration is raised to the power corresponding to the
  coefficient expressing the number of its molecules taking part
  in the action. For instance, for ‹A› + 2 ‹B› → ‹C› + ‹D›,
  ‹v›_{1} = ‹k›_{1} × [‹A›] × [‹B›]^2; (see below).

  [172] ‹Cf.› Van 't Hoff, ‹loc. cit.›, I, 206.

  [173] The concentrations are calculated from the data given by
  Bodenstein, ‹Z. phys. Chem.›, «22», 16 (1897). (‹Cf.› Van 't Hoff
  ‹loc. cit.›, «I», 110.)

  [174] The fundamental meaning of the law is most accurately defined
  in thermodynamic terms, that is, in terms of the work or energy
  relations connected with changes of gaseous or osmotic pressures.

  [175] Van 't Hoff, ‹loc. cit.›, «I», 104, 159, etc.

  [176] In regard to the variations of the equilibrium constant with
  changes of temperature and the relations which govern these changes
  see Smith's ‹Inorganic Chemistry› (1909), p. 260.

  [177] The limitations are indicated in the preceding section.

  [178] Stieglitz, ‹Am. Chem. J.›, «23», 406 (1900).

  [179] ‹Vide› Stieglitz, ‹loc. cit.›

  [180] The table is based on the results of Noyes and Cooper, given
  in "The Electrical Conductivity of Aqueous Solutions," ‹Carnegie
  Institution Publications›, No. «63», pp. 138, 141 (1907).

  [181] Ostwald [‹Z. phys. Chem.›, «2», 278 (1888)], was the first
  to develop this relation from the conductivity data for so-called
  "weak acids," and the law of chemical equilibrium, holding in such
  and similar cases, is often called ‹Ostwald's Law of Dilution›.

  [182] The equilibrium ratio, used as an illustration in the text,
  is the equilibrium ratio for monobasic acids. For polybasic acids,
  the ratio would have the form demanded by the rule given p. 94.
  For instance, for H_{2}X ⇄ 2 H^{+} + X^{2−}, the expression
  [H^{+}]^2 × [X^{2−}] / [H_{2}X] should be constant, provided the
  ionization occurs according to the law of chemical equilibrium
  in its simplest terms. In point of fact, for ‹strong› acids,
  this ratio holds as little as does the equilibrium ratio for the
  monobasic acids.

  [183] Owing to the instability of carbonic acid, which breaks down
  into carbon dioxide and water (H_{2}CO_{3} ⇄ H_{2}O + CO_{2}),
  the carbonic acid is, in turn, in equilibrium with the carbon
  dioxide. For the sake of simplicity, this relation is not included
  in the detailed discussion, and wherever the symbols H_{2}CO_{3}
  and [H_{2}CO_{3}] are used, they are intended to represent ‹the
  total carbonic acid, present› as such and as carbon dioxide. The
  detailed discussion of the complication mentioned will be given
  in connection with the analogous case of ammonium hydroxide and
  ammonia, and, as will be shown there, ‹with the significance just
  attached to the symbols›, the relations developed in the text are a
  rigorous expression of the facts.

  [184] [H^{+}], in all the equations used, represents as usual, the
  total concentration of hydrogen-ion.

  [185] Walker and Cornack, ‹J. Chem. Soc.› (London), «77», 20 (1900).

  [186] McCoy, ‹Am. Chem. J.›, «29», 437 (1903); Stieglitz, ‹Carnegie
  Institution Publications›, No. «107», p. 245 (1909).

  [187] In a solution of phosphoric acid, all the possible forms
  of ionization, described in the text, occur simultaneously, but
  the secondary and tertiary forms of ionization, as far as the
  concentration of the hydrogen-ion is concerned, are entirely
  subordinate to the primary ionization.

  [188] ‹Vide› footnote, p. 79.

  [189] Luther, ‹Z. Elektrochem.›, «3», 296 (1907). Noyes and
  Eastman, ‹Carnegie Institution Publications›, «63», 274 (1907).
  Noyes and Stewart, ‹J. Am. Chem. Soc.›, «32», 1133 (1910).

  [190] The apparatus described on p. 77 is used. ‹Vide› Noyes and
  Blanchard, ‹loc. cit.›

  [191] Hydrogen ions move five to ten times as fast as the anions
  and carry 80–90 per cent of the current; see p. 56.

  [192] The solution of these salts is due to the action of hydrogen
  ions on their anions; see Chap. VIII.

  [193] Goodwin, ‹Z. phys. Chem.›, «21», 1 (1896).

  [194] See Kohlrausch and Holborn, ‹loc. cit.›, p. 194. Their values
  for K (last column) must be divided by 100 to express the constants
  in terms of the same units as those used in the above table.

  [195] J. H. Long, ‹J. Am. Chem. Soc.›, «18», 693 (1896). Ley, ‹Z.
  phys. Chem.›, «30», 322 (1899); Bruner, ‹ibid.›, «32», 133 (1900);
  Walker, ‹J. Chem. Soc.›, (London), «67», 585 (1895).

  [196] Instances are found in the laboratory experiments, Parts III
  and IV.

  [197] The ionization of salts of other types, ‹e.g.› MeX_{2},
  Me_{2}Y, etc., likewise fails to conform to the law of chemical
  equilibrium.

  [198] See below (pp. 112–4), also, further, confirmatory evidence,
  derived from the application of the same law to the influence upon
  the degree of ionization of weak acids and weak bases, exerted by
  the presence of their own salts.

  [199] See below, in regard to evidence that the disturbing
  factors, predominant with strong electrolytes, are exhibited in
  much slighter, but perceptible measure in the case of the weak
  electrolytes.

  [200] See also the interpretation of the law of chemical
  equilibrium from the viewpoint of the kinetic theory, Nernst,
  ‹Theoretical Chemistry›, p. 428.

  [201] For a more detailed discussion of these views, see Lehfeldt's
  ‹Electrochemistry› (1904), pp. 78, 79.

  [202] Various empirical laws, expressing the behavior of strong
  electrolytes, have been suggested: see Nernst, ‹Theoretical
  Chemistry›, p. 498, as to Rudolphi's and van 't Hoff's rules; see
  also A. A. Noyes, ‹Report of the Congress of Arts and Science›,
  «IV», p. 316 (1904).

  [203] Wegscheider, ‹Z. phys. Chem.›, «70» (I), 603 (1909).

  [204] It is possible that this effect is only another form of
  expressing the very relation discussed in the preceding paragraph.

  [205] Arrhenius, ‹Z. Elektrochem.›, «6», 10 (1899); ‹Z. phys.
  Chem.›, «31», 197 (1899).

  [206] Salts have constants averaging about 7, and running from
  5 to 28; the constant for ice is about 3. Landolt, Börstein,
  Meyerhoffer, ‹Tabellen›, p. 766 (1905).

  [207] We have: Ice, 3, water (at 0°), 80; glacial acetic acid, 2.8,
  acetic acid (liquid), 10; cane sugar, 4, cane sugar in aqueous
  solution (40%), 67.5, (6.5%), 45.3. ‹Ibid.›

  [208] ‹Z. phys. Chem.›, «23», 280 (1897).

  [209] ‹Wiedemann's Ann.›, «60», 625 (1897).

  [210] See Walden, ‹Z. phys. Chem.›, «61», 636 (1908), in regard to
  the difficulties of the problem.

  [211] ‹Loc. cit.›

  [212] ‹Cf.› Szyszkowski, ‹Z. phys. Chem.›, «58», 420 (1907).

  [213] Arrhenius made a calculation of the effect, taking into
  account all the rather involved changes produced by the salt. ‹Loc.
  cit.›

  [214] For instance, the principle of "isohydric solutions,"
  discovered by Arrhenius, has been established empirically and
  it involves relations which are in marked disagreement with the
  demands of the law of chemical equilibrium. ‹Vide› A. A. Noyes,
  ‹Report of the Congress of Arts and Sciences›, «IV», p. 318 (1904).

  [215] The most reliable estimates of the concentrations of ions
  in these solutions are based on determinations of the degrees of
  ionization by means of conductivity measurements (see Chap. IV, and
  the previous footnote).

  [216] Salts MeX ionize more readily (80–85% in 0.1 molar solution)
  than do salts Me″X_{2} or Me_{2}X″ (50 to 70% in 0.1 molar
  solution), and these, again, more readily than salts Me″X″ (about
  40% in 0.1 molar solution).

  [217] The calculation of the condition of equilibrium can be
  made, with sufficient accuracy for our purpose, as follows: The
  denominator 0.9958 in the original proportion, being near its
  limit (its highest possible value is 1 in a molar solution),
  cannot change appreciably. Consequently, when the one factor in
  the numerator, [CH_{3}CO_{2}^{−}], is made 0.53 / 0.0042, or 126
  times as large as it was, the other factor, [H^{+}], to maintain
  a constant proportion, must be made 1 / 126th of its original
  value and 0.0042 / 126 = 0.000,034. For more exact work, the new
  concentrations of the three components may be found by solving a
  simple quadratic equation.

  [218] Küster, ‹Z. für Elektrochem.›, «4», 110 (1897).

  [219] See note, p. 79.

  [220] See Part III for the application of this principle to
  ammonium hydroxide and its experimental confirmation. (‹Cf.›
  Arrhenius, ‹Z. phys. Chem.›, «2», 28 (1888); Stieglitz, ‹Am. Chem.
  J.›, «23», 406 (1900).)

  [221] For instance, in the first place, the action of 0.1 mole
  of HCl on 0.1 mole of C_{2}H_{3}O_{2}Na, dissolved in a liter of
  water, and, in the second place, the action of 0.1 mole of NaOH on
  0.1 mole of NH_{4}Cl, in a liter of water, may be considered. The
  strong electrolytes (HCl, C_{2}H_{3}O_{2}Na, NaCl, NH_{4}Cl, NaOH)
  may be taken to be (roughly) 80% ionized. From the concentrations
  given and the constants involved, the direction and the presumable
  intensity of the main change in each of the two cases should be
  determined.

  [222] Instances of such displacement are given in the footnote of
  the previous paragraph.

  [223] ‹E.g.› 50 c.c. of 0.2 molar solutions.

  [224] Mercuric cyanide and mercuric chloride are largely present in
  aqueous solution as [Hg(CN)_{2}]_{2} and [HgCl_{2}]_{2}; see Chap.
  XII.

  [225] See Chapter VIII in regard to this proof that mercuric
  sulphide is less soluble than mercuric oxide and in regard to
  the question how, by a continuous disturbance of the equilibrium
  conditions, all the mercury may be precipitated from the cyanide
  solution as the sulphide, in spite of the very slight degree of
  ionization of the cyanide.

  [226] The chloride is, however, sufficiently ionized to make
  possible the precipitation of the very insoluble silver chloride,
  when silver nitrate is added to its solution.

[p118]




 CHAPTER VII

 «PHYSICAL OR HETEROGENEOUS EQUILIBRIUM.—THE COLLOIDAL CONDITION»


The law governing ‹physical› or ‹heterogeneous equilibrium› applies
to all cases where, at a constant temperature, one and the same
chemical substance is present in two or more physical conditions, or
"phases," in contact and in equilibrium with each other. We have, for
instance, the common case of a liquid, say water, in contact with
its vapor, or the liquid in contact with its solid phase (ice) and
its vapor; or, we may have a gas, say oxygen, in contact with its
solution in some solvent like water. We may have a solid, like cane
sugar, in contact with its solution. We may also have a substance
like bromine, which is soluble both in chloroform and in water,
present in both solutions at the same time, the two solutions being
in contact but immiscible. These cases represent the most common
types of systems to which the law of physical equilibrium may be
applied, although the list has by no means been exhausted. ‹The law
of physical or heterogeneous equilibrium states that when one and the
same chemical compound is present in two physical states or phases›,
as expressed in the equation S_{1} ⇄ S_{2}, then ‹when equilibrium is
reached›, at a given temperature, ‹the ratio of the concentrations of
the substance in the two phases is some constant number›:

 [S_{1}] : [S_{2}] = «k.»

The bracketed symbols denote concentrations.

It should be noted that the condition of equilibrium is independent
of the total quantity[227] of substance present in either phase or in
both phases; that is, provided the ‹ratio› of the ‹concentrations›
is maintained constant at a given temperature, the ‹quantity of
substance present in both phases or in either phase is variable›.
For instance, the condition of equilibrium between water and [p119]
water vapor is independent of the quantity of water or of water vapor
present: in a closed liter bottle containing water and water vapor,
the ratio of the concentrations is maintained, irrespective of the
question whether the bottle contains 10 c.c. of water and 990 c.c. of
vapor or 990 c.c. of water and 10 c.c. of vapor.

The law is one of experience; instances of its application are
given below. Its probable theoretical significance may be explained
mechanically with the aid of the kinetic theory of gases and
solutions, as follows: If chloroform is added to a solution of
bromine in water, the chloroform takes up part of the bromine and,
if the mixture is vigorously shaken, a condition of equilibrium and
a definite distribution of bromine between the two solvents will
result (‹exp.›[228]). Now, if one imagines a liter of the aqueous
solution to contain ‹one mole› of bromine at some given temperature
and to cover a liter of chloroform, the whole system being left
to itself, then all the conditions affecting the migration of the
bromine into the chloroform will be definite ones—the concentration
of the bromine, the temperature, the surface between the two
solvents—and bromine will pass from the aqueous solution into the
chloroform solution at a definite speed. We may call the ‹quantity›
(in moles) of bromine which would enter the chloroform in one minute,
if the concentration of the bromine in the water were kept constant
(one mole) throughout the minute, the ‹velocity of migration› of
the bromine—this velocity, like chemical velocity, representing
a quantity, not a distance. The velocity being a definite one
under these conditions, we have ‹v›_{1} = ‹k›_{1}. Now, if all the
conditions are left unaltered, except that the concentration of the
bromine is changed, say kept at one-hundredth its original value,
then only one one-hundredth as many molecules of bromine as in the
first case will come into contact with the chloroform surface in unit
time. The chances for migration are one one-hundredth as great, and
the quantity entering the chloroform in unit time—the velocity of the
[p120] change—will be one one-hundredth of the original velocity.
In general, ‹the velocity will be proportional to the concentration
of the bromine› [Br]_{aq.} ‹in the water at any moment› and to the
characteristic constant ‹k›_{1}.

 ‹v›_{1} = [Br]_{aq.} × ‹k›_{1}.

On the other hand, if a solution of bromine in chloroform is covered
with water, bromine enters the water (‹exp.›).[229] We would find, by
the method of analysis used before, and for the same conditions, that
the velocity of migration, ‹v›_{2}, of the bromine into the water is
also proportional to a characteristic constant, ‹k›_{2}, and to the
concentration of the bromine in the chloroform [Br]_{ch.}. We have,
therefore ‹v›_{2} = [Br]_{ch.} × ‹k›_{2}.

Equilibrium between the two solutions will be reached when

 ‹v›_{1} = ‹v›_{2} or [Br]_{aq.} × ‹k›_{1} = [Br]_{ch.} × ‹k›_{2},

from which follows that[230] for the condition of equilibrium

 [Br]_{aq.} / [Br]_{ch.} = ‹k›_{2} / ‹k›_{1} = ‹k›.

«Applications of the Law of Physical Equilibrium.»—(1) The
law of physical equilibrium may be applied first to the case
of a liquid, say chloroform, in contact with its vapor.
For the condition of equilibrium at a fixed temperature
[CHCl_{3}]_{vap.} : [CHCl_{3}]_{liq.} = ‹k›.

Now, at a fixed temperature, a pure liquid has a fixed concentration,
its specific gravity being a definite one. Hence, for a fixed
temperature, the second term of the constant ratio being definite,
the first term, [CHCl_{3}]_{vap.}, representing the concentration of
the vapor, must also have a fixed, constant value for the condition
of equilibrium, ‹i.e.› when the space above the liquid is saturated
with its vapor. This is in agreement with well-known facts. The
concentration of the vapor is usually expressed in terms of its
[p121] pressure, and is called the ‹vapor pressure› or ‹vapor
tension› of the liquid at the temperature in question. Tables giving
the definite vapor pressures of important liquids at the various
fixed temperatures are in common use.

(2) For oxygen in equilibrium with its saturated solution, say
in water, at a fixed temperature, we have, according to the law,
[O_{2}]_{gas} : [O_{2}]_{solut.} = ‹k›.

If the oxygen is under a given pressure at a definite temperature,
its concentration [O_{2}]_{gas} is fixed, and consequently the
second term, [O_{2}]_{solut.}, of the ratio, the concentration of
the dissolved oxygen, or ‹its solubility, must also be definite›,
‹i.e.› oxygen must have a definite solubility in water at a given
temperature under a given pressure. If the pressure on the gas is
doubled, its concentration is doubled and, to maintain the constant
ratio, its solubility must also be doubled—which is in agreement
with the facts (Henry's law). If air of the same pressure is taken,
in place of pure oxygen, then the concentration of the oxygen (first
term of the above ratio) is only about one-fifth as great as for the
pure gas, and the water must be saturated with oxygen when it has
taken up only one-fifth (second term of the ratio) as much as it
would from the pure gas (Dalton's law): ‹Each gas in a mixture is
soluble in proportion to its own partial pressure› or ‹concentration›.

(3) For sugar in equilibrium with its solution in water, ‹i.e.› in
contact with its saturated solution, at a given temperature, we
should have

 [C_{12}H_{22}O_{11}]_{aq.} : [C_{12}H_{22}O_{11}]_{solid} = ‹k›.

Since a pure solid like sugar at a given temperature has a definite
specific gravity, the concentration of the sugar in the solid
condition should also be a definite one. Consequently, according to
the law under discussion, the first term, [C_{12}H_{22}O_{11}]_{aq.},
of the ratio, the concentration of the sugar in its saturated
solution in contact with the solid phase, must also have a definite
value. This is in agreement with fact, the concentration of the sugar
in the saturated solution, termed its solubility, being a definite
one for a given temperature. (See below, p. 123, in regard to the
solubility of fine powders.)

«Supersaturated Solutions.»— It is well known, however, that by
dissolving a substance, such as sugar, in hot water and carefully
[p122] cooling the solution, we may obtain a solution of sugar
containing much more sugar in unit volume than is represented by its
solubility at the lower temperature. The concentration of the sugar
at the temperature in question, instead of having the definite value
represented by [C_{12}H_{22}O_{11}]_{aq.}, can easily have a value
several times as large. This phenomenon ‹is not at variance with
the law of physical equilibrium›, inasmuch as the law states that,
when a given compound is present in ‹two› physical states or phases,
then a constant ratio between the concentrations of the substance
in the two phases is established when equilibrium is reached at a
given temperature. In the solution prepared as described, we have the
substance present only in one phase, and we have what may be called a
metastable condition, as long as the second phase is not introduced.
As soon as a minute crystal of the solid phase is added or is formed
in the solution, change immediately ensues, and the excess of solid
is deposited. If the mixture be kept perfectly quiet, the excess will
in most cases be deposited on the ‹surfaces› of the added crystal,
which thereby grows larger (rock-candy manufacture).

 EXP. Supersaturated solutions of sodium sulphate and sodium
 thiosulphate, into which crystals of the salts are dropped, show how
 the crystal starts crystallization. The crystals develop as branches
 from the crystal first introduced and from the new crystals formed.

This phenomenon of ‹supersaturation› is one which analytical
chemists must always take into consideration. Tests which involve
the precipitation of substances that are merely difficultly soluble,
rather than exceedingly insoluble, or of substances present only in
very small quantities, may well lead to entirely wrong conclusions,
if precautions are not taken against the possibility of the
failure of a precipitate to appear as a consequence of persistent
supersaturation. For instance, a common test for the presence of
potassium salts consists in the precipitation of ‹potassium acid
tartrate› by the addition of tartaric acid to the solution of a
potassium salt (‹exp.›). The tartrate is somewhat soluble and tends
to form supersaturated solutions; if we proceed without due regard
for this phenomenon, we may readily have a quantity of potassium salt
present and fail to obtain the test for it. Simply mixing tartaric
acid and potassium chloride solutions (‹exp.›) may fail to [p123]
give any precipitate, and if the test is thrown away and potassium
reported absent, a glaring blunder is committed. To insure against
the error of supersaturation, we try to start crystallization by the
common devices of shaking the solution or "scratching" the walls
of the vessel, the object being to facilitate the formation of the
first crystal. The surest method is to ‹inoculate› a small portion
of the mixture with a ‹minute› crystal of the substance we expect to
be formed. If no precipitate results in a short time, the solution
is not supersaturated—it may be too dilute and may require further
concentration, but the error of supersaturation has been excluded.

The relation between supersaturated solutions and crystals brings out
sharply the fact that physical equilibrium is essentially a condition
of equilibrium between the substance at the ‹surface› of the solid
and the substance in its dissolved state. In terms of the molecular
theory, equilibrium is established when the molecules of the crystal
surface dissolve as rapidly as molecules from the solution are
deposited on the surface. If the concentration of the dissolved
molecules is reduced below the point required for equilibrium, the
velocity of deposition is diminished. The velocity of solution will
then be greater than the velocity of deposition and ‹solution›
will result. The reversed relations hold when the concentration
of the solution is greater than that demanded by equilibrium: the
velocity of deposition will be the greater than that of solution and
‹precipitation› follows.[231]

«Solubility of Fine Powders.»—Consideration of the surface forces,
acting between crystals and the liquids wetting them, led to the
interesting prediction[232] that the more minute crystals of a given
specimen would not only dissolve more rapidly, on account of the
larger surface exposed, but would also be ‹more soluble› than the
larger crystals, and for the same reason. Surface tension always
tends to produce the smallest possible free surface of a liquid,
and the free surface between a liquid and a given weight of solid
material in a fine powder is much larger than between the liquid and
the same weight in larger crystals. The surface tension [p124] will
therefore tend to convert the smaller crystals into larger ones, and
it can do so only by means of a greater degree of solubility of the
former. This prediction has now been fully verified by experiments on
the solubility of barium sulphate and of gypsum.[233] The solubility
of barium sulphate in a very fine powder (with an average diameter of
10^{−4} mm.) is almost twice as great as the solubility of a coarser
material (18E−4 mm. average diameter).

The application of these relations to analysis is as follows: If
a crystalline precipitate is in contact with a solvent, ‹e.g.› if
barium sulphate is in contact with the liquid from which it has
been precipitated, then this liquid must be continually in a state
of change, not of equilibrium, with respect to the solution and
the deposited barium sulphate. The more minute crystals, being a
little more soluble than the larger ones, will supersaturate the
solution in respect to the larger crystals and the excess will
be deposited on these larger crystals and make them grow still
larger. This deposition will make the solution unsaturated with
respect to the smaller crystals and more of these will dissolve.
The process is obviously a continuous one, and must lead in time
to the disappearance of the minute crystals and the growth of the
larger ones. That is a result which analysts aim to attain,—which in
quantitative work it is in fact necessary to attain, since the more
minute crystals are likely to pass through filters and be lost in
the analysis. The views expressed, and the experimental confirmation
of the conclusion reached, form the theory of what is called the
"digesting" of precipitates before they are brought on filters. It is
clear that every condition facilitating contact between solvent and
solid will accelerate the desired change and continuous ‹stirring› is
therefore desirable. Heating is, as a rule, also to be desired for
very insoluble precipitates, as it will, in the majority of cases,
facilitate the solution of the undesirable, finer crystals.

In conclusion, these considerations will also indicate the
precautions to be observed in the precipitation of difficultly
soluble substances. If this is not properly carried out, endless
trouble in [p125] the analytical laboratory results. Except when
heating is, for some special reason, undesirable—as inducing a
chemical change (like hydrolysis) that is not wanted—solutions are
brought to the boiling-point, and ‹the precipitant added drop by
drop›, in order not to supersaturate the solution too strongly.
The solution is thus allowed time to deposit its excess as far as
possible on the ‹first crystals formed›, which it will do rather
than to form new, minute ones (see supersaturation, p. 121).
‹Constant stirring› is prescribed in order to bring older crystals,
as far as possible, into contact with all parts of the slightly
supersaturated solution. After the precipitation is complete, it is
usually desirable to allow the mixture to "digest" for some time, for
the reasons given above—stirring and a high temperature during the
process being desirable. (See further Chap. VIII, p. 147, ‹in regard
to the use of an excess of precipitant›.)

THE COLLOIDAL CONDITION

When a difficultly soluble substance is formed in a solution beyond
the point of saturation of the solution, the substance in question
‹separates› from the solution ‹in a new phase›, according to the
principles just laid down. Ordinarily, if the substance is a solid,
a ‹precipitate› is formed; if a gas, a gas escapes; if a liquid, a
liquid separates out, which is immiscible with the solution in which
it is formed. Occasionally, the condition of supersaturation which
precedes the separation is somewhat persistent, but this resistance
to the separation of the phase may be overcome by vigorous agitation
of the solution or, as in the case of supersaturation with a
crystallizable salt, by inoculation of the solution with a particle
of the new phase (p. 123).

Under certain conditions, however, a difficultly soluble substance
may be produced in a solution, in a concentration far beyond its
solubility, ‹without the separation of a precipitate› (evolution
of a gas or formation of a separate liquid) ‹and also without the
formation of a supersaturated solution›. Thus, when hydrogen sulphide
is passed into an aqueous solution of arsenious oxide, the liquid
acquires the yellow to orange color of ‹arsenious sulphide› and
becomes opalescent. But no ‹precipitate› is seen (‹exp.›), in spite
of the fact that the sulphide is extremely insoluble and is formed
practically quantitatively according to the equation As_{2}O_{3} +
3 H_{2}S ⇄ As_{2}S_{3} + 3 H_{2}O. The orange liquid passes through
a [p126] filter unchanged (‹exp.›). But if some hydrochloric acid
or a salt (‹e.g.› sodium chloride) solution is added to a portion of
it, a heavy precipitate of arsenious sulphide is immediately produced
(‹exp.›); its quantity is a good indication of the great amount of
sulphide that is ‹not› precipitated before the addition of the acid
or salt. If some pure arsenic sulphide (solid) is added to another
portion of the orange liquid, in order to overcome any possible
condition of supersaturation, the liquid is found to remain clear
(but opalescent), excepting for the few particles of added sulphide
(‹exp.›); even when it is vigorously shaken (‹exp.›), or allowed
to stand for days, no precipitate is formed. We are therefore not
dealing with a case of supersaturation.

A liquid, in which a very insoluble substance appears thus to be in
solution far beyond its usual degree of solubility, and yet does
not show at all the behavior of a supersaturated solution, is said
to contain the substance in the «colloidal condition». After a few
more instances of the colloidal condition have been presented, the
significance of the condition and the meaning of the term used to
designate it will be explained.

 «Colloidal Gold.»—When a solution of gold chloride[234] is treated
 with a solution of stannous chloride which contains a little stannic
 chloride,[235] a purple-red, flocculent precipitate—the "purple of
 Cassius"—is formed; in extremely dilute solutions only a purple-red
 liquid[236] may be produced. If the precipitate is collected on a
 filter, washed with water and then treated, on the filter, with a
 few drops of ammonium hydroxide solution and some water (‹exp.›),
 it is seen to ‹dissolve› and a beautifully colored liquid, of
 purple-red or claret-red tint, is found to pass through the filter.
 In spite of the extreme insolubility of metallic gold, the red
 ammoniacal solution (as well as the first red precipitate) contains
 «metallic gold», in the colloidal condition, formed according to
 the equation[237] 2 Au^{3+} + 3 Sn^{2+} ⥂ 2 Au + 3 Sn^{4+}. By the
 careful [p127] reduction of gold chloride with phosphorus,[238]
 or with formaldehyde in dilute, slightly alkaline solution,[239]
 brilliant red liquids, containing metallic gold in the colloidal
 condition, may be prepared, which remain clear for months. The
 passage of an electric current, in the form of an arc, between two
 gold points under pure water produces similar red liquids[240]
 containing metallic gold.

 «Colloidal Silver.»—Further, although silver is likewise an
 extremely insoluble metal, solid preparations of silver are known
 which, on treatment with water, form apparently perfectly clear
 (opalescent) liquids or solutions (‹exp.›).[241] From these silver
 is not deposited, even in the course of months. If a little of the
 black solid is heated on the lid of a porcelain crucible, the metal
 may be readily recognized by its white color and luster.[242]

«Colloidal Ferric Hydroxide.»—Further, if to a solution of ferric
chloride an excess of ammonium hydroxide is added, the well-known,
rust-red precipitate of very difficultly soluble ferric hydroxide
is formed: FeCl_{3} + 3 NH_{4}OH ⥂ Fe(OH)_{3} ↓ + 3 NH_{4}Cl.
The precipitate is so insoluble that it is a favorable form for
precipitating the ferric-ion in quantitative analysis. If, however,
a solution of ferric chloride be carefully neutralized with
ammonium carbonate[243] and be then placed in a vessel (called a
dialyzer), in such a way that it is separated, by an animal membrane
or by parchment, from pure water, ferric hydroxide is obtained
in an apparently soluble form. The ammonium chloride, as well as
hydrochloric acid which is formed by the decomposition of the
chloride by water (FeCl_{3} + 3 HOH ⇄ Fe(OH)_{3} + 3 HCl, see Chapter
X), are found to pass through the membrane readily, while the ferric
hydroxide produced does not pass through such [p128] membranes[244]
and is retained in the dialyzer ‹without forming a precipitate›.
The acid and salt pass through such membranes in either direction,
indeed, but flow mainly from their solutions of higher concentration
to those of lower concentration. The water on the outside of the
dialyzer is, therefore, continuously renewed, in order to insure a
concentration of these substances on the outside of the dialyzer
lower than that within it. As the hydrochloric acid is thus removed
through the membrane, the condition of equilibrium between the ferric
chloride, water, ferric hydroxide and acid is continuously disturbed
and, in the reversible reaction, expressed in the above equation, the
action is carried more and more towards the right, and more and more
ferric hydroxide is formed. The salt is, at last, practically all
decomposed and a ‹clear red opalescent liquid, which contains ferric
hydroxide in enormous excess beyond its solubility in water›, is left
in the dialyzer.

Exactly as in the case of the other liquids discussed above, in which
very insoluble substances appear to be in solution far beyond their
usual degree of solubility, so the present liquid does not show the
behavior of a supersaturated solution and it is ‹said to contain the
ferric hydroxide in the› «colloidal condition».[245]

«Solution Theory of the Colloidal Condition.»—For many years the
belief was prevalent among chemists that these liquids represent true
solutions of difficultly soluble substances, in the form of soluble
(colloidal) ‹modifications› of the substances. Like ordinary [p129]
solutions, the liquids are found, indeed, to show a certain ‹osmotic
pressure›, but, unlike ordinary solutions, the osmotic pressure is
exceedingly small in proportion to the quantity of the substance
present. Since the osmotic pressure is proportional to the number
of molecules in unit volume (Chap. II), this observation proved the
presence of a relatively very small number of molecules in solution,
and chemists were led to assign, therefore, a relatively very great
weight to each. Hence, the data led to the assumption that the
colloidal modifications consist of molecules of very large, sometimes
enormous molecular weight. From the fact that colloids are unable to
traverse membranes, through which crystalloids readily pass, Graham
had reached the same conclusion.

The following measurements of osmotic pressures may be given:[246]

                                Osmotic
  Substance.   Concentration   Pressure.
                 Per cent.      Cm. Hg.
  Gum arabic        1             6.9
  Dextrin           1            16.6
  As_{2}S_{3}       4             1.7
  Fe(OH)_{3}        1.1           0.8
                    2.0           2.8
                    3.0           5.6
                    5.3          12.5
                    8.9          22.6

 The last results, obtained with special care to exclude soluble
 impurities, are more reliable than the older results on gum arabic
 and dextrin. For the purpose of comparison it may be said that a
 1% solution of cane sugar (molecular weight = 342) has an osmotic
 pressure of 53 cm. Hg at 18°, a 5% solution a pressure of 265 cm.

«The Suspension Theory of the Colloidal Condition.»—On the other
hand, a number of chemists considered the colloidal liquids to
represent, essentially, ‹suspensions of minute solid particles›[247]
in an extreme state of subdivision, or, in some instances, perfect
[p130] emulsions of difficultly miscible liquids.[248] Observations
with the ultramicroscope[249] finally proved,[250] beyond question,
the correctness of this theory of the colloidal condition. Thus,
the colloidal "solutions" of gold are seen to contain minute solid
particles of gold, the diameter of which varies[251] between
(approximately) 60 µµ and 6 µµ and the color of which varies with
their size. Still finer subdivisions, the diameter of whose particles
cannot be measured, are also found to exist. Colloidal silver,
platinum, arsenious sulphide and other colloidal metals and sulphides
have also been shown, in the same way, to be suspensions of solid
particles.

«The General Character and the Definition of the Colloidal
Condition.»—Recent investigations have shown that the colloidal
condition is possible, not only for a limited class of substances,
but is, in general, possible for all substances.[252] Thus, even such
an eminently crystallizable, readily soluble (in water) substance
as sodium chloride may be obtained, under certain conditions, in
colloidal suspension in benzene,[253] in which it is insoluble.

For our purposes it will be sufficient to define the colloidal
condition, on the basis of these results, as the condition of an
insoluble substance in which, as far as ordinary observation and the
common methods for separation of heterogeneous phases (filtration,
sedimentation, etc.) are concerned, ‹the substance appears to be
present in a homogeneous clear solution›, whereas ‹in reality› it is
present in a ‹heterogeneous mixture›. An extremely finely divided
solid suspended in a liquid, or an emulsified liquid suspended in
another liquid, are the most common types[254] of such mixtures.
[p131]

«Relations to Analysis.»—Since the colloidal condition of insoluble
substances interferes with the precipitation of the latter, and
with their separation by filtration from the liquids in which
they are suspended, and since the majority of the separations and
tests of analytical chemistry depend on the successful formation
of precipitates and on their successful separation by filtration,
analytical chemistry is primarily[255] concerned with the colloidal
condition as a condition that is to be ‹avoided as completely as
possible› in order to escape error. In other fields of chemistry,
notably in physiological chemistry and in some branches of technical
chemistry, it is a source of effects so momentous and specific that
a new branch of chemistry, the chemistry of colloids,[256] has grown
out of the investigations of its relations and laws. The present
discussion will be limited to the presentation of such of the
fundamental facts concerning the colloidal condition as are of chief
importance in analytical work.[257]

«Electrical Conditions of Colloids.»—One of the most important
discoveries made on colloids is the observation that the suspended
particles of a large class of colloids carry electrical charges,
so that there is a potential difference between the particles
and the liquid in which the suspension exists.[258] Thus, in the
colloidal suspension of arsenious sulphide (prepared as described
on p. 125) the ‹sulphide particles› carry ‹negative› charges, and
the solution bathing them is ‹positive›. Conversely, colloidal
‹ferric hydroxide› (p. 127), in water, is charged with ‹positive›,
the water with ‹negative›, electricity. The existence and character
of these charges may be readily demonstrated by the passage of a
current of electricity through the colloidal suspension in U tubes
(‹exp.›).[259] Colloidal arsenious sulphide is found to migrate
toward the positive pole, ferric hydroxide [p132] to the negative
pole, the movement being easily followed by the color of the
suspended particles.

The following colloids, which are of interest in analytical
chemistry, are found to carry a ‹negative› charge in pure water:
Colloidal ‹acids› (silicic, stannic), ‹sulphides› (As_{2}S_{3},
As_{2}S_{5}, CdS, etc.), ‹salts› (AgI, AgCl) and ‹metals› (Au, Pt,
Ag). It is noteworthy that the suspensions of finely divided clay,
kaolin, quartz, carbon, carry the same charge as these colloidal
suspensions. On the other hand, ‹metal hydroxides› (ferric,
aluminium, chromic), and ‹basic› substances in general, carry
‹positive› charges.

On the other hand, the colloids of one important group are found
to be almost without any electric charges;[260] the passage of
an electric current through their suspensions has little or no
effect on them. Perfectly neutral albumen and gelatine are common
representatives of this group.

 The charge on a colloid seems to be liable to variation with the
 nature of the liquid in which it is suspended. Colloidal platinum in
 water is negative, in a mixture of water and alcohol, positive.[2]
 Of peculiar interest and importance is the fact that some colloids
 ‹change› the ‹character› of their ‹charge› when the liquid, in which
 they are suspended, is made to pass from an ‹acid› to an ‹alkaline›
 condition, and ‹vice versa›.[261] For instance, albumen[262],
 colloidal silicic acid[263] and colloidal stannic acid[264] are
 negative in alkaline liquids, positive in acid. The relation of
 these facts to the chemical nature of the substances will be
 discussed presently.

 «The Source of the Electrical Charges on Colloids.»—Different
 views are held as to the source of electrification of colloidal
 suspensions. Only the two views of most direct interest in analysis
 can be considered here. In the first place, it is possible that
 ‹partial ionization› of the colloidal suspension produces the
 electrical charge. It is a significant fact that ‹basic colloids›
 (metal hydroxides, some basic dyes) receive a ‹positive› charge,
 such as would be left, if they were slightly ionized as bases
 (or salts of bases) and insoluble (suspended) [p133] ‹positive
 ions were retained by the particles›. That would be the case,
 for instance, if particles of colloidal ferric hydroxide,
 [Fe(OH)_{3}]_{‹x›}, sent a few hydroxide ions into solution and
 the suspended particles included positive insoluble ions. ‹Acid›
 colloids, on the other hand, assume a ‹negative› charge, as would
 be expected from this point of view. Then, the behavior of silicic
 acid is particularly suggestive; in alkaline or ‹slightly› acid
 liquids, in which its ‹ionization as a weak acid› is favored or
 predominant (Chapter X), it carries a ‹negative› charge, the charge
 that would be left on it, if it ionized, in part, as an acid or
 its salt. Silicic acid shows some slight tendency to ionize also
 as a base (see Chapter X) and the basic form of ionization would
 be favored by the presence of a strong acid (Chapter X). Colloidal
 silicic acid, as stated above, ‹changes its charge› from negative
 to positive as the solution passes from an alkaline to a (strong)
 acid reaction,[265] just as if, in the acid liquid, it ionized
 slightly as a base (salt of a base) and ‹retained a difficultly
 soluble positive ion›. Albumen, which has the property of being both
 a base and an acid,[266] shows the same change of charge[267] in the
 colloidal condition and the change has been ascribed[268] to the
 change of basic and acid functions.

 According to the other of the two theories, here considered, the
 electrification of the colloid may result from what is known as
 contact or surface electricity.[269] At the surface of two different
 substances there is always a potential difference.[270] In the
 case of finely divided suspensions, like the colloids, the contact
 surfaces are enormous, as compared with the surfaces involved in
 ordinary contact. Whether metals (Au, Pt, Ag) owe their charges to
 simple contact effects or to their (minimal) tendency to ionize
 (Chapters XIV and XV) is not known. In fact, no exact knowledge of
 the source of electrification of any colloid has yet been obtained.

«Precipitation of Colloids by Electrolytes and by
Colloids.»—Substances in the colloidal condition, ‹which carry
an electrical charge›, are readily precipitated by the addition
of electrolytes to the colloidal suspensions (see the behavior
of arsenious sulphide, p. 126). Negatively charged colloids are
precipitated by the action of positive ions, positively charged
colloids by the action of negative ions (Hardy's rule[271]).
The precipitated colloid carries [p134] with it a part of the
precipitating ion[272] (‹adsorption›) and the weights of ions,
carried down by a given quantity of a given colloid, are proportional
to the equivalent weights of the ions.[273] The precipitation thus
appears to be intimately associated with the neutralization of the
charge on the colloid. In accordance with this conclusion, it has
also been found that a colloid may be precipitated by a colloid
carrying the opposite charge.[274] Thus, colloidal arsenious
sulphide, carrying a negative charge, and colloidal ferric hydroxide,
carrying a positive charge, mutually precipitate each other
(‹exp.›[275]).

 The purple precipitate (‹purple of Cassius›), which is formed when
 stannous chloride is added to gold chloride (p. 126), contains
 ‹colloidal gold›,[276] which, in suspension, is charged with
 negative electricity, and ‹colloidal stannic acid›,[276] which in
 acid solution, presumably, carries a positive charge[277]: these
 two colloids mutually precipitate each other in the presence of
 hydrochloric acid.[278]

 When the precipitate is treated with an alkaline liquid (ammonium
 hydroxide solution), the charge on the stannic acid becomes
 negative, both colloids acquire the same charge and the precipitate
 dissolves, to form the beautifully tinted suspensions of colloidal
 gold (p. 126). In this condition the colloids (gold and stannic
 acid) are sensitive to precipitating electrolytes, and the solution
 is more sensitive to a mixture of magnesium nitrate and ammonium
 nitrate than to ammonium nitrate alone (‹exp.›), as is to be
 expected from a ‹negative› suspension (see below).

 The characteristic difference in behavior between ‹ortho-›,
 ‹pyro-› and ‹metaphosphoric acids› toward albumen, which is used
 as a characteristic analytical test to distinguish metaphosphoric
 acid from the other two acids,[279] appears to be due to similar
 relations[280]: metaphosphoric acid, which precipitates (coagulates)
 albumen, is colloidal, ortho- and pyrophosphoric acids are not.
 The [p135] coagulation seems to be the result of the union of
 the ‹negative colloid› metaphosphoric acid (or a complex negative
 colloidal ion thereof) with the ‹positive colloid› albumen (or a
 positive colloidal ion thereof).

«The Precipitating Power of Electrolytes and the Valence of their
Ions.»—The complete precipitation of colloids, which carry electric
charges, depends on the concentrations of the colloid and the
electrolyte; in this connection the important observation has been
made that the ‹precipitating power› of electrolytes ‹increases
decidedly with the valence of the precipitating ions› (H. Schulze's
rule[281]). Bivalent ions are far more efficient than univalent;
trivalent, in turn, still more effective than bivalent.

 Thus, colloidal As_{2}S_{3}, carrying a negative charge, is
 precipitated by the positive ions of added electrolytes.
 The addition of a few drops of a molar solution of ammonium
 nitrate (the precipitating ion is NH_{4}^{+}) to 20 c.c. of the
 colloidal suspension[282] produces a slight precipitate; complete
 precipitation requires 3.5 to 3.6 c.c. of the ammonium nitrate
 solution.[283] Only 0.06 c.c. of an equivalent solution[284] of
 magnesium nitrate (the precipitating ion is Mg^{2+}) is required,
 and as little as 0.015 c.c. of an equivalent solution of aluminium
 nitrate[285] (the precipitating ion is Al^{3+}) has the same effect
 (‹exp.›). An increase in valence of the ‹negative› ion, which is
 not the precipitating ion in this case, does not affect the result
 appreciably: 3.5 c.c. of a solution[286] of ammonium sulphate,
 (NH_{4})_{2}SO_{4}, equivalent to the solution of NH_{4}NO_{3},
 is also required for the complete precipitation of the colloidal
 As_{2}S_{3} (‹exp.›), although the one contains the univalent ion,
 NO_{3}^{−}, the other the bivalent ion, SO_{4}^{2−}.

 Conversely, a ‹positively› charged colloid, like ferric hydroxide,
 may be precipitated by much smaller quantities[287] of bivalent
 negative ions than of univalent ions, etc. [p136]

«Nonprecipitation of Nonelectrified Colloids by
Electrolytes.»—Colloids which do not carry any electric charges of
moment (see p. 132) are also not precipitated by dilute solutions
of electrolytes. Heat, the addition of concentrated salt solutions
in great excess (whose effect is probably a dehydrating one), or of
other solvents (‹e.g.› alcohol), are the agents most commonly used to
effect coagulation in such cases.

«Protective Action of Colloids on Other Colloids.»—Colloids,
particularly such as are not sensitive to precipitation by
electrolytes, increase in a remarkable degree the stability of the
colloidal condition of substances, that carry electrical charges
and, ordinarily, would be very sensitive to precipitation. Thus,
small quantities of albumen are used to render colloidal silver
preparations more stable. Tannic acid, gelatine and albumen and
related compounds are frequently used as such protective agents. It
is supposed that they form protecting films around the colloidal
particles.

«Applications in Analysis.»—From the preceding discussion we may now
draw the following conclusions concerning the consideration that is
to be given to the colloidal condition as a factor in qualitative
analysis. The ‹absence of electrolytes› in solution must favor the
production of the colloidal condition, which would result in the
nonprecipitation or "solution" and ‹consequent loss of› substances,
which it is intended to precipitate. Such absence of electrolytes
in solution is most likely to be met with, in the first place,
in the ‹washing› out of ‹precipitates›. When the larger part of
the mother liquor is washed away by the use of pure water, many
precipitates show a tendency to "run through a filter," forming
colloidal suspensions in the pure water in the filter and being
again precipitated as the colloid mixes with the electrolytes in the
filtrate. Precipitates, showing this tendency to assume the colloidal
condition, are therefore washed with appropriate solutions of
electrolytes, rather than with pure water. Ammonium nitrate solution
is most frequently available in qualitative analysis, because
neither the ammonium-ion nor the nitrate-ion tends to interfere with
the subsequent examination of the solution. When chloride-ion is
not likely to interfere, ammonium chloride may be used. Thus, the
sulphides of the arsenic, copper and zinc groups are washed with
solutions containing ammonium nitrate (the [p137] chloride may be
used for the zinc group[288]) rather than with pure water (or pure
hydrogen sulphide water[288]). In quantitative analysis, aluminium
hydroxide is also washed with ammonium nitrate solution, silver
chloride with acidulated (nitric acid) water, lead sulphate with
dilute sulphuric acid, etc.

In the second place, if precipitations are attempted either in
rather dilute solutions or in solutions of little ionized substances
(arsenious acid and hydrogen sulphide), the addition of an
electrolyte is frequently required ‹to insure precipitation›. Thus,
the presence of ammonium chloride, or nitrate, in excess, is helpful
in the precipitation of the sulphides of the zinc group; the addition
of hydrochloric acid (or other electrolyte) is required to effect the
precipitation of arsenious sulphide from a solution of the oxide (p.
126).

In the next place, account must be taken, in analytical work, of the
fact that ‹colloids carry down› with them the ‹precipitating ion›
by which they are coagulated, a fact which may lead to the ‹loss of
ions› which, it is intended, should be kept in solution. To a certain
extent, this loss may also be avoided by insuring the presence of
electrolytes (acids, ammonium salts) in sufficient concentration
to cause the coagulation without the aid of the ions which, it is
intended, should not be precipitated. In view of the much weaker
precipitating power of univalent ions (of hydrochloric acid, ammonium
nitrate and chloride), as compared with that of polyvalent ions,
which may be present, the acid and ammonium salts must not be used in
too small concentrations. In quantitative analysis, when conditions
permit it, ammonium or sodium sulphate is frequently substituted for
the ammonium salts of the univalent monobasic acids. The washing
of the precipitated colloid with such salt solutions gradually
removes[289] the ions which are precipitated with the colloid and
forms a further safeguard against their loss. But this source of
loss is avoided only with great difficulty and is seldom absolutely
removed.

Finally, the presence of ‹protective colloids›, especially of the
[p138] gelatine and albumen type, may interfere so decidedly with
the common precipitation tests for ions, that ‹their destruction
is imperative›, before these tests can be applied with any degree
of confidence. Thus, the mixing of solutions (0.1 molar) of
silver nitrate and hydrochloric acid, each containing one per
cent of gelatine, fails to produce the ordinary, characteristic
precipitate[290] of silver chloride, ‹the reaction which is used to
determine the presence of the silver-ion in systematic analysis›.

 The mixture is opalescent and, in reflected light, looks
 opaque-white; on somewhat prolonged standing a white ‹milk› is
 produced, but no precipitate. When the mixture is boiled, the
 same deep white milk is formed, but no coagulated precipitate,
 the mixture running unchanged through a filter. Hydrogen sulphide
 converts the mixture into a similar suspension of the black
 sulphide.


  FOOTNOTES:

  [227] The ratio is affected somewhat by the fineness of division
  of liquids and solids as a result of surface tension phenomena, as
  explained below.

  [228] An aqueous solution of iodine and potassium iodide shaken
  with chloroform gives similar results, and the difference in color
  between the two layers is an advantage for a lecture experiment.
  But the iodine is partially combined with the iodide, according
  to KI + I_{2} ⇄ KI_{3}, or I^{−} + I_{2} ⇄ I_{3}^{−}, and the
  theoretical relations are not so simple as for bromine in aqueous
  and chloroform solutions.

  [229] To accelerate the action, the mixture is shaken vigorously.
  After the separation of the layers, the bromine may be recognized
  in the aqueous layer by its color, or by the addition of potassium
  iodide (liberation of iodine).

  [230] [Br]_{aq.} and [Br]_{ch.} are used to express the actual
  concentrations at any given moment we wish to consider, for
  instance at the moment equilibrium is reached. The ratio
  ‹k›_{2} / ‹k›_{1} for any substance S is found to be equal to the
  ratio of the ‹solubilities› of the substance in the two solvents.
  That it must be so can be proved by applying the law of physical
  equilibrium to the mixed solvents in contact with an excess of the
  substance, ‹i.e.› to its ‹saturated› solutions (see below).

  [231] Similar relations hold for the condition of equilibrium
  between a liquid and its vapor.

  [232] Curie, ‹Bull. Soc. Min.›, «8», 145 (1885); Ostwald,
  ‹Grundlagen der Anal. Chem.›, p. 22 (1894).

  [233] Hulett, ‹Z. Phys. Chem.›, «37», 384 (1901). See also Ostwald,
  ‹ibid.›, «34», 495 (1900), on the solubilities of finely divided
  mercuric oxide ("yellow oxide") and of larger crystals ("red
  oxide").

  [234] A 1 / 1000 solution of AuCl_{3}, 2 aq., and a 1.2 / 1000
  solution of SnCl_{2}, 2 aq., may be used conveniently. When equal
  volumes of the solutions are mixed, the desired precipitate is
  formed.

  [235] Stannous chloride is usually sufficiently contaminated with
  stannic salt. Add a few drops of bromine- or chlorine-water to 100
  c.c. of a ‹pure› stannous chloride solution.

  [236] The action is an exceedingly sensitive qualitative ‹test
  for gold›. By a modification of the test Donau was able to detect
  as little as 2E−9 gram of gold (‹Monatshefte f. Chem.›, «25», 545
  (1904)).

  [237] The nature of the reduction reaction is discussed in Chapters
  XIV and XV.

  [238] Faraday, ‹Proc. Royal Soc.›, «8», 356 (1857), ‹Phil. Mag.›
  (4), «13», 401 (1857) (Stud.).

  [239] Zsigmondy, ‹Liebig's Annalen›, «301», 30 (1898).

  [240] Bredig, ‹Z. f. Elektrochem.›, «4», 514, 547 (1898), and
  ‹Anorganische Fermente›, 1901. Colloidal preparations of platinum,
  silver and many other metals may be prepared in the same way. In
  ether, colloidal preparations of the alkali metals may be made
  (Svedberg, ‹Ber. d. chem. Ges.›, «38», 3616 (1905), «39», 1708
  (1906)).

  [241] ‹Argentum Credé› may be conveniently used. It contains, with
  the metallic silver, a small percentage of albumen, which is added
  for reasons discussed below. Brown solutions are formed at once.

  [242] First a thin ‹film of› black ‹carbon› is produced ‹round the
  metal›, then the latter appears in the form of a filigree of silver.

  [243] For details of the preparation, see A. A. Noyes, ‹J. Amer.
  Chem. Soc.›, «27», 94 (1905).

  [244] This process of separation of substances, which do not pass
  through membranes, from such as do, is called ‹dialysis›. It was
  first used by Graham, ‹Trans. Royal Soc.›, London, «151», 183–224
  (1861) («Stud.»).

  [245] Graham made the first extended investigations in this field:
  ‹Trans. Royal Soc.›, «151», 183 (1861); ‹J. Chem. Soc.› (London),
  «17», 318 (1864) («Stud.»). He found that amorphous, gelatinous
  bodies like ferric hydroxide, aluminium hydroxide, silicic acid,
  gelatine, glue, dextrin, caramel, albumen and similar bodies do
  not pass through membranes and may be obtained by dialysis in the
  ‹colloidal› condition. Such substances were called "colloids" by
  Graham, the name referring to the Latin for gelatine. Substances
  which pass through membranes readily were found by Graham to
  resemble in behavior such bodies as are crystallizable when solid;
  such compounds were classified by him as "crystalloids." That
  liquids containing substances in the colloidal condition (‹e.g.›
  arsenious sulphide, gold, silver and many other substances) may be
  prepared by methods other than dialysis, was found later by many
  investigators and, in a few cases, previous to Graham, ‹e.g.› by
  Faraday, ‹loc. cit.› A brief history of the chemistry of colloids
  is found as an introduction to Wo. Ostwald's ‹Kolloidchemie›, pp.
  1–63 (1909).

  [246] ‹Cf.› Wo. Ostwald, ‹loc. cit.›, p. 193.

  [247] Before Graham's time, and for the few colloidal liquids then
  known, this view was held by such men as J. B. Richter, Berzelius
  and Faraday (‹loc. cit.›) (‹cf.› Wo. Ostwald, ‹loc. cit.›, p. 19).
  The first extended experimental investigation in support of it was
  made by Barus and Schneider, ‹Z. phys. Chem.›, «8», 278 (1891).
  Bredig was also an early and consistent champion of this view
  (‹vide› his ‹Anorganische Fermente›, 1901).

  [248] ‹Cf.› Wo. Ostwald, ‹loc. cit.›, pp. 102–114. Graham
  considered "colloidal silicic acid a liquid miscible with water in
  all proportions." According to modern ideas, no true miscibility
  exists, but a suspension or emulsion is formed (see Ostwald, p.
  237).

  [249] Siedentopf and Zsigmondy, ‹Drude's Annalen›, «10», 1 (1903).
  Zsigmondy, ‹Colloids and the Ultramicroscope› (1909), Chapter V.

  [250] Zsigmondy, ‹Z. für Elektrochem.›, «8», 684 (1902); Siedentopf
  and Zsigmondy, ‹loc. cit.›

  [251] Zsigmondy, ‹loc. cit.›, p. 161. A µµ is 1E−6 mm. The hydrogen
  molecule is considered to have a diameter of 0.1 µµ (O. E. Meyer),
  the alcohol molecule one of 0.5 µµ (Zsigmondy, ‹loc. cit.›, plate
  IV, p. 157).

  [252] Weimarn, ‹Chem. Zentralblatt›, 1907, II, p. 1293.

  [253] Paal, ‹Ber. d. chem. Ges.›, «39», 1436, 2859 (1906).

  [254] Other varieties of heterogeneous colloidal mixtures are
  tabulated by Wo. Ostwald, ‹loc. cit.›, p. 96.

  [255] The "Cassius' purple" test for gold is an instance where the
  colloidal condition is used in analysis for a positive test. See
  Wo. Ostwald, ‹loc. cit.›, p. 68, for other, similar applications
  for positive tests.

  [256] ‹Vide› Wo. Ostwald's ‹Kolloidchemie›, 1909, and the
  references given by Noyes, ‹loc. cit.›, p. 86.

  [257] A general discussion of the preparation and properties of
  colloidal mixtures is given by A. A. Noyes, ‹J. Am. Chem. Soc.›,
  «27», 86–104 (1905) («Stud.»).

  [258] Picton and Linder, ‹J. Chem. Soc.› (London), «61», 160
  (1892), «67», 63 (1895), «71», 568 (1897), etc., and others. Wo.
  Ostwald, ‹loc. cit.›, p. 240, gives a list of references.

  [259] The arrangement of the experiment is described by Noyes,
  ‹loc. cit.›, p. 98.

  [260] ‹Cf.› Wo. Ostwald, ‹loc. cit.›, p. 108. Billitzer has found
  that gelatine is positive in acid solution, negative in alkaline,
  ‹Z. phys. Chem.›, «51», 147 (1905). The charges are, however,
  relatively small ones.

  [261] Billitzer, ‹Z. f. Elektrochem.›, «8», 638 (1902). This
  is probably true of all amphoteric colloids (Chapter X); it is
  also true of many other substances, which are not pronouncedly
  amphoteric. (‹Cf.› Perrin, ‹Comp. rend.›, «136», 1388 (1903);
  Billitzer, ‹Z. phys. Chem.›, «51», 157 (1905).)

  [262] Hardy, ‹J. of Physiology›, 24, 288 (1899); ‹Z. phys. Chem.›,
  «33», 387 (1900).

  [263] Billitzer, ‹loc. cit.›, p. 159; Müller's ‹Allgemeine Chemie
  der Kolloide›, 1907, p. 79.

  [264] See below, p. 134.

  [265] In a slightly acid solution colloidal silicic acid is
  negatively charged; in a ‹strong› acid solution, positively—a
  relation which agrees with its ‹predominantly acid character›.

  [266] The general class of substances, showing both basic and acid
  properties, of which albumen is a derivative, is described in a
  footnote on glycocoll, Chapter X, p. 188.

  [267] Hardy, ‹loc. cit.›

  [268] J. Loeb, University of California Publications, ‹Physiology›,
  «2», 149 (1904).

  [269] Very little is known about the nature of contact electricity.
  It is even doubtful whether it is different, in principle, from
  ionization.

  [270] W. Ostwald, Lehrbuch der Chem., «2», (1) 553 (1903).

  [271] Hardy, ‹Proc. Royal Soc.›, «66», 110 (1899); ‹Z. phys.
  Chem.›, «33», 391 (1900).

  [272] Picton and Linder, ‹J. Chem. Soc.› (London), «67», 63 (1895).

  [273] Whitney and Ober, ‹J. Am. Chem. Soc.›, «23», 852–856 (1901)
  (Stud.).

  [274] Picton and Linder, ‹loc. cit.› «71», 572 (1897); Lottermoser,
  ‹Anorganische Kolloide›, p. 76; Biltz, ‹Ber. d. chem. Ges.›, «37»,
  1095 (1904).

  [275] Precipitation is complete only when the colloids are used
  in the proportions required to neutralize each other's charges
  [Billitzer, ‹Z. phys. Chem›., «51», 140 (1905)]. The proportions
  to be used must be determined in each case, most simply by trial
  (Noyes, ‹loc. cit.›, p. 101), but quantitative methods for
  determining the charges, by titration, are also known (‹cf.›
  Billitzer, ‹loc. cit.›).

  [276] E. A. Schneider, ‹Z. anorg. Chem.›, «5», 80 (1894).

  [277] See the above discussion on silicic acid. Stannic acid has a
  greater tendency to form a base than has silicic acid.

  [278] Zsigmondy, ‹Liebig's Annalen›, «301», 361 (1898).

  [279] ‹Cf.› Fresenius, p. 334, or Smith's ‹Inorganic Chemistry›, p.
  468.

  [280] Mylius, ‹Ber. d. chem. Ges.›, «36», 775 (1903); Biltz,
  ‹ibid.›, «37», 1116 (1904).

  [281] ‹J. für prakt. Chem.›, «25», 431 (1882).

  [282] The suspension used is prepared by saturating, with hydrogen
  sulphide, an aqueous solution of arsenious oxide. The latter is
  saturated on a steam bath, cooled to 20°, filtered and diluted with
  an equal volume of water before it is used.

  [283] Eight grams of NH_{4}NO_{3} per 100 c.c.

  [284] 0.6 c.c. of a ‹tenth›-normal solution is used, containing
  1.28 gram Mg(NO_{3})_{2}, 6 aq., in 100 c.c. Precipitation was
  found to be incomplete with 0.5 c.c.

  [285] 0.15 c.c. of a ‹tenth›-normal solution is used, containing
  1.2 gram Al(NO_{3})_{3}, 4 aq., in 100 c.c. Precipitation was found
  to be incomplete with 0.1 c.c. of the solution.

  [286] 3.3 grams (NH_{4})_{2}SO_{4} in 100 c.c.

  [287] Freundlich found, for instance, that NaCl, KCl, BaCl_{2},
  in equivalent concentrations, had practically the same effect on
  colloidal ferric hydroxide, but only ‹one-fortieth› as much of a
  ‹sulphate› (the precipitating ion is SO_{4}^{2−} versus Cl^{−}) was
  required; ‹Z. phys. Chem.›, «44», 129 (1903).

  [288] For other reasons (‹e.g.› to prevent oxidation of the
  sulphides), hydrogen sulphide is also used in the solution for
  washing the arsenic group, and ammonium sulphide in that for the
  zinc group (see Lab. Manual, pp. 101 and 110).

  [289] Picton and Linder, ‹loc. cit.›, and Whitney and Ober, ‹loc.
  cit.›

  [290] A. A. Noyes describes a similar experiment with sodium
  chloride and silver nitrate, ‹loc. cit.›

[p139]




 CHAPTER VIII

 «SIMULTANEOUS CHEMICAL AND PHYSICAL EQUILIBRIUM.—THE SOLUBILITY- OR
 ION-PRODUCT.»


It frequently happens that we have to deal, simultaneously, with
conditions of chemical and of physical equilibrium, obtaining in the
same system. For instance, a gas like carbon dioxide, in contact
with its saturated solution in water, is in equilibrium with the
dissolved carbon dioxide, and this, in turn, is in equilibrium with
its hydrate, carbonic acid. A substance may be distributed between
two solvents and show a different molecular weight in the two (see
p. 18); it may exist, in the one, primarily in polymeric form, and
only to a slight extent in the simple form, the two forms being
in equilibrium (chemical equilibrium). In the other solvent, it
may exist only in its simple molecular form, and this will be in
equilibrium with the same simple molecular form in the first solvent
(physical equilibrium). In matters dealing with the solubility
of electrolytes in water, and, therefore, in questions of their
‹precipitation› or ‹solution›, such simultaneous conditions of
chemical and physical equilibrium are constantly occurring. Since
qualitative analysis deals to a very considerable extent with just
such precipitates of salts, acids and bases, these cases are of
particular importance to us.

«Earlier Derivation of the Solubility-Product Principle.»—A very
simple relation was derived by Nernst[291] for the combined
conditions of chemical and of physical equilibrium, where difficultly
soluble electrolytes (precipitates) were concerned. We shall develop
the relation first for a simple salt, such as silver acetate.

When water is added to solid silver acetate, the salt will dissolve.
If an excess of the acetate is used, equilibrium will result between
the solid salt and its solution, when the solution is saturated at
the temperature used. As the salt dissolves, it is more or less
ionized, and in the saturated solution we have a [p140] condition of
chemical equilibrium between the salt and its ions:

 CH_{3}COOAg ⇄ CH_{3}COO^{−} + Ag^{+}.                             (1)

If the law of chemical equilibrium is applied to this reversible
action, we have (p. 98)

 [CH_{3}COO^{−}] × [Ag^{+}] / [CH_{3}COOAg] = K_{Ionization}.      I

The nonionized silver acetate is present in two phases, in the solid
phase and also in solution:

 CH_{3}COOAg ↓ ⇄ CH_{3}COOAg.                                      (2)

Applying the law of physical equilibrium to this system, we have
further (p. 121)

 [CH_{3}COOAg] / [CH_{3}COOAg]_{solid} = K.                         II

The concentration of a pure solid, as we have seen, may be considered
a constant at a given temperature. Consequently, if we consider the
question of the size of the solid particles as a minor factor and
negligible, we shall conclude, that, for saturated solutions of
silver acetate, the concentration of the solid silver acetate being
a constant, the concentration of the nonionized or molecular silver
acetate, the first term of our constant ratio II, must also have some
definite, constant value at a given temperature. We may call this
concentration the "molecular solubility" of silver acetate and may put

 [CH_{3}COOAg] = K_{mol. sol.}                                     III

for a ‹saturated› solution of silver acetate in water at the given
temperature. Now, since the concentration of the nonionized silver
acetate, [CH_{3}COOAg], in the saturated solution also forms the
second term of equation I, representing the condition of chemical
equilibrium between the acetate and its ions, we obtain, by combining
I and III,

 [CH_{3}COO^{−}] × [Ag^{+}] = K_{Ionization} × K_{mol. sol.}
   = K_{Solubility-Product}.                                        IV

Further, if the assumption is made that the presence of foreign
electrolytes, in not too concentrated solutions, does not affect
either the molecular solubility, K_{mol. sol.}, of silver acetate
or its tendency to ionize—as expressed in K_{Ionization}—then, the
[p141] relation, which has been developed, would hold for saturated
aqueous solutions of silver acetate in the presence of foreign
electrolytes, as well as for a saturated, pure, aqueous solution.
A single, simple equation would thus express the conditions for
simultaneous chemical and physical equilibrium between a difficultly
soluble ionogen, of the type of silver acetate, and its saturated
solutions, at a given temperature, in the presence or the absence of
foreign electrolytes.

«The Solubility- or Ion-Product Principle.»—We may formulate this
important conclusion by stating, that, ‹in saturated solutions of
silver acetate, the product of the concentrations of its ions has a
constant value at a given temperature›. Analogous relations may be
developed for the saturated solutions of other difficultly soluble
ionogens. The constant has been called the ‹solubility-product
constant› or the ‹ion-product constant› of the ‹ionogen›. For salts
like lead iodide PbI_{2}, silver chromate Ag_{2}CrO_{4}, etc.,
each molecule of which forms more than one of a given ion, the
concentration of such an ion is raised, in the solubility-product,
to the power corresponding to the number of ions of this kind formed
from a single molecule of the electrolyte.[292] Thus, lead iodide
ionizes according to the equation PbI_{2} ⇄ Pb^{2+} + 2 I^{−} and,
for a saturated solution of lead iodide[293] at a given temperature,
[Pb^{2+}] × [I^{−}]^2 = K. For silver chromate, ionizing according to
the equation Ag_{2}CrO_{4} ⇄ 2 Ag^{+} + CrO_{4}^{2−}, the form of the
solubility-product equation is [Ag^{+}]^2 × [CrO_{4}^{2−}] = K. In
general, for a saturated solution of a difficultly soluble salt at a
given temperature ‹the product of the ion concentrations, each raised
to the power corresponding to the number of that kind of ion formed
from the ionization of one molecule of the salt, is a constant›.

«Criticism of the Derivation of the Principle.»—Nernst developed this
important relation in 1889, shortly after the theory of ionization
was formulated. Since then, however, the soundness of the theoretical
development, on which it was based, has been rendered open to
question in a way that could hardly have been foreseen at that
early stage in the development of the theory of ionization. In the
first place, it is known now that the ionization of easily ionizing
substances (strong electrolytes) does [p142] not conform to the
law of chemical equilibrium (‹vide› p. 108); as far as our present
knowledge goes, the ratio in equation I is not a constant, but grows
‹larger› with an increasing total concentration of good electrolytes.
In the present case, this total concentration may be increased by the
introduction of ‹foreign salts›.[294] In the second place, the second
fundamental principle used, the principle of the constant solubility
of the dissolved molecular or non-ionized salt, as expressed in
equation III, was questioned and disproved by Arrhenius in 1899. The
molecular solubility depends on the total concentration of salts in
the solution and, in general, decreases with increasing concentration
of the total dissolved salts. This result does not invalidate the law
of physical equilibrium; it merely means that the presence of salts,
especially in appreciable quantities, modifies the nature of the
solvent and changes its dissolving power, much as we have different
dissolving power shown by different pure solvents, such as water and
alcohol.

It appears, however, that while the soundness of this theoretical
development of the relations expressed by the solubility-product must
be questioned, nevertheless as a ‹matter of experiment›, the ‹product
of the ion concentrations› of a difficultly soluble salt is found,
in dilute solutions, to be a constant, or sufficiently close to a
constant to satisfy all but the most rigorous requirements.[295]

It is, in fact, quite evident, that a ‹decreasing value for the
second term of the ratio I›—namely, for [CH_{3}COOAg], the molecular
solubility of the salt—as the total concentration of the electrolytes
present increases, together with an ‹increasing value for the whole
ratio I› under the same conditions, are ‹not incompatible with a
constant value› of the first term of the ratio. That is, ‹the product
of the ion concentrations›, [CH_{3}COO^{−}] × [Ag^{+}], ‹may well
remain constant› (equation IV), or approximately constant, in dilute
salt solutions, even if equations I and III do not hold for salt
solutions. [p143]

Whether in the case of all difficultly soluble salts, as the total
salt concentration increases, the increasing values of the chemical
equilibrium ratio (equation I) will be so nicely balanced by the
decreasing values of the molecular solubility, that the first term
of the first ratio (the solubility-product) will always be constant,
is a question demanding further extended investigation.[296] The
range of the investigation must be extensive, because it must include
several other classes[297] of salts (‹e.g.› Me_{2}X, MeY_{2}, etc.),
for which the first equation has a different form; for instance, for
Me_{2}X,

 [Me^{+}]^2 × [X^{2−}] / [Me_{2}X] = K.

For the present we must remain content with the result of the
past investigations and consider the principle of the constant
solubility-product to be essentially an empirical one. It is an
extremely convenient condensation, into a very simple mathematical
form, of the main factors involved in the precipitation and solution
of difficultly soluble salts, acids, and bases. It should be used
with due knowledge of its character and limitations.

 Washburn[298] derives the principle of the constancy of the
 solubility-product, without involving in his derivation the relation
 between ions and nonionized molecules—a relation which, as was
 stated above, deviates from the law of chemical equilibrium. The
 deviation, it will be recalled (p. 109), is generally supposed to be
 due to the fact that the fundamental kinetic assumption which must
 be made to derive the law of chemical equilibrium from the kinetic
 theory, the assumption that there should be none but negligible
 forces of attraction and repulsion between the molecules (of a gas
 or solute) which are in equilibrium, is not fulfilled in the case of
 solutions of strong electrolytes (p. 109). According to Washburn,
 if it is assumed that the ‹ions› of an electrolyte fulfill this
 fundamental condition and that only the nonionized ‹molecules›
 do not—the latter causing the deviation from the law of chemical
 equilibrium—then the principle of the solubility-product constant
 follows.[299] He sees an approximate confirmation of the assumption
 made, in the fact that the principle is found, empirically, to be
 true, and that other relations, developed on the basis of the same
 assumption, agree with the observations made. [p144]

 This theoretical derivation of the principle, like the derivations
 of the law of chemical equilibrium and of all our laws of dilute
 solutions, assumes[300] that the nature of the solvent, and
 consequently of the solution-process, is not changed by added
 substances, for instance by an excess of the precipitating ionogen.
 There can be no question, however, that the nature of the solvent
 must change, as a ‹continuous function›, by the addition of
 electrolytes to solutions. The changed solubilities of inert gases
 in salt solutions,[301] and a mass of other evidence,[302] lead to
 this conclusion. The addition of a half mole of sodium chloride
 to a liter of water reduces the dissolving power of the liquid
 towards oxygen at 25° by 15%, ‹i.e.› by 30% per mole of salt. A
 weak electrolyte, such as acetic acid, has practically no effect at
 this concentration, and so the effect must be chiefly due to the
 ions of sodium chloride; since the salt, in half-molar solution,
 is ionized 73%, the reduction in the dissolving power would be
 30 / 0.73 = 41% per mole of fully ionized salt. The principle of
 the constant solubility-product cannot be considered as established
 for solutions more concentrated than 0.2 to 0.3 molar; but it is
 evident that, in any comprehensive theoretical formulation of the
 principle for the range in which it is found empirically to hold,
 the change in the nature of the solvent, which in some cases is
 conspicuous in 0.5 molar solution, must be taken into consideration
 as a factor even in more dilute solutions (say 0.05 to 0.3 molar).
 It seems at present, quite possible, perhaps even probable, that the
 constancy, in all but the most dilute solutions, is the result of
 the approximate balancing of two (or more) opposing factors.[303]
 When we leave the range of concentrations mentioned, and go to more
 concentrated solutions, these factors seem to be less well balanced
 and the validity of the principle ceases.[304] For the present it
 will be safe to consider the principle as an empirical one, holding
 for solutions of total salt content up to 0.25 or 0.3 molar.[305]
 For quite dilute solutions the effect of the electrolyte on the
 solvent would be negligible, and only to such solutions would the
 theoretical derivation brought forward by Washburn be applicable.

«Influence of a Common Ion.»—For a saturated aqueous solution
of silver acetate at a given temperature, the product of
[p145] the ion concentrations may be considered a constant,
[CH_{3}COO^{−}] × [Ag^{+}] = K_{S.P.}.

In such an aqueous solution, containing no foreign salts, the
concentration of the silver-ion is equal to the concentration of the
acetate-ion, since a molecule of silver acetate, when it ionizes,
gives one silver ion for every acetate ion formed. The numerical
value of the solubility-product may then be calculated, if the
solubility of the salt and its degree of ionization are known. For
instance, at 16° one liter of water dissolves 10.07 grams of silver
acetate, that is, 10.07 / 167, or 0.0603 gram-molecule (mole).
Conductivity measurements show that 70.8% of the salt is ionized in
such a solution, and consequently the concentration of the silver-ion
is 0.708 × 0.0603, or 0.0427. The concentration of the acetate-ion
is the same, and the value of the solubility-product constant,
obtained by inserting these quantities in the above equation, is
K_{S.P.} = 0.0427 × 0.0427 = 0.00182.

Now, if, to the saturated solution of the silver acetate, there
are added a few drops of a concentrated solution of sodium acetate
or some crystals of solid sodium acetate, the concentration of the
acetate-ion is thereby increased and the condition of equilibrium in
the solution is disturbed:

 ‹x› [CH_{3}COO^{−}] × [Ag^{+}] > K_{S.P.}.

The concentration of the acetate-ion having been increased, the ion
will combine more rapidly than before with the silver-ion, and the
concentration of the ‹nonionized salt› will be ‹increased›. The
solution being already saturated with nonionized silver acetate,
the excess formed must be ‹precipitated›. As a matter of fact,
a precipitate of silver acetate is readily obtained in this way
(‹exp.›). Precipitation will cease when sufficient silver acetate has
crystallized out to make the product of the concentrations of the
ions again equal to the solubility-product constant. If, after the
crystallization is complete and equilibrium has been reëstablished,
the acetate-ion is ‹x′› times as concentrated as it was in the pure
aqueous solution, the concentration of the silver-ion must be reduced
to 1 / ‹x′› its original value:

 ‹x′› [CH_{3}COO^{−}] × [Ag^{+}] / ‹x′› = K_{S.P.}.

«Precipitation.»—We see thus that ‹precipitation› of a difficultly
soluble ionogen ‹will result when the product of the ion
concentrations› [p146] ‹is made greater than the value of the
solubility-product constant for that substance›. In the second
place, it is seen that the concentration of an ion of an insoluble
salt, which can be present in the saturated solution of the salt,
‹is dependent on the concentration of the other ion (or ions) of the
salt›. This fact is a very important one in analytical chemistry and
it is taken advantage of in many ways, as we shall presently see.

It is clear that a corresponding result should be obtained
when, to the saturated aqueous solution of silver acetate, an
excess of the silver-ion is added—for instance by the addition
of solid silver nitrate or of a little of a concentrated
solution of this salt (‹exp.›). Here again, the product of
the ion concentrations is greater than the constant, ‹i.e.›
[CH_{3}COO^{−}] × ‹y› [Ag^{+}] > K_{S.P.}, and precipitation results.
Silver acetate therefore crystallizes out, until

 ([CH_{3}COO^{−}] / ‹y′›) × ‹y′› [Ag^{+}] = K_{S.P.}.

 The following table shows the relations when sodium acetate is
 added to the saturated solution of silver acetate. Column 1 gives
 the concentration of the sodium acetate in the solution saturated
 with silver acetate, column 2 the percentage of the sodium acetate
 that is ionized, column 3 the total concentration of silver acetate
 in the saturated solution, column 4 the percentage of it which is
 ionized, column 5 the concentration of the acetate-ion, column 6
 the concentration of the silver-ion and column 7 the value of the
 solubility-product.

     1        2        3        4         5          6         7
  Na-Acet.  100 p.  Ag-Acet.  100 p′.  acetate.  [Ag^{+}].  K_{S.P.}.
   0        ....    0.0603     70.8     0.0427    0.0427     0.00182
   0.061    78.6    0.0392     64.5     0.0735    0.0258     0.00185
   0.119    75.8    0.028      59.7     0.1065    0.0167     0.00179
   0.239    70.8    0.0208     52.3     0.1727    0.0109     0.00188

 The second table shows the relations when an excess of the
 silver-ion is present, silver nitrate having been added to the
 saturated silver acetate solution. The columns have the same
 significance as in the first table, excepting that the first column
 gives the concentration of silver nitrate present and the second
 column its degree of ionization.[306]

 It is clear from these results that a difficultly soluble salt is
 rendered less soluble (see column 3 of the tables) by the presence
 of another salt, when the [p147] latter has an ‹ion in common with
 the former›. This conclusion has been well established[307] for a
 considerable number of salts.[308]

     1         2         3       4         5         6          7
  AgNO_{2}.  100 p.  Ag-Acet.  100 p′.  acetate.  [Ag^{+}].  K_{S.P.}.
   0.        ....     0.0603    70.8     0.0427    0.0427     0.00182
   0.061     82.0     0.0417    64.0     0.0267    0.0767     0.00204
   0.119     78.4     0.0341    58.6     0.0200    0.1142     0.00227
   0.239     74.0     0.0195    51.7     0.0100    0.1809     0.00182

«Applications in Analysis.»—A few instances of the application
of this relation in analysis follow. The determination of the
sulphate-ion is based on the precipitation of barium sulphate from
solutions of sulphates. The solubility of barium sulphate in water
at 18° is 0.0023 gram, or 0.0023 / 233 = 1E−5 mole per liter. In
such an extremely dilute solution, the salt may be considered to be
completely ionized, and the value of the solubility-product constant
is found from K_{S.P} = [Ba^{2+}] × [SO_{4}^{2−}] = (1E−5)^2, or
1E−10. Now, the amount of sulphate-ion left in solution, which
would be about one milligram per liter of the aqueous solution,
may be reduced by the use of a small excess of the precipitant,
barium chloride. An excess of as little as 0.2 gram or 0.001 mole of
BaCl_{2} per liter would increase the concentration of the barium-ion
about one hundredfold, and barium sulphate would be precipitated,
until the concentration of the sulphate-ion had been reduced about
one hundredfold. The loss of the sulphate-ion is thus reduced to
approximately 0.01 milligram per liter.

In passing, we may ask what the approximate loss of dissolved
nonionized barium sulphate would amount to. The value of the ratio
([Ba^{2+}] × [SO_{4}^{2−}]) : [BaSO_{4}], representing the ionization
of barium sulphate, is unknown for the extreme dilution represented
[p148] by the saturated solution. If we assume it to be roughly of
the order 2000 : 1,[309] the solubility of nonionized barium sulphate
at 18° would be roughly 0.05 milligram per liter.

As a rule, then, in the absence of complicating conditions,[310] an
excess of the precipitant promotes the complete precipitation of an
ionogen.

«Washing of Precipitates.»[311]—When barium sulphate has been brought
on the filter and the excess of precipitant is to be washed out,
then, as the excess of barium chloride is removed, the sulphate
becomes more soluble again. It is advisable, therefore, to wash the
precipitate as effectively as possible with a very small volume
of water—as a rule, the water is used in a very fine stream or is
applied drop by drop.

Such precautions are still more important in the case of precipitates
which are somewhat more soluble than is barium sulphate, and in such
cases the question must be considered, whether as a washing fluid,
some solution may not be used, which contains an ion in common
with the precipitate, and which has, therefore, according to the
principle of the solubility-product, a very much smaller dissolving
power for the precipitate in question than pure water. That is a
resource of the analyst to which recourse is occasionally taken.
Lead sulphate, for instance, is washed with a very dilute solution
of sulphuric acid, rather than with pure water;[312] potassium
cobaltinitrite, K_{3}Co(NO_{2})_{6}, which is used in the separation
of cobalt from nickel, is washed[313] with a ten per cent solution of
potassium acetate, containing a little potassium nitrite. Ammonium
phosphomolybdate, used in determinations of phosphates, is washed
with a solution of ammonium nitrate. [p149]

The use of such solutions for washing precipitates is limited by the
necessity, first, of avoiding salts which interfere with subsequent
operations (‹e.g.› which would leave nonvolatile residues in the
subsequent ignition of a precipitate, that is to be weighed after
ignition) and, second, of avoiding the loss of precipitate by the
formation of complex ions between an ion of the precipitate and a
component of the washing mixture (see p. 148). But wherever such
complications can be excluded, the method is a desirable one.

 It has sometimes been recommended to wash a precipitate with a
 ‹saturated› aqueous solution of the precipitate itself, in place of
 with pure water. It was reasoned that the solution, being already
 saturated with the salt, would not be able to dissolve any of the
 precipitate obtained. That is true; but if a saturated solution of
 a salt, MeX, is placed on a filter still holding an excess of the
 precipitant, ‹i.e.› one of the ions, say X, of the precipitate, then
 this excess may cause supersaturation of the saturated washing fluid
 and some of the salt may be precipitated out of the washing fluid.
 The method, as commonly employed, has therefore the inherent fault,
 theoretically at least, of being liable to give too high results.
 If it is to be employed without error, precautions must be taken
 first to remove, from the precipitate and filter, the mother liquor
 (containing the excess of precipitant) as completely as possible.
 If in a given case this can be accomplished, then the danger of
 precipitating any of the salt (MeX) from the saturated solution is
 avoided, and the precipitate (MeX ↓) may then be further washed
 with a saturated solution of the same salt (MeX), with advantage,
 in certain cases. Thus, in the Lindo-Gladding method[314] of
 determining potassium in the form of potassium chloroplatinate, the
 source of error, just discussed, has been avoided in the following
 way: the excess of precipitant, chloroplatinic acid H_{2}PtCl_{6},
 which has the ion PtCl_{6}^{2−} in common with the precipitate, is
 ‹first removed› from the precipitate by thorough washing of the
 precipitate with alcohol; subsequently, other impurities, ‹e.g.›
 sulphates, soluble in water but not in alcohol, are washed out
 with an aqueous solution of ammonium chloride[315] that has been
 saturated with potassium chloroplatinate. The method gives good
 results.

 «The Solubility-Product in Volumetric Analysis.»—A final instance of
 the application of the solubility-product principle to the ordinary
 methods of analytical chemistry, may be taken from the field of
 quantitative, volumetric analysis. A particularly accurate method of
 determining silver consists in precipitating it as silver chloride
 by means of a standardized solution of sodium chloride. The aim of
 the method is to recognize, as exactly as [p150] possible, the
 point where the action AgNO_{3} + NaCl → AgCl ↓ + NaNO_{3} has just
 completed itself, ‹i.e.› where one equivalent of sodium chloride
 has been added for just one equivalent of silver nitrate present. A
 very sensitive method[316] depends on the fact that silver chloride
 can be made to coagulate by the vigorous shaking of its suspensions,
 and that the coagulated chloride settles rapidly, leaving a clear
 supernatant liquid, in which the appearance of the faintest
 turbidity may be recognized, when the sodium chloride solution is
 carefully added to the silver nitrate solution under investigation.
 Now, when sodium chloride solution is added in this way to silver
 nitrate, a point is reached (called the "neutral point"),[317]
 where the addition of a further drop or two of sodium chloride
 solution will still produce a precipitate, and where one would be
 inclined to decide that too little of the chloride had been used to
 complete the action. But, at the same time, the addition of a few
 drops of silver nitrate solution to the solution at the "neutral
 point" also produces a precipitate of silver chloride, seemingly
 indicating that an excess of sodium chloride had been used, and
 apparently contradicting the previous result. As a matter of fact,
 such a behavior is exactly what is to be expected from a solution,
 when exactly equivalent quantities of silver nitrate and sodium
 chloride have been brought together in solution. The solution is
 then saturated with silver chloride, K_{S.P.} = [Ag^{+}] × [Cl^{−}]
 and [Ag^{+}] = [Cl^{−}], and the further addition ‹either›
 of the silver-ion (silver nitrate) ‹or› of the chloride-ion
 (sodium chloride) should produce a precipitate, according to the
 principle of the solubility-product. The correct end-point in the
 determination is, thus, the "neutral point," for at that point the
 quantity of silver present is equivalent to the quantity of sodium
 chloride added.

«Effect of Electrolytes with No Ion in Common with the
Precipitate.»—In the precipitation of silver acetate from
its saturated solution by the addition of sodium acetate (p.
145), it is the acetate-ion, according to the principle of the
solubility-product, which is effective—the sodium-ion has no part in
the action. Also, in a similar way, the precipitation produced by the
addition of silver nitrate is ascribed to the increased concentration
of the silver-ion—the nitrate-ion has no share in the action. We
may ask, what the effect on the solubility of silver acetate will
be, if a salt, sodium nitrate, yielding ‹only foreign ions›, and
no common one, is added to its saturated solution. The presence of
sodium and of nitrate ions will not increase the concentration of
either of the ions of silver acetate, will not increase the value
of either factor in the product of ion concentrations; the addition
of sodium nitrate, therefore, should not lead to the precipitation
of any silver acetate, and as a matter of experiment it does not
(‹exp.›). A closer study [p151] of the conditions will show, in
fact, that it renders silver acetate somewhat ‹more soluble›. The
addition of the sodium-ion will lead to the suppression of some of
the acetate-ion, nonionized sodium acetate being formed to a certain
extent; the nitrate-ion will combine with some of the silver-ion
to form nonionized silver nitrate: thus the concentrations of both
of the ions of silver acetate ‹are reduced›, and the product of
ion concentrations is rendered smaller than the solubility-product
constant, ([CH_{3}COO^{−}] − ‹x›) × ([Ag^{+}] − ‹y›) < K_{S.P.}.

Since the concentrations of both the silver and the acetate ions
are reduced, they will not combine as rapidly as before to form
nonionized silver acetate, and the conditions of equilibrium
between the latter and its ions must be disturbed. The nonionized
salt ionizes, for a moment, more rapidly than it is formed and its
concentration will thus be reduced. We, therefore, might expect
the solution to become ‹unsaturated› in respect to the nonionized
form, and the solid salt, if present, should go into solution. In
other words, the addition of a salt with two foreign ions should
‹increase the solubility of a difficultly soluble salt› (it is
understood that no salt is used which would precipitate a new, less
soluble salt). This expectation has also been fully confirmed by
careful quantitative determinations, especially by A. A. Noyes and
his collaborators. The effect may be demonstrated more easily by
the addition to silver acetate of an electrolyte which will very
thoroughly suppress one of its ions. Nitric acid is such an agent.
The hydrogen-ion will very decidedly reduce the concentration of the
acetate-ion, acetic acid being a weak acid (table, p. 104). There is
no difficulty in recognizing the anticipated effect (‹exp.›).

«Solution of Precipitates.»—We find, then, that ‹when the product of
the ion concentrations of a difficultly soluble salt becomes smaller
than the solubility-product constant, the solution is unsaturated› in
regard to the salt, and ‹the solid salt›, if present, ‹will go into
solution›.

«Summary.»—The conclusions concerning the application of the
solubility-product constant may be summarized as follows: A
solution is saturated with a difficultly soluble ionogen when the
product of the concentrations of the ions of the ionogen is equal
to the characteristic solubility-product constant (at the given
temperature). A solution is supersaturated and precipitation will
follow, if the product of the ion concentrations is greater than
the constant. [p152] (See p. 122 in regard to precautions against
prolonged supersaturation.) A solution is unsaturated, and the
ionogen, if present, will dissolve when the product of the ion
concentrations is smaller than the constant.

«Further Considerations Concerning Precipitation and Solution.»—It is
further evident that precipitation is favored, if the precipitating
agent contains an electrolyte which produces the precipitating ion
readily; for instance, carbonic acid does not precipitate any barium
carbonate from a solution of barium chloride (‹exp.›)—carbonic
acid being an exceedingly weak acid and producing only a minute
concentration of the carbonate-ion CO_{3}^{2−}, necessary for the
precipitation; but sodium carbonate, a readily ionized salt, will
precipitate the barium carbonate quantitatively (p. 90). If some
alkali is added to the mixture of barium chloride and carbonic acid
(‹exp.›), the latter is converted into a readily ionized salt, the
concentration of the carbonate-ion is thus decidedly increased,
and the precipitate forms instantly. In the same way, if hydrogen
sulphide—a still weaker acid (table, p. 104), which forms only
minute quantities of sulphide and hydrosulphide ions (S^{2−} and
HS^{−})—is passed through a solution of ferrous sulphate, it fails
to precipitate ferrous sulphide; but a salt of hydrogen sulphide,
ammonium sulphide, for instance, precipitates ferrous sulphide
quantitatively (‹exp.›).

On the other hand, solution of an ionogen is evidently favored and
its precipitation rendered more difficult, if we suppress one (or
both) of its ions. Thus barium phosphate, calcium carbonate, silver
borate, and many salts of weak acids, that are very difficultly
soluble in water, are quite easily soluble in strong acids, which
suppress the anions by converting them into little ionized acids.
When a precipitate is dissolved by the addition of a reagent, such as
an acid, an alkali, ammonia, ammonium sulphide—chemical solvents most
frequently used in analytical work—we may, as a general principle,
consider that the reagent must affect one or both of the ions of
the precipitate in question, suppressing it (or them) and thereby
making solution possible. The problem of determining in what way
the suppression of the ion is effected, must then be faced. Many
occasions to determine such questions[318] will arise. [p153]

We have, therefore, a certain degree of control over the
precipitation and solution of electrolytes, the control depending
upon, and being limited by, the fact that the ‹factors of the product
of ion concentrations are variables›.

On the other hand, we have little control, in a given solvent, over
the question of solution or precipitation as affected by the value
of the ion product ‹constant›, the remaining term in the equation
of the solubility-product for saturated solutions. These constants
cover a very wide range of values for the various salts, which are
most frequently used in analytical work for the precipitation of the
common ions.[319] They are subject to variation with the temperature,
and, as a rule, as most salts are more soluble at higher than at
lower temperatures, the values of the constants increase with the
temperature. For exceedingly difficultly soluble salts, the increase
is commonly of no practical moment in analytical work, when, by an
excess of the precipitant, the ion, which is to be precipitated, can
be precipitated quantitatively; the solubility of the nonionized
salt, that is precipitated, is so minute (see p. 148) in this case,
even at high temperatures, that it is altogether negligible for
ordinary purposes.[320] On the other hand, precipitates are often
used which are not at all extremely insoluble but merely rather
difficultly soluble; they are used in spite of their relatively
slight insolubility because they are the best available forms
for our purposes. Such salts are, for instance, lead chloride,
magnesium-ammonium phosphate, potassium chloroplatinate. When these
are precipitated, not only must the fact that they are appreciably
soluble at ordinary temperature be taken into account, but also the
fact that they are very much more soluble at higher temperatures.
Lead chloride and potassium chloroplatinate are, for instance, quite
soluble in hot water.

As a rule, we select for the form in which a given ion is to be
precipitated, a form which, in a saturated aqueous solution, shows
the ‹smallest concentration of the ion in question›. But if no form
is [p154] known which is sufficiently insoluble to give satisfactory
quantitative results, then we have recourse to a ‹change› in the
‹solvent›.

«Solubility and Solvent.»—For instance, a mixture of alcohol and
water may be used, or water be excluded altogether; and either
absolute (water-free) alcohol or a mixture of alcohol and ether
may be employed. In the quantitative treatment of potassium
chloroplatinate, the last-named mixture is used in place of water.
The change of solvent affects the solubility by a change both in
the solubility of the ionized portion of a salt and in that of the
nonionized salt. An important quantitative relation between the
solubility of a given ionogen in different solvents and the ionizing
powers of the solvents, as determined by their dielectric constants
(p. 63), was predicted, on the basis of theoretical considerations,
by Malström[321] and by Baur.[322] Walden[323] has furnished
experimental confirmation of the relation: ‹The degree of ionization
of a salt is found to be the same in its saturated solutions in
different solvents›, when the solutions are saturated at the same
temperature.

 If this relation is combined with that discussed on page 63,
 according to which the degree of ionization of a given salt, in
 different solvents, ‹is the same›, when the cube roots of its
 concentrations are directly proportional to the dielectric constants
 of the solvents (‹e›_{1} : ∛‹c›_{1} = ‹e›_{2} : ∛‹c›_{2} = a
 constant), then we find, that in ‹saturated solutions of a given
 salt, in different solvents, the cube roots of the concentrations,
 or solubilities, are directly proportional to the dielectric
 constants of the solvents›, or, ‹the solubilities are proportional
 to the third powers of the dielectric constants›.

 ‹e›_{1} : ∛‹c›_{1} = ‹e›_{2} :∛‹c›_{2} = a constant, or
   ‹e›_{1}^3 : ‹e›_{2}^3 = ‹c›_{1} : ‹c›_{2},

 ‹c›_{1} and ‹c›_{2} representing the solubilities, in molar
 concentrations, in two solvents of dielectric constants ‹e›_{1} and
 ‹e›_{2}.

 The following table illustrates the relations for a salt examined by
 Walden, a derivative of ammonium iodide, namely tetraethyl ammonium
 iodide (C_{2}H_{5})_{4}NI. The first column gives the name of the
 solvent, the second the solubility or concentration in the saturated
 solution, in terms of the proportion of moles of the solute to the
 total number of moles present[324] [p155] (solute + solvent);
 the third column gives the dielectric constant, under comparable
 conditions, and the last column gives the relation ‹e› : ∛‹c›.

   Solvent.       Solubility.   ‹e›_{5}   ‹e› : ∛‹c›
  Water             0.0332       75.0       50.5
  Nitrobenzene      0.0020       32.2       54.8
  Ethyl alcohol     0.00201      26.6       45.5
  Acetone           0.00072      21.8       52.8
  Amyl alcohol      0.00031      15.0       48.

 In view of the difficulties in determining the values for the
 dielectric constant, the agreement in the values of the last column
 must be considered satisfactory.[325]

 This important principle forms another striking instance of the
 ‹supreme influence of electrical relations in determining the
 behavior of ionogens in solution› (see p. 111).

Since, in solutions saturated at the same temperature with a given
ionogen, the degree of ionization of the ionogen is the same in both
solvents, the proportion of nonionized to ionized salt is also the
same. If a salt, ‹e.g.› calcium sulphate, is less soluble in alcohol
than in water, the alcohol must hold less of the nonionized form, as
well as less of the ionized salt, than does an equal volume of water
at the same temperature.

The development of further relations, of fundamental importance
to analytical chemistry, with the aid of the laws of chemical and
physical equilibrium and of the principle of the solubility-product,
will be taken up in the study of the reactions of the various
analytical groups of ions.


  FOOTNOTES:

  [291] ‹Z. phys. Chem.›, «4», 372 (1889). See also van 't Hoff,
  ‹ibid.›, «3», 484 (1889).

  [292] ‹Cf.› page 94.

  [293] A. A. Noyes, ‹Z. phys. Chem.›, «9», 618 (1892); Findlay,
  ‹ibid.›, «34», 409 (1900).

  [294] As foreign salts affect the ionization of poor «electrolytes»
  (p. 109), the ratio of equation I would hold as little for poor
  electrolytes, and would grow larger with an increased concentration
  of the foreign salts.

  [295] ‹Cf.› A. A. Noyes, ‹Congress of Arts and Sciences› (St.
  Louis), «4», 321 (1904) and Stieglitz, ‹J. Am. Chem. Soc.›, «30»,
  946 (1908) («Stud.»), and the references to literature given there.
  The empirical relation seems to hold for dilute solutions, the
  total electrolyte concentration of which is not greater than 0.2 to
  0.3 gram-equivalent per liter, and, roughly, for concentrations not
  greater than 0.5 gram-equivalent per liter.

  [296] See Stieglitz, ‹loc. cit.›

  [297] Since the writing of this it has been learned that such
  investigations have been carried out by Harkins. ‹Cf.› ‹J. Am.
  Chem. Soc.›, 1911.

  [298] ‹J. Am. Chem. Soc.›, «32», 488 (1910).

  [299] Otherwise a ‹perpetuum mobile› of the ‹second class›
  (footnote 3, p. 12) could be constructed, which is at variance with
  experience.

  [300] This sentence is quoted from a letter from Dr. Washburn, who
  is at present investigating moderately concentrated solutions of
  electrolytes, to determine the range of concentrations in which it
  is possible to apply the laws of ideal solution.

  [301] ‹Cf.› Geffcken, ‹Z. Phys. Chem.›, «49», 257 (1907), and the
  references given there.

  [302] ‹Cf.› Arrhenius, ‹loc. cit.›, and similar investigations on
  the "salt effect" (p. 109).

  [303] ‹Vide› Geffcken, ‹loc. cit.›, 295, and Stieglitz, ‹loc.
  cit.›, and p. 142.

  [304] See also Hill, ‹J. Am. Chem. Soc.›, «32», 1186 (1910). Hill
  attacks the principle as a whole, but brings no evidence against
  its validity for solutions of concentrations up to 0.3.

  [305] The limit of concentration depends, for constancy, upon the
  nature of the salts. The calculations, on which the data in the
  tables on pp. 146–7 are based, involve extrapolations which prevent
  the results, especially for the more concentrated solutions, being
  considered as final.

  [306] For further illustrations, ‹vide› Stieglitz, ‹J. Am. Chem.
  Soc.›, «30», p. 947 (1908), and the references given there to the
  work of Noyes, Findlay, etc.

  [307] Some instances are known where the solubility of a salt is
  ‹increased› by the addition of a salt with a common ion. In such
  cases it is extremely likely that an ion of the salt in question
  forms a ‹complex ion› with a component of the solution. ‹Vide›
  A. A. Noyes, ‹Z. phys. Chem.›, «6», 241 (1890), and «9», 603
  (1892). In Chapter XII we shall discuss, in detail, instances of
  this nature where the formation of complex ions is particularly
  susceptible of ‹exact experimental verification›.

  [308] Especially by Noyes, ‹loc. cit.›, and later papers; Findlay,
  ‹loc. cit.›

  [309] This is the value for a similar ratio for KCl of the same
  concentration as found, by extrapolation, from the data in the
  table on p. 108.

  [310] Owing to the possibility of the formation of complex ions
  (Chapter XII), each individual case must be considered by itself
  and the most favorable conditions for the complete precipitation
  determined experimentally. The rule mentioned is to be used as
  a guide, and the reference to the possibility of the formation
  of complex ions considered as a warning, in the planning of such
  investigations.

  [311] ‹Cf.› p. 136, concerning precautions used to prevent
  precipitates from assuming the ‹colloidal› state.

  [312] Fresenius, ‹Quantitative Analysis›, I, 355 (1904).

  [313] ‹Ibid.›, I, 307.

  [314] Official Methods of Analysis, Bulletin 107, p. 11, U. S.
  Dept. of Agriculture.

  [315] The excess of chloroplatinic acid is first washed out of the
  precipitate primarily to avoid subsequent precipitation of ammonium
  chloroplatinate, but its removal also avoids the error discussed in
  the text.

  [316] Gay-Lussac's method.

  [317] Mulder. See Sutton's ‹Volumetric Analysis›, p. 304 (1904).

  [318] ‹Vide› Chapters XII and XIII.

  [319] A table of exact solubilities is given at the end of the Lab.
  Manual, ‹q.v.›

  [320] In the most exact quantitative work, as demanded in the
  determinations of atomic weights, every known loss must, as far as
  possible, be measured and taken into account. Beautiful instances
  of such work are found in T. W. Richards' classic determinations of
  atomic weights. See, for instance, Richards, ‹Carnegie Institution
  Publications›, No. 125 (1910), Determinations of the Atomic Weights
  of Silver, Lithium and Chlorine («Stud.»).

  [321] ‹Z. Elektrochem.›, «11», 797 (1905).

  [322] ‹Ibid.›, «11», 936 (1905), and «12», 725 (1906).

  [323] ‹Z. phys. Chem.›, «55», 707 (1906), and «61», 638 (1907).

  [324] If ‹n› is the number of moles of solute dissolved in ‹N›
  moles of solute, the concentration of the solute may be expressed
  as ‹n› / (‹n› + ‹N›), which is called its "mole fraction." This
  form of expressing concentrations is in many particulars preferable
  to the mole / liter form. For very dilute solutions (‹n› is
  very small compared with ‹N›) the two forms become practically
  identical, but they are not so for more concentrated solutions, and
  the ‹mole-fraction› expression is then easier to treat rigorously.

  [325] See Walden, ‹loc cit.›, for more extended data.

[p157]




 PART II

 «SYSTEMATIC ANALYSIS AND THE APPLICATION OF FUNDAMENTAL PRINCIPLES»




 CHAPTER IX

 «SYSTEMATIC ANALYSIS FOR THE COMMON METAL IONS. THE IONS OF THE
 ALKALIES AND OF THE ALKALINE EARTHS. ORDER OF PRECIPITATION OF
 DIFFICULTLY SOLUBLE SALTS WITH A COMMON ION»


In systematic analysis it is most convenient to make separate
examinations for the metal and for the acid ions. The examination for
metal ions usually precedes that for the acid ions, and the scheme of
analysis for the former will be considered first.

The analytical grouping of the metallic elements is not a natural
one, as far as their chemical behavior is concerned. Such a grouping
is found in the Periodic System of Mendeléeff and is used in
systematic inorganic chemistry.[326] The groups in analysis are based
chiefly, but not exclusively, on the physical property of greater or
smaller solubility of certain salts of the metals. According to the
salts chosen, different systems vary somewhat in detail. Frequently
elements of the same natural family are also found in the same
analytical group, relationship in chemical properties being often
coincident with relationship in the physical behavior of the salts of
the metals.

In the following list, the common metal ions are arranged in groups,
which are given in the order in which they are precipitated in the
method of systematic analysis adopted. In each case, a group name and
the characteristic reagents used in separating a group from those
following it, are given.

«The Silver Group.»—Ions whose chlorides are insoluble in dilute acid
solutions. The precipitating agent is HCl. [p158]

 «Pb»^{2+} (the chloride is somewhat soluble), «Ag»^{+}, «Hg»^{+}.

«The Copper and the Arsenic Groups.»—Ions whose sulphides are
insoluble in dilute acids. The precipitating agent for the two groups
is H_{2}S, ‹in acid solution›. The ‹sulphides of the arsenic group
are soluble in a mixture of› (NH_{4})_{2}S ‹and› (NH_{4})_{2}S_{x}
and are separated thereby from the sulphides of the ‹copper group›.

 «The Copper Group.»—«Hg»^{2+}, («Pb»^{2+}), «Bi»^{3+}, «Cu»^{2+},
 «Cd»^{2+}.

 «The Arsenic Group.»—«As»^{3+}, «As»^{5+}, «Sb»^{3+}, «Sb»^{5+},
 «Sn»^{2+}, «Sn»^{4+}, «Pt»^{2+}, «Pt»^{4+}, «Au»^{+}, «Au»^{3+}.

«The Aluminium and the Zinc Groups.»—Ions whose sulphides or
hydroxides are insoluble in neutral or slightly alkaline (ammonium
hydroxide) solutions. The two groups are precipitated together by a
mixture of NH_{4}Cl, NH_{4}OH, (NH_{4})_{2}S. The ‹aluminium group›
may be ‹separated› from the ‹zinc group› by treatment of solutions of
the chlorides or nitrates with ‹barium carbonate›.

 «The Aluminium Group.»—«Fe»^{3+}, «Al»^{3+}, «Cr»^{3+}.

 «The Zinc Group.»—«Fe»^{2+}, «Ni»^{2+}, «Co»^{2+}, «Mn»^{2+},
 «Zn»^{2+}.

«The Alkaline Earth Group.»—Ions whose carbonates and phosphates are
insoluble in neutral or alkaline solutions. The precipitating agent
is NH_{4}Cl, NH_{4}OH, (NH_{4})_{2}CO_{3} for «Ba»^{2+}, «Sr»^{2+},
«Ca»^{2+}, and (NH_{4})_{2}HPO_{4} for «Mg»^{2+}.[327]

«The Alkalies.»—Ions whose chlorides, sulphides, hydroxides,
carbonates and phosphates are soluble. «K»^{+}, «Na»^{+},
«NH_{4}»^{+}.

In considering the analytical reactions and the analysis of these
groups of metal ions, we shall take up the groups in the order
reversed to that given in the table. We shall begin with the group
of alkali metals, follow this group with the alkaline earths, then
take the aluminium and zinc groups, the copper and silver groups,
and finish with the arsenic group. This order is chosen because the
chemistry of the reactions involved is simplest in the groups to be
studied first and grows more complicated as we advance to those to be
studied later.

It is not intended to discuss in detail all the reactions and
methods; our attention will be limited rather to the study of
‹typical general relations›, and the student is expected to acquire
the power to apply the general conclusions reached, to any specific
case demanding it. [p159]

«The Alkali Group.»—The group includes the ions of «sodium» and
«potassium», the most common and most important of the alkali metals,
and the «ammonium»-ion. Characteristic of the ions of the group is
the fact that all of their common salts are easily soluble in water.
They remain in solution in systematic analysis, while other metal
ions are removed in the form of various insoluble precipitates.

The ammonium-ion is recognized, and may be removed from a mixture of
the salts of the group, on the basis of a fundamental distinction in
its chemical behavior, namely its instability and the instability
of its compounds. Sodium-ion and potassium-ion, are recognized,
and separated from each other, by physical methods. All ammonium
compounds, NH_{4}X, decompose more or less readily into ammonia and
the free acids,[328] according to the reversible reaction,

 NH_{4}X ⇄ NH_{3} + HX.

The stronger the acid combined with ammonia, the more stable is the
salt, and the higher is the temperature, at which the salt decomposes
readily and rapidly. Ammonium chloride, one of the most stable of
the salts, is decomposed rapidly only at about 350°, which is,
however, still below red heat; ammonium carbonate, the salt of a very
much weaker acid, decomposes appreciably at ordinary temperatures,
and exposed to the air, it gradually disappears as ammonia, carbon
dioxide and water. If the acid of the salt is volatile at the
dissociation temperature of the salt, the whole salt is volatilized,
and if the ammonia and volatile acid vapor reach a colder space,
recombination to form the original solid salt occurs to a
considerable extent (the "smoking off" of ammonium chloride). If the
acid is not volatile, the salt, nevertheless, loses its ammonia at
temperatures below red heat, while the acid remains. Sodium-ammonium
phosphate, for instance, when heated, loses its ammonia, and
sodium-dihydrogen phosphate is left as a nonvolatile residue.

Ammonium happens to form salts which closely resemble the
corresponding salts of potassium in physical properties, such as
[p160] solubility and insolubility, salts which could readily be
mistaken for potassium salts. Advantage is taken of the chemical
instability of the ammonium salts, just described, to remove ammonium
completely from mixtures, by ignition, before tests for potassium are
made.

Water is a far weaker acid (see table, p. 104) than carbonic acid
and it is not surprising to find the compound formed by water and
ammonia, ammonium hydroxide, one of the least stable of the ammonium
compounds. Even at ordinary temperature, the hydroxide is more or
less decomposed, according to a reversible reaction of the same type
as that found for the ammonium salts, NH_{4}OH ⇄ NH_{3} + HOH.

 Chemists have always been interested in the problem of the exact
 degree of stability of ammonium hydroxide, and, more particularly,
 in the problem whether ammonia gives solutions in water showing
 very much weaker basic strength[329] than equivalent solutions of
 potassium and sodium hydroxides, primarily ‹because only a small
 proportion of the ammonia is combined with water to form the real
 base, ammonium hydroxide› (which would be present then in much
 more dilute solution than the alkali metal hydroxides are in the
 solutions with which the comparison is made), or chiefly ‹because
 ammonium hydroxide is much less readily ionizable› than potassium or
 sodium hydroxide.

 For the reversible action NH_{3} + HOH ⇄ NH_{4}OH we would have, at
 a constant temperature, according to the law of chemical equilibrium,

 [NH_{3}] × [HOH] / [NH_{4}OH] = ‹k›.

 For a dilute solution at a given temperature the concentration of
 the water may be considered a constant, and therefore

 [NH_{3}] / [NH_{4}OH] = ‹k› / [HOH] = ‹k›_{NH_{3}}.               (I)

 For the ionization of ammonium hydroxide,
 NH_{4}OH ⇄ NH_{4}^{+} + HO^{−}, we would have in turn,

 [NH_{4}^{+}] × [HO^{−}] / [NH_{4}OH] = ‹k›_{base}.               (II)

 This constant represents ‹the real ionization constant of ammonium
 hydroxide as a base›, and its approximate value has only recently
 been determined by Moore[330] and found to be about 5E−5. The
 ratio [NH_{3}] / [NH_{4}OH] was found to be approximately 2 at
 20°. According to this result, ammonium hydroxide is really a
 much weaker, less readily ionized base than potassium or sodium
 hydroxide. The ‹efficiency of ammonium hydroxide as a base› depends
 [p161] on both conditions of equilibrium; the first equation
 states what proportion of ammonium hydroxide can exist, as such,
 in solution, if a given amount of ammonia is dissolved in a given
 amount of water, and the second equation shows the proportion of the
 hydroxide, which is ionized. The equations may be combined[331] into
 one expression,

 [NH_{4}^{+}] × [HO^{−}] / ([NH_{4}OH] + [NH_{3}]) = K.        (III)

 That is, ‹the ratio of› [NH_{4}^{+}] × [HO^{−}] ‹to the total
 concentration of nonionized ammonium hydroxide and ammonia, is
 a constant›. This constant has the value 0.000,018 at 18° (as
 given in the table, p. 106) and, as said, comprises in a single
 expression a statement measuring the ‹efficiency›, as a base, of a
 solution of ammonium hydroxide and ammonia in aqueous solutions.
 The concentration of the hydroxide-ion, on which the efficiency as
 a base depends, can be ascertained directly from the expression,
 provided we know the total concentration of the ammonia and ammonium
 hydroxide and the concentration and degree of ionization of any
 ammonium salt, which may be present with the base (see p. 161).
 These data are easily obtained by direct measurement.

The instability of ammonium hydroxide is used as a means for
‹detecting ammonium-ion› in its salts. The latter are treated
with some strong base, such as sodium or calcium hydroxide, and
the ammonia, liberated by the decomposition of its hydroxide, is
recognized by its odor or by the more sensitive test of its action on
moist litmus. The delicacy of the test is dependent on the conditions
expressed in the equilibrium equation (p. 160).

Sodium and potassium resemble each other so profoundly in the
chemical behavior of their compounds, that they are recognized, and
separated from each other, by ‹physical› methods. A very simple
physical test is based on the color of their heated vapors, the color
imparted to the nonluminous bunsen flame by the introduction and
volatilization of their salts. The sodium flame is so intense that,
if sodium is present in any quantity, the color of its flame easily
masks the faint color of potassium vapor. The color of the flame is
best examined, in such a case, with the aid of a spectroscope, in
which the light emitted by the two elements may be readily recognized
side by side, or with the aid of cobalt glass, which absorbs the
sodium light. [p162]

The ions of the two metals may be separated and identified by
means of difficultly soluble salts. There are so few of these in
the case of both ions, that recourse must be taken to the salts
of comparatively uncommon acids. ‹Potassium chloroplatinate›
K_{2}PtCl_{6}, precipitated by the addition of chloroplatinic
acid H_{2}PtCl_{6} to concentrated solutions of potassium
salts, gives very satisfactory results, both in qualitative and
in quantitative work. The acid tartrate, KHC_{4}H_{4}O_{6},
the picrate, KC_{6}H_{2}N_{3}O_{7}, and the cobaltinitrite,
K_{3}Co(NO_{2})_{6},[332] are difficultly soluble and are sometimes
used to ‹identify potassium-ion›. The corresponding ammonium salts
are also difficultly soluble and resemble the potassium salts, and
ammonium-ion must therefore be removed, as stated above, if present,
before any of these precipitates may be used for the identification
of potassium-ion. In the case of sodium-ion, recourse is taken to
the salt of a still more uncommon acid; ‹pyroantimonate of sodium›,
Na_{2}H_{2}Sb_{2}O_{7}, 6 aq., is sufficiently difficultly soluble
and characteristic to be used as a means of ‹identifying sodium-ion›.

«The Alkaline Earth Group.»—This group includes «magnesium»,
«calcium», «strontium», and «barium.» Chemically, the analogous
compounds of the four alkaline earths resemble one another so much,
that physical differences alone are used in their separation and
identification. For qualitative work, the colors of their heated
vapors,[333] especially when examined in the spectroscope, give us
sensitive and reliable tests for their presence. The alkaline earth
ions, especially the ions of barium, strontium and calcium, form a
great number of insoluble salts, which may be used to separate them
from each other. Salts used for this purpose and the methods of
employing them are considered in detail in the laboratory work (see
Part III). Here some general principles, only, will be considered in
connection with the behavior of some of the most important of the
precipitates.

There is a very wide range in the degree of the insolubility of such
precipitates as are used in analysis. In the table at the end of Part
IV, the exact solubilities of the most important [p163] precipitates
of the alkaline earths are given, for 18°, in grams and moles per
liter. The values are instructive in a number of respects.

Inspection of the table shows which are the least soluble (in
molar terms), and therefore the best salts, for precipitating
barium, strontium and calcium, in order to insure the use of the
most sensitive tests for the ions of each of these metals. It also
shows which salts must be treated with special precautions to
escape error. It is further seen, that if the carbonates of these
alkaline earths are precipitated by a moderate excess of ammonium
carbonate, the addition of a sulphate (for instance ammonium
sulphate), to the filtrate from the precipitated carbonates, will
only precipitate barium sulphate, the only sulphate whose solubility
(and solubility-product) is smaller than that of the corresponding
carbonate. In the same way, calcium oxalate is the only oxalate of
these three alkaline earths that will be precipitated by ammonium
oxalate in the filtrate from the carbonates (see Part III in regard
to precautions against difficultly soluble double oxalates of
magnesium). Again, calcium sulphate is the only one of the sulphates,
which is sufficiently soluble in water to give an immediate ‹heavy›
precipitate, when the sulphates are shaken for a few moments with
water and the filtered solution is treated with a few drops of
ammonium oxalate solution.

«Fractional Precipitation.»[334]—If sulphuric acid is added to a 0.5
molar solution of the chloride either of barium, of strontium or of
calcium, the corresponding sulphate is precipitated. We may ask which
sulphate will be precipitated first, when sulphuric acid is added,
drop by drop, to a solution containing the three chlorides. This
problem, a case of the ‹fractional precipitation of salts containing
a common ion›, may be treated from the point of view of the
solubility-product principle as follows, the problem being limited,
for the sake of simplicity, to only two of the sulphates, those of
barium and strontium.

For a saturated solution of barium sulphate,[335] at 18°, in contact
with the solid salt, we have, according to the principle of the
solubility-product,

 K_{BaSO_{4}} = [Ba^{2+}] × [SO_{4}^{2−}] = 1E−10,

[p164]

and for a saturated solution of strontium sulphate, we have
similarly[336]

 K_{SrSO_{4}} = [Sr^{2+}] × [SO_{4}^{2−}] = 2.5E−7.

Now, we may ask what the conditions are under which ‹both›
precipitates can be present ‹together› in a condition of equilibrium
with a supernatant saturated solution. In such a solution we have
simultaneously

 K_{BaSO_{4}} = [Ba^{2+}]_{1} × [SO_{4}^{2−}]_{1},

 K_{SrSO_{4}} = [Sr^{2+}]_{1} × [SO_{4}^{2−}]_{1}.

New symbols, [Ba^{2+}]_{1}, etc., are used for expressing the
concentrations, as they are not the same as in the pure aqueous
solutions. The much more soluble strontium sulphate makes the
concentration of the sulphate-ion very much greater than it is
in the saturated solution of pure barium sulphate and diminishes
the concentration of the barium-ion proportionately (p. 145). The
concentration, [SO_{4}^{2−}]_{1}, of the sulphate-ion, representing
the actual (total) concentration of the ion in the solution saturated
with both salts, appears in both of the new equations. Combining the
two equations, we have, for the condition of equilibrium between the
two precipitates and the supernatant liquid,

 [Ba^{2+}]_{1} / [Sr^{2+}]_{1} = K_{BaSO_{4}} / K_{SrSO_{4}} =
   1 / 2500.

That is, in a solution in equilibrium with both precipitates at
18°, the strontium-ion must be about 2500 times as concentrated
as is the barium-ion. If we start with equivalent quantities of
barium and strontium chlorides, say in 0.1 molar solutions, and
gradually add sulphuric acid or ammonium sulphate, barium sulphate
will be precipitated alone,[337] until the strontium-ion is in the
excess [p165] indicated by the ratio given. After that, strontium
sulphate will be precipitated, with traces of barium sulphate, the
ratio expressed in the equilibrium equation being maintained in the
supernatant liquid. On the other hand, if we start with a solution
containing a very large excess of a strontium salt, more than is
required by the equilibrium ratio, then strontium sulphate will be
precipitated first, until the ratio given is reached.

Even should the more soluble salt be precipitated first from a
solution containing, say, equal concentrations of barium and
strontium ions, ‹it could not remain in equilibrium with the
supernatant liquid and would be converted into the less soluble one,
before equilibrium was reached in the system›. We can follow similar
relations, experimentally, by using precipitates of different colors.
Silver chromate Ag_{2}CrO_{4} is an intensely red precipitate, that
is rather difficultly soluble in water (‹exp.›); a liter of water
dissolves[338] 0.0252 gram or 8E−5 mole at 18°. The concentration of
the silver-ion in the saturated solution is then 0.00016 mole.[339]
Silver chloride AgCl, a white salt, is still less soluble in water,
a liter of water at 18° dissolving 0.00134 gram or 1E−5 mole, and
the concentration of the silver-ion in the saturated solution is,
therefore, only 1E−5 mole, as compared with 1.6E−4 in the saturated
silver chromate solution. If a mixture of potassium chromate and
potassium chloride, containing approximately equal (0.01 molar)
concentrations of the two salts, is prepared and silver nitrate
solution added, drop by drop, to the mixture, the first ‹permanent
precipitate› is the white silver chloride (‹exp.›). However, as the
silver nitrate solution strikes the surface of the liquid, a red
precipitate of the chromate, mixed with chloride, is momentarily
seen, where the silver nitrate temporarily produces a ‹local excess›
of the precipitant. But the red precipitate disappears rapidly and
gives way to the white precipitate of the less soluble chloride.
The quantitative relations, which may be developed with the aid of
the principle of the solubility-product (see below), are such that,
if little chromate is used, it may serve as an [p166] ‹indicator to
determine quantitatively the moment when all the chloride, within
the limits of allowed quantitative error, is precipitated›, the first
‹permanent› tinge of pink (solid Ag_{2}CrO_{4}), mixed with the
yellow color of the solution, being used as the indication that the
precipitation of the chloride is complete. Potassium chromate is used
as a favorite indicator in quantitative analysis, for this purpose.

 The quantitative relations[340] for the precipitation may be
 developed as follows: For a supernatant liquid in which a
 precipitate of silver chromate just appears permanently, together
 with the chloride, ‹i.e.› for the condition of saturation with both
 silver salts at 18°, we have

 K_{AgCl} = [Ag^{+}] × [Cl^{−}] = (1E−5)^2 = 1E−10

 and

 K_{Ag_{2}CrO_{4}} = [Ag^{+}]^2 × [CrO_{4}^{2−}] =
   (1.6E−4)^2 × (8E−5) = 2E−12,

 and therefore:

 [Cl^{−}]^2 / [CrO_{4}^{2−}] = (K_{AgCl})^2 / K_{Ag_{2}CrO_{4}} =
   (1E−10)^2 / 2E−12 = 1 / 2E8.

 For a solution containing one or two drops (0.1 c.c.) of saturated
 potassium chromate solution per 100 c.c., a proportion frequently
 used in quantitative analysis, the concentration of the chromate-ion
 is approximately 2.5E−3 and the chloride-ion will consequently be
 precipitated until [Cl^{−}] = 3E−6. The chief source of error in the
 method, then, will not be due to the incompleteness of the prior
 precipitation of the chloride, but rather to the use of the small
 excess of silver nitrate required to precipitate sufficient chromate
 to be visible. This error may be avoided, and is avoided in very
 accurate work (‹e.g.› in water analysis), by determining, in a blank
 test, the amount of silver nitrate required to show the change of
 tint of a pure chromate solution of the concentration to be used in
 the titration and by titrating to this tint in the determination
 of the chloride: the volume of silver nitrate (‹e.g.› 0.2 c.c. of
 a 0.01 molar solution), required to produce the tint in the blank
 test, is subtracted from the total volume of silver nitrate used in
 the chloride determination.

We find thus, that the ‹order› of ‹precipitation› of ‹difficultly
soluble salts, which contain a common ion› (fractional precipitation),
is ‹subject to the equilibrium conditions derived from the application
of the principle of the solubility-product to the salts in
question›.[341]

It should be further noted that the condition of equilibrium between
two precipitates, containing a common ion, and a supernatant liquid,
depends on the concentrations ‹in the supernatant liquid›, in the
‹liquid phase›, and not on the quantities of the solids [p167]
present. This conclusion was first reached by Guldberg and Waage, to
whom we owe the law of mass action, and was fully confirmed by them.
The modern treatment of the subject substitutes ion concentrations,
i.e. the concentrations of the active components,[342] for the total
concentrations used by these investigators.[343]

That the condition of equilibrium is dependent on the liquid phase
can easily be demonstrated if mercurous chloride and mercurous
hydroxide are selected as the two precipitates, in order that we may
follow changes of concentration in the liquid phase by color changes.
For the condition of equilibrium between the two precipitates and the
supernatant liquid we may develop the relation

 [OH^{−}] / [Cl^{−}] = K_{HgOH} / K_{HgCl} = K.

 EXP. A few drops of phenolphthaleïn are added to 100 c.c. of a very
 dilute solution of potassium hydroxide (1 / 500 molar); the usual
 indication of the presence of the hydroxide-ion is shown and the
 intensity of the color will be a measure of its concentration. Three
 identical solutions are prepared and then a pinch of calomel is
 added to two of the solutions,—‹their pink color fades decidedly›.

Some of the calomel is decomposed into dark-colored mercurous oxide,
which is precipitated, and sufficient ‹potassium chloride› is formed
to bring the ratio [OH^{−}] / [Cl^{−}], in the solution, down to
the value required by the constant K. Since no chloride-ion is
present at the start, this result can be brought about only by the
change indicated. Now, some chloride, say a little of a concentrated
solution of potassium chloride, which reacts perfectly neutral, is
added to one of the mixtures of the hydroxide and chloride. The
concentration of the chloride-ion is increased in the solution,
the ratio [OH^{−}] / [Cl^{−}] is made much ‹too small› and the
condition of equilibrium is disturbed. Consequently, mercurous
oxide reacts with potassium chloride, as expressed in the equation
HgOH ↓ + KCl → HgCl ↓ + KOH, until the ratio [OH^{−}] / [Cl^{−}]
[p168] has the value required by the constant K. The phenolphthaleïn
is colored by the increased concentration of the hydroxide-ion and
shows the direction of the change.[344]

«Precipitation by a Weak Base in the Presence of its
Salts.»—Magnesium, in contrast to the other alkaline earth metals,
forms very few difficultly soluble compounds. Magnesium-ammonium
phosphate, Mg(NH_{4})PO_{4}, a double salt, is the most
characteristic precipitate for identifying it. Magnesium hydroxide,
as the table of solubilities shows, is also very difficultly soluble.
It is readily precipitated by potassium or sodium hydroxide, but
ammonium hydroxide, at best, precipitates it only incompletely[345]
from solutions of its salts, and very commonly does not precipitate
it at all—namely, when ammonium salts in sufficient quantity are
present (‹exp.›). This peculiar behavior of ammonium salts, in
interfering with the precipitation of magnesium hydroxide, puzzled
chemists for many years, and a number of "theories" were offered
in explanation of it. But they all proved untenable, and the first
adequate explanation, the one in accord with all the facts, was
only found after the development of the theory of ionization. Its
quantitative application to the case in question gives a perfect
insight into the relations, and brings important confirmation of the
correctness of its fundamental assumptions.[346]

The fact that ammonium salts prevent the precipitation of magnesium
hydroxide was formerly explained as being due to the formation of
"double salts," such as MgCl_{2},NH_{4}Cl. It is true that such
double salts exist, but, if their formation should prevent the
precipitation of magnesium hydroxide, possibly by including the
magnesium as part of a negative ion or radical,[347] MgCl_{3}, then
the corresponding double salts of magnesium chloride with potassium
and sodium chloride (‹e.g.› MgCl_{2},KCl), which are just as stable
as the ammonium salts, should show the same behavior; but, as a
matter of fact, the addition of potassium chloride does not interfere
with the precipitation of the hydroxide by either [p169] potassium
hydroxide or ammonium hydroxide (‹exp.›). So the explanation is
untenable. Obviously, a ‹specific interference of ammonium salts
with the precipitating power of ammonium hydroxide is involved›.
But that is exactly what the law of chemical equilibrium, applied
to the ionization of ammonium hydroxide, would demand: As a weak
base, which is little ionized in pure aqueous solutions, it is ‹very
much weaker as a base, produces a far smaller concentration of the
hydroxide-ion, when readily ionizable salts of ammonium are added to
the solution›,[348] and the precipitation of magnesium hydroxide, and
of metal hydroxides in general, depends on the concentration of the
hydroxide-ion, which is a factor in the solubility-products of bases.

 The precipitation of magnesium hydroxide, in particular, depends
 on the relation of the product [Mg^{2+}] × [HO^{−}]^2 to the
 solubility-product constant of magnesium hydroxide. For the
 saturated aqueous solution, the product [Mg^{2+}] × [HO^{−}]^2 is
 equal to the solubility-product constant, and from the solubility
 of magnesium hydroxide (see the table) the value of the constant is
 found to be 15E−12 at 18°. The concentration of magnesium-ion is
 0.000,154 in this solution. In a 0.1 molar solution of magnesium
 sulphate, which is ionized to the extent of 37.3%, the concentration
 of magnesium-ion is 0.0373, and it would require a concentration
 ‹greater› than 2E−5 of hydroxide-ion to precipitate any magnesium
 hydroxide.[349] Now, the concentration of the hydroxide-ion, in an
 ammoniacal solution, can easily be reduced far below this value
 by the addition of ammonium chloride, nitrate, sulphate or other
 readily ionizable ammonium salt to the solution, and then magnesium
 hydroxide will ‹not› be precipitated.

 In solutions of ammonium hydroxide the concentration of hydroxide
 ion for 18° is found from the relation [NH_{4}^{+}] × [HO^{−}] :
 ([NH_{4}OH] + [NH_{3}]) = 18E−6 (p. 161). (1) For ammonium
 hydroxide, for instance in 0.2 molar solution, and in the absence
 of any ammonium salt, [HO^{−}] = [NH_{4}^{+}] = 0.0019.[350] This
 concentration of the hydroxide-ion should be more than sufficient
 to ‹precipitate› magnesium hydroxide in a 0.1 molar solution of the
 sulphate.[351]

 EXP. 100 c.c. of a mixture which should contain magnesium sulphate
 in 0.1 molar solution would require 246 / (10 × 10) or 2.46 grams
 of MgSO_{4}, 7 H_{2}O. [p170] This weight of the salt is dissolved
 in 50 c.c. of water and 50 c.c. of 0.4 molar solution of ammonium
 hydroxide is added to it. Magnesium hydroxide is ‹precipitated›.
 (The precipitation is incomplete because the ammonium sulphate,
 formed in the reaction, reduces the ionization of ammonium
 hydroxide.)

 (2) In the presence of 0.25 molar ammonium chloride, the chloride
 being dissociated to the extent of 80%,[352] the concentration of
 the hydroxide-ion in a 0.2 molar ammonium hydroxide solution is
 reduced to 18E−6.[353] According to the above calculation this is
 ‹too small› a concentration to precipitate magnesium hydroxide in a
 0.1 molar solution of the sulphate.

 EXP. 1.35 grams ammonium chloride (the weight corresponding to
 100 c.c. of a mixture containing ammonium chloride in 0.25 molar
 solution) is dissolved in 50 c.c. of 0.4 molar ammonium hydroxide
 and 2.46 grams of magnesium sulphate, dissolved as before in 50 c.c.
 of water, is added to the mixture. ‹No precipitate› of magnesium
 hydroxide is formed.

In a similar fashion and for the same reason, ammonium salts
interfere more or less with the precipitation of other hydroxides,
for instance with the precipitation of manganous, nickelous,
cobaltous, ferrous, zinc, cupric and cadmium hydroxides. But ammonium
salts do not prevent the precipitation of aluminium, chromium and
ferric hydroxides, which are much less soluble than the hydroxides
just mentioned, and as much weaker bases, (Chap. X) are also much
less readily ionized. They are precipitated by smaller concentrations
of the hydroxide-ion than are the hydroxides of the first group, and
their precipitation may be made quantitative.

 EXP. Ferric hydroxide is readily precipitated when 2.7 grams of
 ferric chloride FeCl_{3}, 6 H_{2}O, the weight of the chloride
 required to give 100 c.c. of a 0.1 molar solution, is dissolved in
 as little water as possible. The solution is added to the mixture
 of magnesium sulphate, ammonium chloride and ammonium hydroxide
 obtained in the previous experiment, in which no magnesium hydroxide
 was precipitated.


  FOOTNOTES:

  [326] See Smith, ‹General Inorganic Chemistry›, p. 414, ‹General
  Chemistry for Colleges›, p. 277; Remsen, ‹Inorganic Chemistry
  (advanced course)›, p. 158.

  [327] Mg^{2+} may also be precipitated as a carbonate with the
  other ions of the group (see Part III).

  [328] In the case of ammonium nitrate a different form of
  decomposition, namely into nitrous oxide and water, predominates,
  and, in the case of ammonium nitrite, decomposition into nitrogen
  and water takes place so readily, that the decomposition of the
  salt takes that direction chiefly.

  [329] Table, p. 106.

  [330] T. S. Moore, ‹J. Chem. Soc.› (London), «91», 1379 (1907).

  [331] From equation (I) we obtain directly, by the application
  of a simple mathematical transformation, that [NH_{3}] +
  [NH_{4}OH] / [NH_{4}OH] = ‹k›_{NH_{3}} + 1 = ‹k′›, and, therefore,
  [NH_{4}OH] = [NH_{3}] + [NH_{4}OH] / ‹k′›. Inserting this value
  for [NH_{4}OH] in equation (II) and transferring ‹k′›, we have
  [NH_{4}^{+}] × [HO^{−}] / ([NH_{3}] + [NH_{4}OH]) = ‹k›_{base} /
  ‹k′› = K.

  [332] Water of crystallization, found in many of the precipitates
  used in qualitative analysis, will, as a rule, be indicated only
  in the formulas used in Part III, in the study of the reactions of
  ions.

  [333] See Part III as to the method of vaporizing magnesium.

  [334] ‹Cf.› Findlay, ‹Z. phys. Chem.›, «34», 409 (1900).

  [335] The solubility of barium sulphate at 18°, according to the
  table, is 0.0023 / 233, or 1E−5 mole per liter, and the salt may be
  considered completely ionized at this dilution.

  [336] The solubility (see the table) is 0.114 / 183.6, or 6.2E−4
  mole per liter, 84% of which is ionized (according to conductivity
  determinations, Kohlrausch and Holborn, ‹loc. cit.›, p. 200). Hence
  [Sr^{2+}] = [SO_{4}^{2−}] = 0.00062 × 0.84 = 0.0005.

  [337] To establish equilibrium, prolonged "digesting" is sometimes
  required. Double salts, solid solutions and mechanical enclosures
  are liable to interfere with the completeness of such separations
  by fractional precipitation. Resolution and reprecipitation will
  then usually effect a sufficiently accurate separation for most
  purposes. On account of the possibility of such complications, the
  conditions for a successful separation, within limits such as those
  described in the text, must in all cases be investigated.

  [338] See the table at the end of Part IV.

  [339] The salt may be considered completely ionized at this
  dilution. Each molecule of silver chromate forms two silver
  ions when it is ionized. See p. 141 in regard to the form the
  solubility-product takes in the case of a salt of this type.

  [340] The complication, resulting from the hydrolysis of the
  chromate, is not included in this calculation.

  [341] ‹Cf.› Findlay, ‹loc. cit.›

  [342] Even Guldberg and Waage considered the ‹active› mass
  to be the fundamental factor and simply considered the total
  concentrations to be proportional to the "active masses," since
  they had no means of determining the proportion of "active"
  substances in the total concentrations.

  [343] See Nernst, ‹Theoretical Chemistry›, p. 533, for a fuller
  discussion of the relations between the new and the old views on
  this subject.

  [344] Dietrich and Wöhler, ‹Z. anorg. Chem.›, «34», 194 (1903).

  [345] On account of the formation of an ammonium salt in the
  reaction.

  [346] Loven, ‹Z. Anorg. Chem.›, «11», 404 (1896); Herz and Muks,
  ‹ibid.›, «38», 138 (1904).

  [347] In that case the salts would be called "complex" salts, salts
  of a complex ion, MgCl_{3}^{−}. See Chapter XII. They are really
  "double salts"; ‹cf.› Smith, ‹General Inorganic Chemistry›, p. 536.

  [348] See p. 114, and recall the laboratory experiments (Lab.
  Manual, p. 9, § 6), which may be given as lecture experiments at
  this point.

  [349] Calling ‹x› the concentration of the hydroxide-ion, required
  to saturate a 0.1 molar magnesium sulphate solution with magnesium
  hydroxide, we have 0.0373 × ‹x›^2 = 15E−12 and ‹x› = 2E−5.

  [350] Putting [HO^{−}] = [NH_{4}^{+}] = ‹y›, we have ‹y›^2 :
  (0.2 − ‹y›) = 18E−6. Then ‹y› = 0.0019.

  [351] 0.0373 × 0.0019^2 = 0.13E−6, which is considerably larger
  than the solubility-product constant for magnesium hydroxide,
  15E−12.

  [352] Kohlrausch and Holborn, p. 159. Minor changes in the degrees
  of ionization of MgSO_{4} and NH_{4}Cl (and consequently of
  NH_{4}OH) occur, when the salts are present together. In a rigorous
  treatment, the ionization of each salt in the mixture would be
  calculated with the aid of Arrhenius's principle of isohydric
  solutions.

  [353] ‹Vide› the analogous calculation on p. 113.

[p171]




 CHAPTER X

 «ALUMINIUM; AMPHOTERIC HYDROXIDES; HYDROLYSIS OF SALTS. THE ALUMINIUM
 AND ZINC GROUPS»


The chemistry of the analytical reactions of the alkalies and
alkaline earths is extremely simple,—it is essentially the chemistry
of well-defined bases and their salts,—and the separations and
identifications, as we have seen, depend almost entirely on physical
differences rather than on chemical contrasts. In the aluminium
and zinc groups, which are precipitated together and which will be
discussed together, the chemistry of the reactions becomes very much
more complex. Therefore, we shall not, as yet, consider the groups as
a whole, but shall first discuss the important analytical reactions
of some compounds of aluminium.

«Aluminium Hydroxide an Amphoteric Hydroxide.»—Whereas the hydroxides
of the alkali and alkaline earth metals are bases, pure and simple,
aluminium hydroxide shows the properties both of a base and of
an acid; it is an ‹amphoteric› hydroxide, the term "amphoteric"
indicating the combination of acid with basic properties in any
compound. Aluminium hydroxide dissolves in acids. From its solution
in hydrochloric acid, an ‹aluminium› salt, aluminium chloride
AlCl_{3}, 6 H_{2}O, is obtained. It also combines with strong
bases, dissolving for instance in a solution of sodium hydroxide
and forming an ‹aluminate›, NaAlO_{2}. The two salts mentioned are
typical representatives of the two series of salts, which aluminium
hydroxide is capable of forming. This dual character of the hydroxide
raises a number of interesting questions, which one meets with quite
frequently in the study of analytical reactions. One may ask, first,
how aluminium hydroxide can ionize both as an acid and as a base;
second, whether any reason can be given, why it should show the dual
nature; and third, if it is both base and acid, why it does not
neutralize itself.

According to the best knowledge we have on the subject, the molecule
of aluminium hydroxide has the following ‹structure› or arrangement
of its atoms: Al(—O—H)_{3}.

It is readily seen that the cleavage of the molecules may produce,
[p172] either aluminium and hydroxide ions, characteristic ions of a
base, or aluminate[354] and hydrogen ions, characteristic ions of an
acid:

 Al^{3+} + 3 ^{−}OH ⇄ Al(—0—H)_{3} ⇄ AlO_{2}^{−} + H^{+} + H_{2}O.

The ionization of the hydroxide both as an acid and as a base is,
thus, quite possible on the basis of the molecular structure assigned
to it. In fact, all of the so-called oxygen acids are considered to
be hydroxides—we have sulphuric acid, O_{2}S(OH)_{2}, phosphoric
acid, OP(OH)_{3}, etc.,—exactly as the bases, Mg(OH)_{2}, etc., are
hydroxides.

That brings us to the second question, why aluminium hydroxide
should show this dual character, whereas, for instance, sodium and
magnesium hydroxides, which have similar structures, do not show
it. The best answer to this question is found when we consider the
properties of the elements and their derivatives in connection with
their position in the periodic or natural system of elements, which
shows the properties as (periodic) functions of the atomic weights.
In the second series of the elements,[355] omitting the zero group
element neon and taking the elements in the order of increasing
atomic weights, we have sodium (23), magnesium (24), aluminium (27),
silicon (28), phosphorus (31), sulphur (32), and chlorine (35.5). One
of the properties that are shown to be functions dependent on the
atomic weight, is the property under discussion, namely the tendency
of the (highest) hydroxides of the elements to ionize as bases or
acids, respectively. It is clear that the hydroxides of the elements
with the lowest atomic weights in the series, sodium and magnesium,
show the most pronounced tendency to ionize as bases; the hydroxides
of the elements with the highest atomic weights show the most
pronounced tendency to ionize as acids—perchloric acid, (HO)ClO_{3},
and sulphuric acid, (HO)_{2}SO_{2}, belong to the strongest acids. In
accordance with the underlying principle of the periodic system, the
change of [p173] properties, in going from one extreme to the other,
is a function of the increase in atomic weight and is not sudden but
‹gradual›. And so the basic function, the tendency to produce the
hydroxide-ion, is found to grow ‹weaker› as one goes from sodium to
magnesium and then to aluminium, hydroxide; and the acid function,
the tendency to produce the hydrogen-ion, grows markedly stronger,
as one goes from phosphoric to sulphuric and perchloric acids. It
is not surprising to find the two functions existing together, ‹but
in rather weak form, in the case of the intermediate hydroxides›,
notably in aluminium hydroxide and, to some degree, in silicic
acid, ‹the acid character beginning before the basic function has
ceased›. In accordance with this view, aluminium hydroxide is found
to be only a ‹weak›, slightly ionized base, and a ‹very weak›, even
less readily ionizable acid. In the case of silicic acid, which is
the next hydroxide one meets as one goes toward the acid end of the
series, the conditions are reversed. As the name indicates, it is
primarily an acid, but it is a very weak one, and a critical scrutiny
of its behavior shows it to have ‹very weak basic› functions, much
weaker than those of aluminium hydroxide. The question may, indeed,
be raised, whether either the basic or the acid properties really die
out altogether in the hydroxides, from one end of the series to the
other. In view of the small tendency toward sudden changes found in
nature, one might suspect traces of basic character to be preserved
right through the series to the strongest acids, like perchloric
acid. As a matter of fact, later (see Chapter XV), we shall be
obliged to consider possible basic functions of the strongest oxygen
acids, such as nitric, perchloric, permanganic acids, and one of
their most important properties, their behavior as oxidizing agents,
will be found to be probably intimately associated with this remnant
of basic ionization. On the other hand, fused sodium hydroxide will
dissolve sodium with evolution of hydrogen, sodium oxide, Na—O—Na,
being formed; and it can readily be shown,[356] that in the fused
hydroxide there must be at least a few ions NaO^{−}, besides HO^{−},
H^{+}, O^{2−}, and Na^{+}. [p174]

The position of aluminium in the periodic system adequately
accounts, then, for the amphoteric character of its hydroxide.[357]

«Common Occurrence of Amphoteric Hydroxides.»—If we consider the
question of amphoteric behavior a little longer—its consequences are
used extensively in analytical work—we find, in the periodic system,
two other regular changes concerning acid and basic functions, only
one of which we shall discuss here.[358] While in a ‹series› of
elements the acid character of the hydroxides increases with the
atomic weight, in a family of elements the reverse relation holds.
From nitrogen to bismuth, in the nitrogen family of the sixth column
of the periodic system, the acid character of the hydroxides grows
steadily weaker, the basic character increases, and we find, again,
that the intermediate elements, notably arsenic and antimony, produce
hydroxides, which show markedly amphoteric character.

If, in the second series of the periodic group, one goes back from
aluminium to magnesium hydroxide, in accordance with the first
general principle laid down a much stronger base is found; and if one
then goes, in the magnesium family, to the hydroxide of the element
of next lower atomic weight, glucinum or beryllium, one again meets,
in accordance with the second principle laid down, a weaker basic
and more acidic hydroxide than magnesium hydroxide; in other words,
the basic and acid functions revert closely to those exhibited by
aluminium hydroxide. Glucinum hydroxide is a pronounced amphoteric
hydroxide and resembles aluminium hydroxide so closely that, in the
early history of chemistry, it was mistaken for the latter.

If one goes from glucinum back to lithium, in the same series of the
periodic system, and from lithium to the element with the next lower
atomic weight in the same group, one comes to hydrogen, which forms
one of the most important and interesting of the [p175] amphoteric
hydroxides, water. The ionization of water, slight as it is, yields
hydrogen-ion and hydroxide-ion, the ions characteristic of acids and
of bases, and water is placed among the weakest of the acids (see
table, p. 104) as well as among the weakest of the bases (table, p.
106). We shall return to these relations, presently, and shall find
that the apparent weakness of water, as a base and as an acid, is
seemingly very largely due to the fact that water represents only an
extremely dilute solution (see p. 66) of the real hydroxide, HOH, or
hydrol, and consists very largely of a compound (H_{2}O)_{2}. H_{2}O,
or hydrol, is, perhaps, not very much weaker as an acid or as a base,
than is aluminium hydroxide.

Lower oxides of elements in the higher (acid-forming) groups show a
less pronounced acid-forming character than the higher oxides, and
a greater tendency to produce bases as well as acids, and are often
amphoteric. Chromium hydroxide is of this type.

In view of all these facts, and in view, also, of the fact that the
majority of the seventy-odd elements cannot lie at the ends of the
periodic system but are found in the middle, it is not surprising to
find that ‹pronounced amphoterism is shown by a large number of metal
hydroxides; it is, perhaps, the rule rather than the exception›. A
considerable number of the elements in the middle of the system are
rare elements and that is perhaps the chief reason why this relation
does not stand out more prominently in the consideration of the
common acids and bases.

«Amphoteric Character of Hydroxides Considered in Analysis.»—The
amphoteric character of hydroxides is frequently made use of in
analytical work in the separation and identification of various
elements and, when present, it must always be considered, in order
to escape possible error. The following hydroxides of the common
elements show ‹pronounced amphoteric› character: aluminium, chromic,
zinc, lead, stannous, antimonous hydroxides and arsenious, platinic,
auric, antimonic and stannic acids. Arsenic acid, ferric hydroxide
and silicic acid show exceedingly slight, but perceptible, amphoteric
character, sufficient to affect, to a certain degree, their
analytical behavior.[359] [p176]

«Self-Neutralization of Amphoteric Substances.»[360]—We may turn now
to the third question raised in connection with aluminium hydroxide,
to the inquiry (p. 171), why aluminium hydroxide, the acid, does not
neutralize aluminium hydroxide, the base. In fact, the base must
and does form a salt with the acid. But the salt is formed only to
a minimal extent, as the result of the fact that the base is a very
weak base, the acid an exceedingly weak acid. Such exceedingly weak
bases and acids show little tendency to combine with each other to
form salts ‹in the presence of water, especially if one or both
are difficultly soluble in water›, as in the present instance. The
behavior of aluminium hydroxide, in this respect, is part of a much
larger and more general question, growing out of the fact that water
is a very weak acid and base, as has been seen, and, to a greater
or lesser extent, reacts as such with salts, which are dissolved in
it. This action of water plays an important rôle in many analytical
reactions, and especially, also, in the reactions of aluminium salts.
We shall, first, discuss this larger question of the action of water,
as an ionogen, on salts, and then return (p. 187) to the problem of
the self-neutralization of an amphoteric hydroxide.

HYDROLYSIS OF SALTS

«Ionization of Water.»—We may first consider, very briefly, the
evidence that water is ionized even to the extent indicated by the
ionization constants given in our tables. It may be said that the
purest water ever prepared[361] shows a minimal conductivity, from
which the concentrations of its hydrogen and hydroxide ions and
the value of the ionization constant may be calculated. For the
ionization of water we have

 [H^{+}] × [HO^{−}] / [Nonionized water] = K_{Ion}.

As the concentration of pure water, or of the water in dilute
solutions, may be considered nearly a constant, we may put

 [H^{+}] × [HO^{−}] = K_{H_{2}O}.

This is the relation most commonly, and most conveniently, used.
It is free from all assumptions as to the molecular weight of the
nonionized water, the calculation of the concentrations [p177]
[H^{+}] and [OH^{−}] being independent of any such assumption. The
value of K_{H_{2}O} increases decidedly with an increase in the
temperature,[362] whereas the ionization constant of an ordinary
acid, such as acetic acid, is affected very little by changes in
temperature. This peculiar increase of the ionization of water at
higher temperatures is undoubtedly due to the increasing dissociation
of the complex water molecules into hydrol molecules (see p. 66),
which, presumably, are most easily ionized. Now, the value of
the constant K_{H_{2}O}, at any temperature, may be determined
in some half a dozen different and independent ways, including
the conductivity method mentioned, and one of the most remarkable
developments of the theory of ionization is that all of these methods
lead to concordant results.[363]

 Aside from considerations based on its ionization, water may be
 shown, by its chemical behavior, to have the functions of an acid
 and of a base, and the conclusions reached are in complete accord
 with those reached with the aid of the theory of ionization.

 «Water is An Acid.»—If the oxide of a metal such as copper, lead
 or calcium, is treated with an acid, a salt is formed by the
 combination of the two; for instance, we have

 PbO + HCl → Pb(OH)Cl,

 Pb(OH)Cl + HCl → PbCl_{2} + H_{2}O,

 PbO + 2 HCl → PbCl_{2} + H_{2}O,

 CaO + 2 HCl → CaCl_{2} + H_{2}O.

 Water will combine with a number of oxides very much in the same
 manner and sometimes with such vigor, that considerable heat is
 evolved, as in the slaking of lime (‹exp.›):

 CaO + HOH → Ca(OH)_{2}.

 Water in this, and similar actions, takes the place of and plays the
 rôle of, an ‹acid›, and ‹the metal hydroxides or bases appear as its
 salts›.[364] It is a ‹very weak› acid, which can easily be driven
 out of its salts by any stronger acid (neutralization of bases),
 but that does not alter the conclusions reached. Considered from
 the point of view of the theory of ionization, the relation [p178]
 would be expressed by saying that in the common bases the positive
 hydrogen ion of water has been replaced by some other positive or
 metal ion. The salt of any acid could be defined in exactly the same
 way.

 «Water as a Base.»—Acid oxides, such as carbon dioxide, silicon
 dioxide, arsenious oxide, combine more or less readily with bases,
 such as sodium hydroxide, to form salts:

 CO_{2} + NaOH → NaHCO_{3},

 As_{2}O_{3} + 2 NaOH → 2 NaAsO_{2} + H_{2}O.

 A number of acid oxides combine with water in exactly the same
 manner, and sometimes with such tremendous vigor, that great care
 must be taken in bringing the two together, as is the case when
 sulphur trioxide or phosphorus pentoxide are added to water (‹Exp.›).

 We have P_{2}O_{5} + HOH → 2 HPO_{3}.

 It is evident that in such actions water may take the place of,
 and play the rôle of, an ordinary base, forming the ‹acids›,
 which may well be defined as hydrogen salts.[365] It is true
 that the basic properties of water are so weak, that the
 metal ion of even a weak base, like ammonium hydroxide, will
 replace the hydrogen-ion in its salts, the acids, quite readily
 (HCl + NH_{4}OH ⥂ NH_{4}Cl + H_{2}O). But such a weak base, in turn,
 will have to give way, of course, to still stronger bases; for
 instances, NH_{4}Cl + NaOH ⥂ NaCl + NH_{4}OH. From the point of view
 of the theory of ionization, the hydrogen-ion is positive, like all
 the other metals ions whose hydroxides are bases.

 There should be no difficulty, therefore, in considering water to
 have the chemical properties of a base as well as of an acid. Its
 chemical activities as such, weak as they may be, must be satisfied
 whenever it is present. These activities lead to the hydrolysis or
 the decomposition of salts by water, in greater or lesser degree,
 whenever water is used as a solvent for salts.

«Action of Water on a Salt of a Strong Base and a Strong Acid.»—If
sodium chloride, a typical salt formed from a strong base and a
strong acid, is dissolved in water, it is ionized to a considerable
extent. Considering the solution from a mechanical point of view, we
would expect that the sodium ions, moving in all directions, would
collide occasionally with hydroxide ions, which are formed from the
water and are present in minute but definite quantity. Some of the
collisions must result in the formation of sodium hydroxide, as we
have no reason to suppose that the result would differ from that in
other cases where positively charged particles meet with negatively
charged ones. However, since sodium hydroxide is an ionogen, with
a very great tendency to ionize, and since there is present only a
minute concentration of the hydroxide-ion, the [p179] equilibrium
conditions will be satisfied when only traces of the nonionized
hydroxide are formed. In a similar manner, we must expect to have
traces, and only traces, of nondissociated hydrochloric acid formed
by the union of chloride ions with some of the hydrogen ions of the
water. Since hydrogen chloride and sodium hydroxide show practically
the same tendency to ionize (tables, pp. 104 and 106), the two kinds
of ions which water forms, the hydrogen-ion and the hydroxide-ion,
will be used up ‹to a very slight› and practically ‹equal› extent
to form nonionized sodium hydroxide and hydrogen chloride, but the
ions will be immediately regenerated, and in equal concentrations,
from the nonionized water which is present. All the equilibrium
requirements will be satisfied when ‹traces› of sodium chloride
have been converted into nonionized sodium hydroxide and hydrogen
chloride. Such a solution, containing no excess of the hydrogen- or
the hydroxide-ion, would react ‹neutral›. The action may be expressed
by the equation[366]

 «NaCl» ⇄ «Na»^{+} + «Cl»^{−}

 «H_{2}O» ⇄ HO^{−} + H^{+}

 Na^{+} + HO^{−} ⇄ NaOH

 Cl^{−} + H^{+} ⇄ HCl.

The decomposition of sodium chloride by water, which one may
predict on the basis of these theoretical considerations, may be
demonstrated, slight as it is, by the following experiment.[367]

 EXP. A pinch of sodium chloride is brought into a platinum crucible,
 which is previously heated in a blast lamp to a bright yellow heat
 (1100°); then 1 c.c. of water is introduced, drop by drop. A steam
 cushion is formed at once (Leidenfrost's phenomenon). After about
 half of the water has been evaporated (half a minute), the water is
 poured into a solution colored with blue litmus; it is changed to
 red by an excess of hydrochloric acid in the water. The crucible is
 cooled, and the salt remaining in it is dissolved in a little water
 and the solution poured into a red litmus solution; the latter turns
 blue.

The sodium chloride has obviously been partially decomposed, by the
water, into its base and its acid; the decomposition is favored by
the high temperature and by the fact that the hydrogen chloride
[p180] formed can pass through the steam cushion into the water,
while the sodium hydroxide is left behind. The removal of a product
of the decomposition would favor its progress (see. p. 114).

The conclusions concerning salts of the type of sodium chloride
may then be summarized in the statement, that ‹salts formed by the
union of a very strong base with an equally strong acid are only
very slightly decomposed by water and their solutions show a neutral
reaction›.

The decomposition of a salt by water into its component base and acid
is called ‹hydrolysis› and the salt is said to be ‹hydrolyzed› in the
action.

«Action of Water on the Salt of a Strong Base with a Weak Acid.»—The
relations are similar in principle, but quite different in degree and
in net result, when the salt of a very strong base, combined with a
weak acid, is dissolved in water. Potassium cyanide is a typical salt
of this kind, and the study of its hydrolysis will illustrate the
behavior of this class of salts. The hydrolysis takes place according
to the equations

 «KCN» ⇄ «K»^{+} + «CN»^{−}

 «HOH» ⇄ «HO»^{−} + H^{+}

 K^{+} + HO^{−} ⇄ KOH

 CN^{−} + H^{+} ⇄ «HCN».

When the cyanide is dissolved in water, we must obtain, for the same
reasons as were developed in the discussion of the hydrolysis of
sodium chloride, a ‹little› nonionized potassium hydroxide, from the
union of potassium ions with hydroxide ions, formed by the water.
Potassium hydroxide being a strong, easily ionizable base, there
will be only a ‹slight tendency› towards this union. Hydrocyanic
acid, on the other hand, is an exceedingly weak acid. The value
of its ionization constant K_{HCN} = [H^{+}] × [CN^{−}] / [HCN]
is only 7E−10, as compared with a similar ratio approximating 1
for potassium hydroxide ([K^{+}] × [HO^{−}] / [KOH] = 1; see the
tables, p. 104 and p. 106 and see pp. 106–7). The hydrogen-ion,
formed from the water, must therefore combine with cyanide-ion, ‹to
form nonionized hydrocyanic acid›, much more completely than the
hydroxide-ion combines with potassium-ion. With the disappearance
of the ions of water, in this case notably of its hydrogen ions,
more water must ionize to satisfy the ionization constant [p181]
for water (p. 176), and the formation of hydrocyanic acid will
continue, towards the satisfying of its own constant. It is important
to note that, for the reasons given, the hydrogen-ion of water ‹is
used up to a far greater extent› than is the hydroxide-ion; ‹the
latter therefore accumulates›, and this accumulation results in the
formation of smaller and smaller concentrations of the hydrogen-ion,
by the water. Since [H^{+}] × [HO^{−}] = 1.2E−14 (at 25°; p.
104), as [HO^{−}] grows larger, [H^{+}] must grow ‹proportionally
smaller›. The ‹suppression of the hydrogen-ion by the accumulation
of the hydroxide ion› will, ultimately, make [H^{+}] so small,
that the equilibrium ratio [H^{+}] × [CN^{−}] / [HCN] will equal
the equilibrium constant. Since the union of the hydrogen-ion with
the cyanide-ion, to form little ionized hydrocyanic acid, is the
main moving cause for the changes, the latter will then come to a
standstill and equilibrium will be established. The net result of
the action of water on potassium cyanide may be said to consist in
the formation of practically nonionized hydrocyanic acid and the
liberation of (chiefly) ionized potassium hydroxide, ‹until all the
equilibrium constants› of the system are satisfied. We note that
potassium cyanide solution must react strongly alkaline (‹exp.›) and
that a free acid (‹e.g.› HCN) may well exist in the presence of a
free base (‹e.g.› KOH), provided the acid is present in a nonionized,
and therefore chemically inactive, condition (inactive as an ‹acid›).

Ignoring the (practically) unimportant formation of small quantities
of nonionized potassium hydroxide, we may summarize the action in a
single equation, which shows the main action:

 CN^{−} + HOH ⇄ HCN + HO^{−}.

Whereas water, as an acid and as a base, is so exceedingly weak,
that it can form but traces of its own salts, sodium hydroxide and
hydrochloric acid, when acting on sodium chloride and competing for
the base with such a strong acid as hydrochloric acid and for the
acid with such a strong base as sodium hydroxide (see p. 179), the
result, evidently, is quite different when water competes for a base
with so weak an acid as hydrocyanic acid. In this case, we note that
a considerable quantity of (ionized) potassium hydroxide, the salt of
water in its rôle of an acid, is formed as a result of the action of
water on potassium cyanide. [p182]

 The theory of ionization, with the aid of the law of chemical
 equilibrium, gives us the means for ‹accurately defining the
 relative concentrations of the products, in the final condition of
 equilibrium›.[368] For the weak acid, hydrocyanic acid, we have the
 condition of equilibrium

 [H^{+}] × [CN^{−}] / [HCN] = K_{HCN} = 7E−10.

 The symbols [H^{+}], [CN^{−}] and [HCN] denote the final
 concentrations for the condition of equilibrium, indicated in the
 equations on p. 180; in such a mixture [H^{+}] is ‹not equal to›
 [CN^{−}], as it is in pure solutions of hydrocyanic acid in water.
 [CN^{−}], representing the total concentration of the cyanide-ion,
 is very much larger than [H^{+}], since the salt, potassium cyanide,
 produces the cyanide-ion in large concentrations.

 For water, we have [H^{+}] × [HO^{−}] = K_{HOH} = 1.2E−14, at 25°.
 Here, again, the symbols represent the final, total concentrations
 of the ions in the mixture and [HO^{−}] is much larger than [H^{+}],
 since hydroxide-ion is formed in large quantities, as described
 above.

 Combining the two equations, we have:

 [CN^{−}] / ([HCN] × [HO^{−}]) = K_{HCN} / K_{HOH} = K_{Hydrolysis}.

 The cyanide-ion, whose concentration is expressed by [CN^{−}],
 is formed practically altogether by the ionization of potassium
 cyanide, which is an easily ionizable and almost entirely ionized
 salt; the hydroxide-ion, whose concentration is expressed by
 [HO^{−}], is formed by the ionization of potassium hydroxide,
 which is an easily ionizable base, ionized to practically the same
 degree as is the potassium cyanide in the solution. If we represent
 the ‹total› concentration of the potassium cyanide, ionized and
 nonionized, at the point of equilibrium, by [KCN] and its degree
 of ionization by α_{1}, and if we represent, similarly, the total
 concentration of potassium hydroxide by [KOH] and its degree of
 ionization by α_{2}, the equilibrium equation may be written:

 α_{1}[KCN] / ([HCN] × α_{2}[KOH]) = K_{HCN} / K_{HOH} = K_{Hydrolysis}.

 Since the degrees of ionization of the two strong electrolytes are
 practically the same, we have further simply

 [KCN] / ([HCN] × [KOH]) = K_{HCN} / K_{HOH} = K_{Hydrolysis}.

 The mathematical equations give us a measure of the extent to
 which water must decompose or ‹hydrolyze› the salt in question, as
 expressed in the chemical equations (p. 180). The ‹extent› of the
 hydrolysis, clearly, depends on the relative ionization constants of
 hydrocyanic acid and water, the ‹two acids competing for the base›.

 From the known values of the constants, one may calculate that,
 at 25°, in a solution of 6.5 grams potassium cyanide in a liter
 (0.1 molar), almost 1.3% of the cyanide is decomposed into
 potassium hydroxide and hydrocyanic acid. Since every molecule
 of hydrolyzed salt forms one molecule of [p183] the hydroxide
 and one molecule of the acid, we may put [KOH] = [HCN] = ‹x› and
 [KCN] = 0.1 − ‹x›. The ionization constant, K_{HCN} = 7E−10,
 and K_{HOH} = 1.2E−14, at 25°. Inserting these values into the
 equation [KCN] / ([HCN] × [KOH]) = K_{HCN} / K_{HOH} we have:
 (0.1 − ‹x›) / ‹x›^2 = 7E−10 / 1.2E−14. Here ‹x› = 0.0013. This is
 1.3% of the 0.1 mole of cyanide used.

 One may convince himself, as follows, that the constants are
 satisfied when the decomposition of the cyanide has proceeded to
 this point: the degrees of ionization of the potassium cyanide and
 potassium hydroxide, α_{1} and α_{2}, may be taken as 85% (the
 same as the degree of ionization of the similar electrolyte KCl
 in 0.1 molar solution). Then [HO^{−}] = 0.85 × 0.0013 = 0.0011;
 [CN^{−}] = 0.85 × (0.1 − 0.0013) = 0.083; [H^{+}] = 1.2E−14 /
 [HO^{−}] = 1.1E−11. For [H^{+}] × [CN^{−}] / [HCN] we have then:
 (1.1E−11 × 0.083) / (0.0013) or 7E−10, the value for the ionization
 constant of hydrocyanic acid. It should be noted that, whereas in
 pure water at 25° [H^{+}] = [HO^{−}] = √(1.2E−14) = 1.1E−7, in the
 solution under consideration [HO^{−}] has increased to the value
 0.0011 and [H^{+}] is only 1.1E−11.

 The relation developed for the ‹hydrolysis› of potassium cyanide
 is a general one, holding for the hydrolysis of salts, of the
 type MeX, of a weak acid with a strong base. It may be expressed
 in general as follows: for the hydrolysis of a salt according to
 MeX + HOH ⇄ MeOH + HX, where HX is a weak acid and MEOH a strong
 base, we have:[369]

 [Salt] / ([Acid] × [Base]) = K_{Acid} / K_{HOH}.

 It is clear, from the equation, that the weaker the acid of the salt
 (measured by the ionization constant K_{Acid}, the numerator on the
 right), the more will water, ‹ceteris paribus›, be able to drive it
 out of its salt and form its own salt, ‹the base› (the smaller the
 numerator on the right, the larger must be the denominator on the
 left).

The conclusions may be summarized in the statement that the salts of
strong bases with weak acids are more or less decomposed by water
(hydrolyzed) and the resulting solutions must react ‹alkaline›.
We find, as a matter of fact, that aqueous solutions of potassium
cyanide, sodium carbonate, sodium sulphide, borax (see the table, p.
104), all react strongly alkaline to litmus (‹exp.›). Conversely,
it may be said, that if the sodium or potassium salt of an acid
dissolves in water with a ‹decidedly› alkaline reaction, it is the
salt of a weak, poorly ionized acid.[370] [p184]

«Action of Water on a Salt of a Strong Acid with a Weak
Base.»—Exactly similar relations obtain in the case of salts of
strong acids with weak bases:[1] they are decomposed, to a greater
or less extent, into the free, strong, largely ionized acid and the
free, scarcely ionized weak base, ‹the decomposition being stopped
by the accumulation of the free strong acid› (more exactly, of the
‹hydrogen-ion›). Such solutions react strongly ‹acid›, as in the case
of the chloride, nitrate, sulphate of aluminium, of iron (ferric), of
chromium, and of similar salts of weak bases.

 For MeX + HOH ⇄ MeOH + HX, where MeOH ‹is a weak base› and HX a
 strong acid, we have as before:[371]

 [Me^{+}] / ([H^{+}] × [MeOH]) = [Salt] / ([Acid] × [Base]) =
   K_{Base} / K_{HOH}.

«Action of Water on a Salt of a Base and an Acid, Both of which are
Weak.»—We will now turn to the consideration of the action of water
on the fourth class of salts, the salts of a weak base with a weak
acid.[372]

Like all salts, such a salt, say MeX, would ionize very readily, when
dissolved in water (the few exceptions to readily ionizable salts
are not under consideration), and, in this case, both the positive
and the negative ions would have to combine respectively with the
hydroxide and the hydrogen ions of water to form the ‹nonionized weak
base› and the ‹nonionized weak acid›, and satisfy ‹two very small
constants›, K_{Base} and K_{Acid}:

 [Me^{+}] × [HO^{−}] / [MeOH] = K_{Base}

 and [H^{+}] × [X^{−}] / [HX] = K_{Acid}.

Both the hydrogen and the hydroxide ions of water would disappear,
and in approximately equal quantity, if the base and acid were
approximately equally weak, and the ions would be regenerated from
water ‹with no accumulation of either one to suppress the other›,
as in the two previous cases considered. Under these circumstances,
the decomposition by water ‹must proceed very much further than in
the previous cases›. For instance, in the hydrolysis of potassium
cyanide in 0.1 molar solution, at 25°, we find the concentration
of the hydrogen-ion [H^{+}] reduced[373] from 1.1E−7, its [p185]
value in pure water, to 1.1E−11, as a result of the accumulation of
potassium hydroxide (the hydroxide-ion), and only ‹this small value›
for [H^{+}] appears in the equation for the formation of the free
acid, HCN (first equation, p. 182; ‹vide› the calculation, p. 183).
But, in the present case, the factors [HO^{−}] and [H^{+}], in the
equations on p. 184, maintain practically their original value, about
the same as in pure water, and the formation of nonionized MeOH and
HX must go correspondingly further to satisfy the constants K_{Base}
and K_{Acid}. Just how far the action must proceed, can be formulated
with the aid of the theory of ionization and the law of chemical
equilibrium,[374] much in the same way as for the hydrolysis of
potassium cyanide.

 The final equation, as developed by Arrhenius, reads:

 [Me^{+}] × [X^{−}] / ([HX] × [MeOH]) =
   α^2 [Salt]^2 / ([Acid] × [Base]) =
   (K_{Acid} × K_{Base}) / K_{HOH} = K,

 in which K_{Acid} and K_{Base} represent the ionization constants of
 the acid and the base, as given in the tables (pp. 104 and 106), and
 α is the degree of ionization of the salt.

For the cyanide of a base, which is as weak a base as hydrocyanic
acid is an acid, we find that the decomposition by water, at 25° in a
0.1 molar solution, must comprise 99.35%[375] of the salt, in order
to establish equilibrium. In the case of potassium cyanide, in 0.1
molar solution, only 1.3% of the salt is decomposed (p. 182).

Now, if both the free base and the free acid are very ‹difficultly
soluble›, then the concentrations [MeOH] and [HX], respectively,
in the solution ‹cannot go beyond a certain minute limit›. In
view,[376] then, of the very small value, K_{Base}, of the ratio
[Me^{+}] × [HO^{−}] / [MeOH] and the minute value that the
second term [MeOH] has under these conditions, the first term
[Me^{+}] × [HO^{−}] must have a correspondingly smaller value. It
is clear, therefore, that in such a solution neither the nonionized
base, MeOH, nor its ion, Me^{+}, can exist in more than minute
quantities when the equilibrium constants are satisfied. The same
conclusion is reached regarding the [p186] possibility of the
existence of the difficultly soluble acid HX and its ion X^{−}, in
more than minimal quantities. Since, then, neither the ion Me^{+} nor
the ion X^{−} can be present in more than traces, their salt, MeX,
which is considered readily ionizable, also ‹cannot exist in aqueous
solutions›, except in traces.

 The ‹quantitative relations› are evident from the equilibrium
 equation (p. 185): [Me^{+}] × [X^{−}] / ([HX] × [MeOH]) =
 α^2 [Salt]^2 / ([Acid] × [Base]) = (K_{Acid} × K_{Base}) / K_{HOH} = K.
 It is evident that the concentration of the salt, [Salt], which is
 capable of existence in aqueous solution, is, in the first place,
 ‹the smaller the smaller the values› for K_{Acid} and K_{Base}
 are, ‹i.e. the weaker the acid and the base are›; and, in the
 second place, it is the smaller the smaller the values for [Acid]
 and [Base] are, which, in the present instance, represent the
 concentrations of the difficultly soluble acid and base in saturated
 solution, ‹i.e. their solubilities›.

We reach the conclusion that ‹salts of very weak bases and very weak
acids are very considerably decomposed by water›, and, if both the
acid and the base are difficultly soluble in water, the decomposition
is ‹practically complete›. ‹Conversely, such a very weak, difficultly
soluble base will not combine with a very weak, difficultly soluble
acid to form a salt in the presence of water.› An instance of the
first kind is found in the case of aluminium sulphide, the salt of
a very weak, difficultly soluble base, aluminium hydroxide, with
a rather little soluble, weak acid, hydrogen sulphide (see table,
p. 104). We find that when a piece of aluminium sulphide, prepared
by dry methods, is dropped into water (‹exp.›), a precipitate of
aluminium hydroxide is immediately formed and evolution of hydrogen
sulphide occurs. We have

 Al_{2}S_{3} ⇄ 2 Al^{3+} + 3 S^{2−},

 «6 HOH» ⇄ 6 HO^{−} + 6 H^{+}

 2 Al^{3+} + 6 HO^{−} ⇄ «2 Al(OH)_{3} ↓»

 3 S^{2−} + 6 H^{+} ⇄ «3 H_{2}S ↑».

An instance where a very weak insoluble acid will not combine,
appreciably, with a very weak insoluble base, is found in the case of
‹aluminium hydroxide›. A development of the equilibrium equations for
its ionization as a base and its ionization as an acid would show,
that all the constants would be readily satisfied, when a very minute
quantity of dissolved ionized aluminium aluminate is formed. [p187]

 «Self-Neutralization of Amphoteric Hydroxides.»—We may consider
 a saturated solution of aluminium hydroxide, in contact
 with the solid hydroxide. For the ‹acid ionization›,[377]
 Al(OH)_{3} ⇄ AlO_{2}^{−} + H^{+} + H_{2}O, we have

 [AlO_{2}^{−}] × [H^{+}] / [Al(OH)_{3}] = K_{Acid}.

 Similarly, for the ‹basic ionization›,[378] Al(OH)_{3} ⇄
 (AlO)^{+} + HO^{−} + H_{2}O, we have

 [AlO^{+}] × [HO^{−}] / [Al(OH)_{3}] = K_{Base}.

 The formation of ‹traces of nonionized› (basic) aluminium
 aluminate would satisfy the equilibrium requirements for
 AlO^{+} + AlO_{2}^{−} ⇄ AlO(AlO_{2}), since the aluminate, like
 other aluminates, is presumably readily ionizable in aqueous
 solutions. Aluminium hydroxide, as a base and as an acid, would
 yield in the ‹first moment› greater concentrations of the hydroxide
 and hydrogen ions than would satisfy the equilibrium constant
 for water (p. 176); the excess of these ions must combine to
 form water, until the product of their concentrations is equal
 to the ionization constant of water. The neutralization of these
 first quantities of hydrogen and hydroxide ions would destroy the
 momentary condition of equilibrium between aluminium hydroxide and
 its ions and would lead to its further ionization, ‹both as a base
 and as an acid›, and to the solution of some aluminium hydroxide
 (see the above equilibrium equations). However, since AlO^{+} and
 AlO_{2}^{−} remain practically uncombined and therefore ‹accumulate›
 in the solution, the concentrations of the hydroxide and hydrogen
 ions formed grow smaller and smaller; for an increasing excess of
 the ion AlO^{+} will allow only smaller and smaller values for
 [HO^{−}], according to the equilibrium equation for K_{Base},
 and, similarly, an increasing excess of the ion AlO_{2}^{−} will
 permit [H^{+}] to reach only smaller and smaller values, according
 to the equilibrium equation for K_{Acid}. When the values for
 [HO^{−}] and [H^{+}] have in this way become small enough to make
 [HO^{−}] × [H^{+}] = K_{HOH}, equilibrium is reached. It is evident
 that in such a solution, in the condition of equilibrium, [HO^{−}]
 is ‹not› equal to [AlO^{+}], as it would ordinarily be, according
 to the ionization equation Al(OH)_{3} ⇄ AlO^{+} + HO^{−} + H_{2}O,
 but is much ‹smaller›. Similarly, [H^{+}] is much smaller than
 [AlO_{2}^{−}].

 Just how much aluminium aluminate must be formed by a
 self-neutralization of the amphoteric hydroxide will depend on the
 values for K_{Base} and K_{Acid} and on the solubility of aluminium
 hydroxide (nonionized Al(OH)_{3}). The two equilibrium equations may
 be combined:

 [AlO^{+}] × [AlO_{2}^{−}] × [H^{+}] × [HO^{−}] / [Al(OH)_{3}]^2 =
   K_{Base} × K_{Acid}.

[p188]

 Since [H^{+}] × [HO^{−}] = K_{HOH}, and since [AlO^{+}] and
 [AlO_{2}^{−}] may be taken to represent ‹each› the concentration of
 the practically completely ionized aluminium aluminate AlO(AlO_{2}),
 we have[379]

 [Alum. Aluminate]^2 / [Alum. Hydroxide]^2 =
   (K_{Base} × K_{Acid}) / K_{HOH},

 or

 [Alum. Aluminate] / [Alum. Hydroxide] =
   √[(K_{Base} × K_{Acid}) / K_{HOH}].

 It is clear, that the smaller the ionization constants K_{Base}
 and K_{Acid} are, and the smaller the solubility of nonionized
 aluminium hydroxide [Alum. Hydroxide] is, the smaller must be the
 concentration of the aluminate formed to satisfy the conditions for
 equilibrium.

 Aluminium hydroxide is a typical ‹amphoteric hydroxide›, and the
 relations developed may be applied, ‹mutatis mutandis›, to the
 conditions of equilibrium for analogous amphoteric hydroxides, such
 as zinc, lead, chromic hydroxides, and so forth. Salt formation or
 self-neutralization will depend, in every instance, on the strength
 of the base and the acid formed, and on the solubility of the
 hydroxide.[380]

With the aid of the preceding considerations the analytical reactions
of aluminium, which are used to separate it from other elements and
to identify it, may be readily understood. They will be discussed in
connection with the analysis of the "Aluminium and Zinc Groups."

«The Analysis of the Aluminium and Zinc Groups.»—The groups of metals
which are here called the [p189] "‹Aluminium and Zinc Groups›"
consist of two groups, which ordinarily are precipitated together
in qualitative analysis, and which are then separated from each
other. We may distinguish the "‹Aluminium Group›" of trivalent metal
ions, including aluminium, ferric and chromium ions, and the "‹Zinc
Group›" of bivalent metal ions, including zinc, nickelous, cobaltous,
manganous and ferrous ions. Of the two groups, the ions of the
second group, in agreement with their lower valence (see p. 172),
form the ‹stronger bases›, and, as such, they are all capable of
forming ‹comparatively stable salts› even with such very weak acids
as hydrogen sulphide and carbonic acid. Ammonium sulphide, added
to a solution of a salt of any one of the ions of the zinc group,
precipitates the corresponding sulphide, sodium or ammonium carbonate
precipitates the corresponding carbonate.[381] We have, for instance:

 FeCl_{2} + (NH_{4})_{2}S → FeS ↓ + 2 NH_{4}Cl,

 FeCl_{2} + Na_{2}CO_{3} → FeCO_{3} ↓ + 2 NaCl.

Only one member of this group, zinc, forms an ‹amphoteric› hydroxide
and advantage is taken of this in identifying zinc.

The members of the aluminium group form hydroxides, which are
much weaker bases than are the hydroxides of the bivalent group
just considered. Their salts with strong acids are considerably
hydrolyzed and react strongly acid, and their salts with very weak
acids, like carbonic acid and hydrogen sulphide, are decomposed so
readily by water, that only ferric sulphide is capable of existence
in its presence. When the sulphide, Al_{2}S_{3}, prepared by heating
aluminium with sulphur, is added to water, it is totally decomposed
into the hydroxide and hydrogen sulphide (p. 186); and ‹if aluminium
chloride is treated with ammonium sulphide› in aqueous solution,
‹aluminium hydroxide, and not its sulphide, is precipitated›. The
latter result may be interpreted in two ways, both of which, in the
ultimate analysis, mean that hydrogen sulphide is too weak an acid
to form a stable sulphide with aluminium hydroxide in the presence
of water, the difficult solubility of aluminium hydroxide and the
limited solubility of hydrogen sulphide being favoring factors (see
p. 186). In a solution of aluminium chloride, the salt of a very
weak base with a strong [p190] acid, more or less of the salt is
hydrolyzed, and we have a condition of equilibrium as expressed in
the equation AlCl_{3} + 3 H_{2}O ⇄ Al(OH)_{3} + 3 HCl. The addition
of ammonium sulphide to such a solution would neutralize the free
hydrochloric acid, and the action would proceed to completion
towards the right, hydrogen sulphide being liberated, by the action
of the acid on the ammonium sulphide. As hydrogen sulphide is too
weak an acid to combine, appreciably, with aluminium hydroxide,
and as the latter is difficultly soluble, the hydroxide is
precipitated. According to the degree of dilution, more or less of
the hydrogen sulphide also escapes. Besides this interpretation of
the precipitation of aluminium hydroxide under these conditions, we
may also consider the following: any aluminium sulphide, formed the
first moment, would remain largely ionized and would be immediately
converted, by the ions of water, into aluminium hydroxide and
hydrogen sulphide. The net result of the action is the precipitation
of aluminium hydroxide and the evolution of hydrogen sulphide:

 2 AlCl_{3} + 3 (NH_{4})_{2}S + 6 H_{2}O →
   2 Al(OH)_{3} ↓ + 6 NH_{4}Cl + 3 H_{2}S ↑

 or 2 Al^{3+} + 3 S^{2−} + 6 HOH → 2 Al(OH)_{3} ↓ + 3 H_{2}S ↑.

A similar result is obtained when the solution of a chromium salt is
treated with a solution of ammonium sulphide. Only ferric hydroxide
is capable of forming a sulphide, ferric sulphide, Fe_{2}S_{3}, which
is precipitated when solutions of ferric salts are treated with
ammonium sulphide.[382]

Ammonium sulphide will, consequently, precipitate aluminium and
chromium ‹hydroxides› and ferric, ferrous, nickel, cobalt, manganese
and zinc ‹sulphides›, from a solution of the chlorides of the metals.

Now, both the sulphides and the hydroxides of the alkaline earths and
alkalies are sufficiently soluble not to be precipitated by ammonium
sulphide, or by a mixture of it with ammonium hydroxide, if ammonium
chloride be added to the mixture to prevent the precipitation of
magnesium hydroxide (see p. 168), which is the least soluble of the
hydroxides of the alkaline earth group. [p191] ‹A mixture of ammonium
sulphide, ammonium hydroxide and ammonium chloride will, therefore,
precipitate the aluminium and zinc groups together, separating them
from the alkaline earth and alkali groups.›[383]

«Separation of the Aluminium Group from the Zinc Group by Means of
Ammonium Chloride and Ammonium Hydroxide.»—The precipitation of the
two groups together makes their subsequent separation necessary.
Some analysts attempt to avoid the extra operations involved, by
making use of the fact that the hydroxides of the bivalent group,
although difficultly soluble, are, like magnesium hydroxide, still
sufficiently soluble not to be precipitated by ammonium hydroxide in
the presence of sufficient ammonium chloride, while the hydroxides of
the trivalent metals of this group are so insoluble that they may be
precipitated quantitatively by such a mixture (p. 170). The trivalent
hydroxides may be first precipitated by ammonium hydroxide, in the
presence of ammonium chloride, and, subsequently, the sulphides of
the bivalent metals may be precipitated by ammonium sulphide, the
two precipitates being collected separately. The method has the
disadvantage that it is not always accurate. The acid character of
aluminium and chromium hydroxides (and even of ferric hydroxide,
see p. 195), as well as of zinc hydroxide, leads, to a certain
extent, to the precipitation, from such ‹alkaline› solutions, of
‹salts› of these amphoteric hydroxides with the basic hydroxides of
the bivalent group; the latter are thus liable to be ‹lost› in the
analysis. It will be recalled, that the equilibrium conditions in
alkaline solutions ‹favor› the ‹ionization› of amphoteric substances
in the acid form (Part III), and ‹alkaline› solutions would favor
the precipitation of aluminates, chromites, etc., of the ions of
the zinc group. Methods have, therefore, been devised to separate
the two groups in neutral, or very slightly acid, media, and they
give quantitative separations and are preferable to the method just
described. The separation by means of suspended ‹barium carbonate›,
in which carbonic acid is liberated and the solution is practically
neutral, will be discussed below on page 193. A second method,
frequently used in quantitative analysis, is based on the [p192]
‹decomposition› of the ‹acetates› of the aluminium group by boiling
water, acetic acid being liberated.[384]

«Separation of Cobalt and Nickel from the Other Members of the
Zinc and Aluminium Groups.»—When the aluminium and zinc groups are
precipitated together, by means of a mixture of ammonium sulphide,
hydroxide and chloride, the precipitate, obtained from a solution
containing, say, the chlorides of all the ions of the groups, would
consist of the following compounds:

 ‹Aluminium Group›: Fe_{2}S_{3}, Al(OH)_{3}, Cr(OH)_{3}.

 ‹Zinc Group›: NiS, CoS, FeS, MnS,[385] ZnS.

If such a precipitate is treated, in the cold, for a short time
with quite dilute (1 to 1.2 molar) hydrochloric acid, all of the
hydroxides and sulphides dissolve, excepting the greater part of the
nickel and cobalt sulphides, ‹which dissolve very much more slowly
than do the other compounds›. Advantage is taken of this fact, to
separate these two elements from the remaining members of these
groups, and if the treatment is carried out with care, the separation
is usually satisfactory. In all cases, however, since it is a
question of delayed solution only, at least traces, and sometimes
considerably more than traces, of the sulphides of nickel and cobalt
go into solution with the other compounds. No sacrifice of analytical
accuracy is involved, if this possible loss is kept in mind and
provision made for the later detection of these small quantities of
nickel and cobalt.

The question of the slow solution, or apparent lack of solubility, of
nickel and cobalt sulphides in dilute hydrochloric acid has formed
an interesting problem for investigation. While nickel and cobalt
sulphides are precipitated by ammonium sulphide, these sulphides, in
common with those of all the other members of the zinc group, are not
precipitated by hydrogen sulphide in the presence of a small excess
of hydrochloric acid.[386] We would have [p193]

 NiCl_{2} + ‹x› HCl + H_{2}S ⥃ NiS + (‹x› + 2) HCl

as representing the condition of equilibrium, if we start with nickel
chloride, hydrochloric acid and hydrogen sulphide; the amount of
sulphide NiS, formed, is insufficient to supersaturate the solution
and form a precipitate. In reversible reactions the final condition
of equilibrium must be independent of the order in which components
are mixed (p. 91), a conclusion which is borne out by experience.
One should expect, then, that nickel sulphide, when treated with
dilute hydrochloric acid, would dissolve and give nickel chloride,
hydrogen sulphide and an excess of acid, and thus produce the
same system, found to be in equilibrium, when one starts with the
chloride, hydrogen sulphide and hydrochloric acid. As a matter of
fact, the same condition of ‹equilibrium› is ‹finally› reached, only
‹it is reached slowly›,[387] much more slowly than ordinarily in such
cases, much more slowly, for instance, than with ferrous sulphide,
hydrochloric acid and hydrogen sulphide (‹exp.›). By taking advantage
of this slow return to equilibrium and by working with the system
‹during the process of slow change› (collecting the undissolved
nickel and cobalt sulphides on a filter), one can separate the
sulphides of nickel and cobalt from the other components of the mixed
precipitate, which dissolve much more rapidly.

«Separation of the Aluminium and Zinc Groups by Means of Barium
Carbonate.»—The solution, obtained by treating the mixture of the
sulphides and hydroxides of the aluminium and zinc groups with
dilute hydrochloric acid (p. 192), contains aluminium, chromium,
manganous, zinc and ferrous chlorides, all the iron being now present
in the ferrous condition because of the reducing action of hydrogen
sulphide on the ferric-ion (Part III). The chlorides of nickel and
cobalt are also present in small quantities (see above). The further
treatment of the solution is directed toward a ‹separation› of the
‹bivalent› ions of the zinc group from the ‹trivalent› ions of the
aluminium group, and the intention is to have all the iron go with
the trivalent metals. The ferrous is, therefore, oxidized to the
ferric-ion. After a part of the solution has been tested to show the
presence or absence of ferric salts, the two groups are separated by
means of a suspension, in water, of finely [p194] divided barium
carbonate. ‹The theory of the separation› may be developed as follows:

When zinc chloride, which may be taken as a representative of the
bivalent group, is treated with sodium carbonate, a difficultly
soluble carbonate is precipitated, since zinc hydroxide, like
the remaining bivalent hydroxides, is a sufficiently strong base
to form a fairly stable carbonate.[388] When ferric chloride, a
representative of the trivalent group, is treated with a solution
of sodium carbonate, ferric hydroxide, mixed with some basic ferric
carbonate[389] Fe_{2}(OH)_{4}CO_{3}, is precipitated and carbon
dioxide escapes (‹exp.›). The trivalent hydroxides are too weak
bases[390] to form stable salts with so weak an acid as carbonic acid.

 2 FeCl_{3} + 3 Na_{2}CO_{3} + 6 H_{2}O ⥂
   2 Fe(OH)_{3} ↓ + 3 H_{2}CO_{3} + 6 NaCl

 3 H_{2}CO_{3} ⇄ 3 H_{2}O + 3 CO_{2} ↑.

Since the bivalent metal ions are precipitated by sodium carbonate
as carbonates and the trivalent ones as hydroxides, the reagent,
obviously, cannot be used to separate the two groups. But ‹barium
carbonate is so little soluble in water that it will not precipitate
manganous, zinc, nickel, cobalious and ferrous carbonates›[391] from
solutions of their chlorides or nitrates. We have, for instance,
ZnCl_{2} + BaCO_{3} ↓ ⥃ BaCl_{2} + ZnCO_{3}. Barium carbonate has,
however, the same effect on ferric chloride (‹exp.›) and on the other
chlorides of the trivalent group, as has sodium carbonate, ‹i.e.›
it precipitates their ‹hydroxides›. By means of barium carbonate
[p195] ‹we can, therefore, precipitate the hydroxides of the
aluminium group without precipitating the ions of the zinc group.›
The separation is carried out in a, practically, neutral medium
(free carbonic acid in excess is evolved; barium carbonate alone,
when treated with water, is slightly alkaline) and thus avoids the
error of facilitating the precipitation of the bivalent metals in
the shape of salts of the acidic forms of the trivalent metals, i.e.
as aluminates, chromites, and so forth. Manganous salts are liable
to oxidation to manganic salts, when exposed to the air, especially
in alkaline, neutral or ‹slightly› acid solutions, and prolonged
exposure of the barium carbonate mixture to the air may result in
the precipitation of manganic hydroxide, Mn(OH)_{3}, with the other
trivalent hydroxides. Provision is made for its detection in the
systematic analysis.

«Analysis of the Aluminium Group.»—The precipitate of the aluminium
group may contain aluminium, chromium and ferric hydroxides (possibly
traces of manganic hydroxide) and their basic carbonates. A color
test for ferric-ion has already been made (see p. 193) and chromium
(and manganese) is readily found and identified by oxidation to the
intensely colored salts of chromic (and manganic) acid (Part III,
‹q.v.›). In ascertaining whether aluminium hydroxide is present or
not, advantage is taken of its ‹amphoteric character›. Chromium
hydroxide, like aluminium hydroxide, is amphoteric; but, in agreement
with the greater atomic weight of chromium, it is an even weaker
acid than is aluminium hydroxide. Its sodium salt, sodium chromite,
is completely decomposed by boiling water, chromium hydroxide
being precipitated in a less hydrated, insoluble form. Ferric
hydroxide, whose metal has the highest atomic weight of the three
elements under consideration, has so little acid character, that
it is not perceptibly soluble in solutions of potassium or sodium
hydroxide. (That it has slight acidic properties is shown by its
capacity to form ferrites, ‹e.g.› Me(FeO_{2})_{2}, which may best be
obtained by dry methods, and of which ferrous ferrite or magnetic
iron ore, Fe_{3}O_{4} or Fe(FeO_{2})_{2}, is the most important
representative.) Of the three hydroxides, aluminium hydroxide
is, therefore, the only one that will dissolve in boiling sodium
hydroxide. In this solution we can best identify it, by converting
the aluminate into an aluminium salt, by means of an excess of acid,
[p196] and by a final precipitation of aluminium hydroxide with
ammonium hydroxide. Aluminium hydroxide is too weak an acid to form
a stable aluminate with so weak a base as ammonium hydroxide, when
the latter is used only in slight excess (p. 186). If we attempt to
prepare ammonium aluminate, by adding ammonium chloride to a solution
of sodium aluminate, a precipitate of aluminium hydroxide is obtained
(‹exp.›). For exact work, an excess of ammonium hydroxide is to
be avoided and ‹its strength as a base should be weakened› by the
addition of some ammonium chloride or nitrate (pp. 114, 169 and Lab.
Manual, p. 9, § 6).

 We have, in this instance, the case of a very weak, difficultly
 soluble acid, aluminium hydroxide, forming a salt with a weak,
 soluble base, ammonium hydroxide. The conditions determining the
 ‹solubility› of aluminium hydroxide in ammonium hydroxide, as an
 aluminate NH_{4}AlO_{2}, may be shown as follows: for the acid
 ionization of aluminium hydroxide, Al(OH)_{3} ⇄ AlO_{2}^{−} +
 H^{+} + H_{2}O (p. 172); the solubility-product for a saturated
 solution is [AlO_{2}^{−}] × [H^{+}] = K_{Ac.S.P.}. Further, from
 [H^{+}] × [HO^{−}] = K_{HOH}, we find [H^{+}] = K_{HOH} / [HO^{−}].
 Then [AlO_{2}^{−}] = [HO^{−}] × K_{Ac.S.P.} / K_{HOH},
 which shows that the solubility of aluminium hydroxide, as
 aluminate, is proportional to the concentration [HO^{−}]
 of the hydroxide-ion in the solution. For NH_{4}OH we have
 [NH_{4}^{+}] × [HO^{−}] / ([NH_{3}] + [NH_{4}OH]) = 0.000,018
 (p. 161), and consequently, [HO^{−}] = 0.000,018 × ([NH_{3}] +
 [NH_{4}OH]) / [NH_{4}^{+}]. Then [HO^{−}] is the smaller, the smaller
 the excess of ammonium hydroxide used (which is approximately equal to
 ([NH_{3}] + [NH_{4}OH])) and the greater the concentration
 [NH_{4}^{+}] of the ammonium-ion, ‹i.e.› of the added ammonium salt.
 The solubility of Al(OH)_{3}, as aluminate, in ammonium hydroxide
 and ammonium chloride is, therefore, directly proportional to the
 excess of ammonium hydroxide, and indirectly proportional to the
 concentration of the ammonium salt present.[392]

 «The Favorable Conditions for a Maximum Precipitation of an
 Amphoteric Hydroxide.»—The precipitation of aluminium hydroxide
 depends also on the solubility-product of aluminium hydroxide,
 ionized as a base. For Al(HO)_{3} ⇄ Al^{3+} + 3 HO^{−}, in a
 saturated solution, [Al^{3+}] × [HO^{−}]^3 = K_{Bas.S.P.}. It is
 evident, that an excess of the precipitating hydroxide-ion would be
 favorable to the precipitation in this form, and that the reduction
 of the concentration of the hydroxide-ion, ‹while acting favorably›,
 as just shown, ‹in preventing the solution of the hydroxide as
 an aluminate, must be, to some extent, detrimental to a maximum
 precipitation of the hydroxide as a base›. One may ask, therefore,
 ‹what the most favorable concentration of the hydroxide-ion› must be
 for a quantitative precipitation of aluminium hydroxide. The problem
 may be treated as follows: According to the solubility-product
 relation for the basic ionization, we have, in a solution saturated
 with aluminium hydroxide, [p197]

 [Al^{3+}] = K_{Bas.S.P.} × [HO^{−}]^{−3}.                           I

 For the sake of a certain simplicity in the result, we will,
 for the moment, consider aluminium hydroxide to ionize as
 an acid according to Al(HO)_{3} ⇄ AlO_{3}^{3−} + 3 H^{+},
 which would resemble the basic ionization. Then we would have
 [AlO_{3}^{3−}] × [H^{+}]^3 = K′_{Ac.S.P.}, and, using the relation
 [H^{+}] = K_{HOH} / [HO^{−}], we have

 [AlO_{3}^{3−}] = [HO^{−}]^3 × K′_{Ac.S.P.} × K_{HOH}^{−3}.         II

 Adding equations I and II we find

 [Al^{3+}] + [AlO_{3}^{3−}] = K_{Bas.S.P.} × [HO^{−}]^{−3} +
   [HO^{−}]^3 × K′_{Ac.S.P.} × K_{HOH}^{−3}                        III

 Aluminium hydroxide will be most completely precipitated when
 [Al^{3+}] + [AlO_{3}^{3−}] is a ‹minimum›, the values [Al^{3+}]
 and [AlO_{3}^{3−}] measuring the solubility of aluminium as
 aluminium-ion and as aluminate-ion. If we put [Al^{3+}] +
 [AlO_{3}^{3−}] = ‹y› and [HO^{−}] = ‹x›, we can find the
 value ‹x› (the concentration of the hydroxide-ion) for which
 ‹y› is a minimum. We have ‹y› = K_{Bas.S.P.} × ‹x›^{−3} +
 ‹x›^3 × K′_{Ac.S.P.} × K_{HOH}^{−3}, and find, by means
 of the calculus,[393] that ‹y› is a minimum, when ‹x› =
 +(K_{HOH}^3 × K_{Bas.S.P.} / K′_{Ac.S.P.})^{1/6}.

 If aluminium hydroxide were as strong an acid as it is a base,
 ‹i.e.› if K_{Bas.S.P.} = K′_{Ac.S.P.}, we would have, simply,
 ‹x› = [HO^{−}] = ((1.2E−14)^3)^{1/6} = √(1.2E−14) (at 25°),
 which is the concentration of the hydroxide-ion in pure water
 at 25° (p. 176). In other words, a perfectly neutral solution
 would then give us the conditions for as complete a precipitation
 as possible. But aluminium hydroxide is a stronger base than
 acid, K_{Bas.S.P.} > K′_{Ac.S.P.}, and consequently we find for
 ‹x› = [HO^{−}] = (K_{HOH}^3 × K_{Bas.S.P.} / K′_{Ac.S.P.})^{1/6}, a
 value somewhat ‹greater› than the concentration of the hydroxide-ion
 in pure water, ‹i.e.› we must use a slightly ‹alkaline› medium—which
 agrees with common practice. In other words, there is less danger
 of losing aluminium hydroxide in the form of aluminate, owing to
 the ‹weaker acid› character of the hydroxide, than there is of
 losing it in the form of aluminium-ion. The most favorable degree
 of alkalinity for the precipitation would depend on the relation of
 K_{Bas.S.P.}. and K′_{Ac.S.P.}.

 The exact values for K_{Bas.S.P.} and K′_{Ac.S.P.}, the two
 solubility-product constants, and for the corresponding ionization
 constants, which would show the same ‹ratio›, are still not known.
 But, if, for the sake of an illustration, we take recourse to
 assumed values for these constants, we find that the solubility
 of aluminium, as aluminium-ion and as aluminate-ion, is, by
 calculation, as anticipated, a ‹minimum› for a solution, which
 contains the concentration of HO^{−} calculated (for ‹x›) in the
 manner indicated above. And the further interesting conclusion is
 reached that this minimum loss of aluminium [p198] hydroxide would
 occur when [Al^{3+}] = [AlO_{3}^{3−}]—which would correspond to a
 saturated solution of aluminium aluminate, Al(AlO_{3}).

 When the ionization of aluminium hydroxide, as an acid, is
 considered to take place according to Al(OH)_{3} ⇄ AlO_{2}^{−} +
 H^{+} + H_{2}O, which agrees best with its real behavior (p.
 172), we can find, similarly, that [Al^{3+}] + [AlO_{2}^{−}] is
 a ‹minimum›, when aluminium hydroxide is precipitated in such a
 way, that an excess ‹x› of the hydroxide-ion is used, and ‹x› =
 [HO^{−}] = (3 K_{HOH} × K_{Bas.S.P.} / K_{Ac.S.P.})^{0.25},—where
 K_{Ac.S.P.} represents the solubility-product constant for
 [AlO_{2}^{−}] × [H^{+}]. That a minimum loss of aluminium hydroxide
 would be suffered when the favorable excess of the hydroxide-ion
 (‹x›) is calculated on the basis of the equation as given, may
 readily be seen by again assuming definite values for K_{Bas.S.P.}
 and K_{Ac.S.P.}. It also appears that this minimum loss[394] of
 aluminium includes one-third as many Al^{3+} ions, as AlO_{2}^{−}
 ions—a relation corresponding, again, to a saturated solution of
 aluminium aluminate, Al(AlO_{2})_{3}.


  FOOTNOTES:

  [354] When all three of the hydrogen atoms in the hydroxide
  are ionized, an aluminate ion, AlO_{3}^{3−} is formed:
  Al(OH)_{3} ⇄ AlO_{3}^{3−} + 3 H^{+}. But, as in the case of
  other weak polybasic acids, a single hydrogen atom is far more
  readily ionized than are the remaining two (p. 102), and the ion
  Al(OH)_{2}O^{−}, which is formed by the ‹primary› ionization,
  readily loses water and forms the anhydride ion AlO_{2}^{−}. The
  most important aluminates are derivatives of this ion.

  [355] See the table at the back of Smith's ‹Inorganic Chemistry›,
  or p. 149 of Remsen's ‹Inorganic Chemistry›.

  [356] The displacement of hydrogen by a metal, like sodium, is the
  result of the displacement of the ‹hydrogen-ion› (see Chapters XIV
  and XV). The hydrogen-ion in fused sodium hydroxide is probably
  formed chiefly by the secondary ionization of the hydroxide-ion
  (HO^{−} ⇄ H^{+} + O^{2−}) (see Chap. XIII). We cannot have positive
  ions, Na^{+}, with negative ions, O^{2−}, without having some
  ions NaO^{−}. (O^{2−} + Na^{+} ⥂ NaO^{−}), NaOH, undoubtedly,
  is much ‹too› ‹weak› an ‹acid› to form salts with bases in the
  presence of water. Such salts would be decomposed by water (see
  below, p. 180), as sodium oxide, indeed, is decomposed; we have
  Na—O—Na + HOH ⇄ 2 NaOH (see Chapter XIII for a detailed discussion
  of this action). These relations sufficiently account for the fact
  that salts of sodium hydroxide, in which it has the functions of an
  acid, are not commonly formed. (‹Cf.› Abegg, ‹Anorganische Chemie›,
  II, (1) p. 247.)

  [357] See J. J. Thomson, ‹Corpuscular Theory of Matter›, pp.
  103–141.

  [358] See Mendeléeff, ‹Principles of Chemistry›, I, 22 (1891), in
  regard to the rôle of "even" and "uneven" series in the system.

  [359] In regard to the indications of the amphoteric character of
  stronger acids, see Chapter XV.

  [360] An elaborate treatment of this problem is given by Walker,
  ‹Z. phys. Chem.›, «49», 82 (1904), «51», 706 (1905).

  [361] Kohlrausch and Heydweiller, ‹Z. phys. Chem.›, «14», 317
  (1894).

  [362] See the table, p. 104.

  [363] See p. 53 and van 't Hoff's remarks, ‹ibid.›

  [364] This suggests a much broader, natural definition of a base
  than the conventional one. All salts of very weak acids, to a
  certain degree, which is determined by the weakness of their acids,
  do exactly what the ordinary bases do, ‹e.g.› neutralize acids.
  Metal derivatives of acids weaker than water, metal amides, like
  Zn(NH_{2})_{2}, metal alkyls, like zinc methyl, Zn(CH_{3})_{2},
  react more vigorously than the hydroxides do, ‹e.g.› in
  neutralizing acids, and water attacks them and acts upon them,
  exactly as ordinary acids interact with metal hydroxides. We have,
  for instance, Zn(CH_{3})_{2} + 2 HOH → Zn(OH)_{2} + 2 CH_{4}.

  [365] See footnote, p. 177. Similar considerations apply to the
  conventional definition of an acid.

  [366] The symbols in «heavy type» indicate the chief components of
  the final system. ‹Vide› Smith's ‹General Chemistry for Colleges›
  and ‹Inorganic Chemistry›, for the form of equations used.

  [367] Emich, ‹Ber. d. chem. Ges.› «40», 1482 (1901).

  [368] Arrhenius, ‹Z. phys. Chem.›, «5», 16 (1890); Shields,
  ‹ibid.›, «12», 167 (1893).

  [369] See below for the corresponding equation, developed by Walker
  for a salt of a weak base and a strong acid.

  [370] Potassium sulphate, K_{2}SO_{4}, reacts ‹faintly› alkaline
  in aqueous solution, the ‹secondary› ionization of sulphuric acid
  (table, p. 104) being somewhat weaker than the ionization of
  potassium hydroxide. We have: K_{2}SO_{4} + HOH ⇄ KHSO_{4} + KOH or
  SO_{4}^{2−} + HOH ⇄ HSO_{4}^{−} + HO^{−}.

  [371] Walker, ‹Z. phys. Chem.›, 4, 319, (1889); Arrhenius, ‹loc.
  cit.›; Bredig, ‹ibid.›, «13», 321 (1894).

  [372] Arrhenius, ‹loc. cit.›

  [373] See p. 183.

  [374] Arrhenius developed the relation for aniline acetate, ‹loc.
  cit.›

  [375] Putting ‹x› = [Acid] = [Base], we have [Salt] = (0.1 − ‹x›),
  and (0.1 − ‹x›)^2 / ‹x›^2 = (7E−10)^2 / 1.2E−14. Then (0.1 − ‹x›) /
  ‹x› = 0.0064 and ‹x› = .09935, which is 99.35% of the total salt
  used. The degree of ionization, α, of the salt, in the extremely
  dilute solution, is taken to be 100%.

  [376] See the equations for K_{Base} and K_{Acid}, on p. 184, and
  their premises.

  [377] See p. 172. The concentration of water may be considered a
  constant and is included in K_{Acid} (and K_{Base}, below).

  [378] Only the ‹primary› ionization (of aluminium hydroxide) is
  considered in the text, because only that is involved, as a rule,
  in the neutralization of very weak bases by very weak acids (see
  footnote 2, p. 194). The relations are also simpler and clearer, if
  we limit the discussion to the formation of a salt AlO(AlO_{2}).

  [379] See the similar equation, p. 185.

  [380] Amphoteric substances of a different class are also known,
  which have, at the same time, moderately ‹strong› acid and
  moderately ‹strong› basic functions. Glycocoll, H_{2}N.CH_{2}COOH,
  a derivative of acetic acid and ammonia, contains an acid group,
  the —COOH group, the hydrogen of which is approximately as
  ionizable as the hydrogen in the corresponding group in acetic
  acid, CH_{3}COOH. The ammonia residue, H_{2}N—, in glycocoll, forms
  with water a hydroxide, corresponding to ammonium hydroxide, which
  likewise is approximately as ionizable as is ammonium hydroxide. In
  the hydroxide of glycocoll we have, consequently, both a moderately
  strong acid, and a moderately strong basic, group. In this, and
  in similar cases, ‹salt formation between the acid and the basic
  groups of the amphoters takes place to as great an extent as if
  the functions were attributes of distinct compounds›. Glycocoll in
  aqueous solution is present, then, chiefly in the form of a salt,
  for instance, H_{3}N^{+}.CH_{2}.COO^{−}, corresponding to ammonium
  acetate, CH_{3}COONH_{4}. For an elaborate discussion of the
  equilibrium conditions in solutions of amphoteric compounds ‹vide›
  Walker, ‹Z. phys. Chem.›, «49» and «51».

  [381] The carbonates are occasionally partially hydrolyzed to basic
  carbonates.

  [382] Stokes, ‹J. Am. Chem. Soc.›, «29», 304 (1907).

  [383] A complication, which leads to the precipitation of alkaline
  earths, along with these groups, as phosphates and similar
  insoluble salts (not as hydroxides or sulphides), when phosphate or
  certain other acid ions are present, is treated in Part IV (‹q.v.›)
  under the systematic analysis of the groups.

  [384] ‹Cf.› Fresenius, ‹Quantitative Analysis›.

  [385] Ammonium sulphide usually precipitates a ‹pink› hydrated
  sulphide of manganese, probably Mn(SH)(OH). Under certain
  conditions of concentration and temperature, the dark ‹green›
  sulphide MnS is precipitated. In quantitative work the chemist aims
  to precipitate this green sulphide, which is more easily collected
  on a filter. (‹Cf.› Fresenius, ‹Quantitative Analysis›.)

  [386] We shall find that this property of the whole zinc group
  makes it possible to separate the following groups, the copper and
  arsenic groups, from the zinc group (see p. 158). The theory of the
  separation will be discussed in detail in Chapter XI.

  [387] ‹Vide› Noyes, Bray and Spear, ‹J. Am. Chem. Soc.›, «30», 483
  (1908).

  [388] See footnote, p. 189.

  [389] The comparative stability of this basic salt represents
  an instance of the different ionizing power, or basic
  strength, of the three hydroxide groups of a trivalent base
  (see p. 106). The hydrolysis of ferric chloride seems to
  involve, primarily, only the third or least ionizable of the
  hydroxide groups of ferric hydroxide, and the hydrolysis,
  except in extreme dilution, proceeds chiefly according to
  Fe^{3+} + 3 Cl^{−} + HOH ⇄ Fe(OH)^{2+} + 3 Cl^{−} + H^{+}. ‹Vide›
  Goodwin, ‹Z. phys. Chem.›, «21», 1 (1896). In the case of the
  salt of the much weaker acid, carbonic acid, the hydrolysis goes
  further, involving two hydroxide groups of ferric hydroxide and, to
  some extent, all three.

  [390] The extreme insolubility of Al(OH)_{3}, Fe(OH)_{3} and
  Cr(OH)_{3}, together with their weakness as bases, facilitates
  their precipitation (see pp. 185–6).

  [391] There is a ‹small degree of hydrolysis› (see footnote, p.
  189), but the hydroxides of the zinc group are not sufficiently
  insoluble to be precipitated under these conditions.

  [392] ‹Cf.› A. A. Noyes, Bray and Spear, ‹J. Am. Chem. Soc.›, «30»,
  496 (1908).

  [393] ‹Cf. The Elements of the Differential and Integral Calculus›,
  based on Nernst and Schönflies's ‹Lehrbuch, etc.›, by Young and
  Linebarger, pp. 363 and 364 (1900).

  [394] Losses due to the tendency of aluminium hydroxide to assume
  the colloidal condition (p. 136) must be guarded against by other
  precautions (‹loc. cit.›).

[p199]




 CHAPTER XI

 «THE COPPER AND SILVER GROUPS. PRECIPITATION WITH HYDROGEN SULPHIDE»


The sulphides of the metal ions of the zinc group are readily
precipitated by ammonium or sodium sulphide, but hydrogen sulphide,
in the presence of a small excess of a strong acid, such as
hydrochloric acid, does not precipitate any of these sulphides (or
any of the sulphides of the aluminium, the alkaline earth and the
alkali groups). Under the same conditions ‹the sulphides of the metal
ions of the silver group›, Ag^{+}, Hg^{+}, Pb^{2+}, of ‹the copper
group›, Hg^{2+}, Pb^{2+}, Bi^{3+}, Cu^{2+}, Cd^{2+}, and also of ‹the
arsenic group›, As^{3+}, As^{5+}, Sb^{3+}, Sb^{5+}, Sn^{2+}, Sn^{4+},
Pt^{2+}, Pt^{4+}, Au^{+}, and Au^{3+}, are precipitated. Advantage
is taken of these relations in the following way, in systematic
analysis: after the separation of the silver group, by precipitation
of the difficultly soluble chlorides, hydrogen sulphide, in the
presence of an excess of acid, is used to precipitate the sulphides
of the ions of the copper and the arsenic groups, the two groups
being precipitated together. Hydrogen sulphide, under these
conditions, does not precipitate any sulphides of the zinc group or
those of any of the remaining groups. Hydrogen sulphide is used, in
this way, as one of the most valuable reagents in analytical work,
enabling the analyst to separate whole groups of metal ions from
other groups. There is also no other agent, equally important, which
is more likely to be used in a wrong way and to lead to error.

«The Ionization of Hydrogen Sulphide.»—Before taking up the theory
of the separation of these groups by precipitation with hydrogen
sulphide in the presence of a strong acid, a discussion of some
of the characteristics of the reagent will be in place. Hydrogen
sulphide, like carbonic acid and other dibasic acids, ionizes in
two stages; it produces first hydrogen-ion and hydrosulphide-ion,
HS^{−}, and this ion in turn dissociates, producing hydrogen-ion and
sulphide-ion, S^{2−}. [p200]

For the first dissociation, HSH ⇄ H^{+} + HS^{−}, we have

 [H^{+}] × [HS^{−}] / [H_{2}S] = K_{1}                           (I)

The value of the constant[395] for this primary ionization of
hydrogen sulphide is 0.91E−7. It is apparent that hydrogen sulphide,
even in the primary ionization, is a very weak acid and produces
a very small concentration of hydrosulphide-ion. In a solution,
saturated at 25°, the total concentration of hydrogen sulphide is
approximately 0.1 molar, and the concentration of hydrosulphide-ion,
therefore, in the absence of any foreign acid, at most[396] 0.95E−4.
The concentration of the dissolved, nonionized hydrogen sulphide,
[H_{2}S], is practically a constant, if solutions saturated with
hydrogen sulphide under a given pressure, say under atmospheric
pressure, are considered. For such solutions, then, we may put more
simply[396]

 [H^{+}] × [HS^{−}] = ‹k› = (0.95E−4)^2 = 0.9E−8.                 (II)

The concentration of hydrosulphide-ion is, therefore, inversely
proportional to the concentration of hydrogen-ion. It is clear that
the addition of a strong acid, readily yielding concentrations of
hydrogen-ion very much greater than 0.95E−4 (the value of [H^{+}]
in a saturated aqueous solution of hydrogen sulphide) will, as the
result of the greatly increased total hydrogen-ion concentration,
reduce the concentration of hydrosulphide-ion to correspondingly
low values. For instance, the presence of 0.1 molar hydrochloric
acid will increase the concentration of hydrogen-ion close to a
thousandfold and will reduce the concentration of hydrosulphide-ion
to 0.9E−7.

For the secondary ionization (see p. 101) of hydrogen sulphide,
HS^{−} ⇄ H^{+} + S^{2−}, we have

 [H^{+}] × [S^{2−}] / [HS^{−}] = K_{2}.                        (III)

The value of this constant has recently been determined[397] and
found to be 1.2E−15. Recalling the fact that the concentrations
[H^{+}] and [HS^{−}] of hydrogen-ion and hydrosulphide-ion, [p201]
respectively, resulting from the primary ionization, are each[398]
0.95E−4, we have for the concentration of the sulphide-ion, in
aqueous solution saturated with hydrogen sulphide at atmospheric
pressure and 25°, [S^{2−}] = 1.2E−15.

Combining equations (II) and (III), we have, further:[399]

 [H^{+}]^2 × [S^{2−}] = ‹k› × K_{2} = ‹k›_{2} = 1.1E−23,          (IV)

‹which shows, directly, the relation between the concentration
of the sulphide-ion and that of the hydrogen-ion, the relation
of primary importance in considering the precipitation of
metal sulphides in acid solutions.› The ‹concentration of the
sulphide-ion› is, thus, ‹inversely proportional› to the ‹square›
of the ‹concentration› of ‹the hydrogen-ion›. A thousandfold
increase in the concentration of the latter, which is very nearly
the effect produced by the presence of 0.1 molar hydrochloric acid
([H^{+}] = 0.091), reduces the concentration of sulphide-ion in the
saturated aqueous solution a millionfold: If we call [S^{2−}]_{Ac.}
the concentration of the sulphide-ion in the acid solution,
[S^{2−}]_{Ac.} = (1.1E−23) / (0.091)^2 = 1.3E−21, whereas, in the
absence of acid, as found above, [S^{2−}] = 1.2E−15.

On the other hand, the addition of alkali to hydrogen sulphide,
by neutralizing and suppressing the hydrogen-ion, and by forming
the ‹salts› MeSH and Me_{2}S, will very greatly increase the
concentrations of the hydrosulphide-ion and of the sulphide-ion.
Since the constant for the secondary ionization of hydrogen sulphide
shows that HS^{−} is an ‹exceedingly weak› acid, its salts, Me_{2}S,
are very largely hydrolyzed, the constant for water being somewhat
greater[400] than its own. According to Knox, in a 0.1 molar solution
of Na_{2}S about 99% of the sulphide is hydrolyzed: Na_{2}S +
H_{2}O ⥂ NaSH + NaOH. In spite of this almost complete hydrolysis,
sufficient sodium sulphide remains in a solution of this [p202]
substance, to yield a concentration of the sulphide-ion that is far
greater than that obtained from a solution of hydrogen sulphide. In
a 0.1 molar solution of sodium sulphide the concentration of the
sulphide-ion is, approximately, [S^{2−}]_{alk.} = 0.9E−3, as compared
with [S^{2−}] = 1.2E−15 in a saturated solution of hydrogen sulphide
(25°, 760 mm.), and with 1.3E−21 in the same solution in the presence
of 0.1 molar hydrochloric acid.

Ammonium sulphide (NH_{4})_{2}S is the salt of an extremely weak
acid with a much weaker base than sodium hydroxide, and it is
correspondingly more completely decomposed by water. In a 0.1 molar
solution of the sulphide (NH_{4})_{2}S, we find the approximate
concentration[401] of the sulphide-ion [S^{2−}]_{am.} = 1.8E−6,
as compared with 0.9E−3 in a similar solution of Na_{2}S. But the
concentration of sulphide-ion is still enormously greater than
its concentrations in hydrogen sulphide in the absence and in the
presence of acids (see above).

The following table[402] contains a ‹summary of the concentrations
of sulphide-ion› in the various solutions discussed, as well as its
concentration in the presence of 0.2 molar hydrochloric acid. In
the separation of the copper and arsenic groups from the zinc and
aluminium groups, a concentration of hydrogen-ion corresponding to
the presence of 0.15 to 0.25 molar hydrochloric acid is satisfactory
for an accurate separation for ordinary purposes.

    Solution.                            [S^{2−}]
  0.1 molar Na_{2}S:                      0.9E−3
  0.1 molar NaSH:                         0.8E−5
  0.1 molar (NH_{4})_{2}S:                1.8E−6
  0.1 molar (NH_{4})SH:                   1.4E−8
  0.1 molar H_{2}S, sat. aq. sol., 25°:   1.2E−15
  0.1 molar H_{2}S, 0.1 molar HCl:[403]   1.3E−21
  0.1 molar H_{2}S, 0.2 molar HCl:        3.5E−22

[p203]

«Precipitation of Sulphides by Hydrogen Sulphide.»—Although the
hydrosulphide-ion most likely takes part in the precipitation of
sulphides, the main effect appears to be due to the sulphide-ion.[404]
The sulphides seem to be both more stable and less soluble, than the
hydrosulphides. It is very likely that hydrosulphides, mixed with
the sulphides, are precipitated to a certain extent, but they are
unstable, lose hydrogen sulphide and go over into sulphides much
more readily than hydroxides, as a rule, change into oxides.[405]
The final condition of equilibrium, if one waited, in a given
case, until equilibrium was established, would depend, under these
conditions, rather on the concentration of the sulphide-ion than on
that of the hydrosulphide-ion, although the latter is present in much
greater concentrations than the former. For the sake of simplifying
the discussion of the theory of the separation of metal ions by
precipitation with hydrogen sulphide, the discussion will be limited
to the consideration of the sulphide-ion as the active precipitating
agent. As stated, this seems to be in accordance with the known facts.

The absolute values of the solubilities of the various sulphides,
which are involved in the discussion, are known, with any degree of
accuracy, only in a few cases. The aim of the discussion will be,
therefore, to develop, rather, the relations in the values involved,
which may be readily determined. Wherever absolute quantities can be
given, they also will be referred to.

«Theory of the Separation of Sulphides by Precipitation with Hydrogen
Sulphide. I. Precipitation of Ferrous Sulphide.»—If we prepare a
solution of ferrous sulphate, containing 27.8 grams of the salt,
FeSO_{4}, 7 H_{2}O, in one liter (0.1 molar), we may call [Fe^{2+}]
the concentration of the ferrous-ion in the solution. If such a
solution is saturated with hydrogen sulphide, under atmospheric
pressure, (‹exp.›), ferrous sulphide is not precipitated. We would
decide, on the basis of the principle of the solubility-product,
that the reason no precipitate of ferrous sulphide is formed is,
that the product of the ion concentrations is ‹smaller› than the
[p204] solubility-product constant characteristic of the sulphide
(p. 151); [Fe^{2+}] × [S^{2−}] < K_{FeS}, in which [S^{2−}] is the
concentration of sulphide-ion in the solution thus saturated with
hydrogen sulphide. If an alkali, sodium or ammonium hydroxide, is
added to the solution, a heavy precipitate of ferrous sulphide is
immediately formed (‹exp.›). The salts of hydrogen sulphide, like
all common salts, as we have just seen, are very much more highly
ionized than is hydrogen sulphide itself, and the addition of the
alkali has the effect of increasing enormously[406] the concentration
of sulphide-ion, say to ‹x›[S^{2−}] (p. 202). Under these conditions,
the product of the ion concentrations has evidently grown larger than
the constant: [Fe^{2+}] × ‹x›[S^{2−}] > K_{FeS}.

«II. Precipitation of Zinc Sulphide.»—Now, if a solution of
zinc sulphate is prepared so as to contain 28.7 grams of
ZnSO_{4}, 7 H_{2}O, per liter, which would make it of the same
molar concentration as the ferrous sulphate solution, we may, in
view of the fact that analogous salts ionize approximately to the
same extent in solutions of the same concentration, consider the
concentration, [Zn^{2+}], of zinc-ion to be practically the same
as the concentration, [Fe^{2+}], of the ferrous-ion in the ferrous
sulphate solution. We may put [Zn^{2+}] = [Fe^{2+}].

If the solution of zinc sulphate is saturated with hydrogen sulphide,
under the same conditions as were used with the ferrous salt solution
(‹exp.›), or if we add the zinc sulphate solution to the mixture
of ferrous sulphate and hydrogen sulphide (‹exp.›), we immediately
obtain heavy white precipitates of zinc sulphide. We would decide,
therefore, on the basis of the principle of the solubility-product,
that in this case [Zn^{2+}] × [S^{2−}] > K_{ZnS}. Since we have used
hydrogen sulphide under practically the same conditions, we may
consider that [S^{2−}], in this experiment,[407] is the same as in
the [p205] test with ferrous sulphate, and, by the conditions of the
experiment, we have also made [Zn^{2+}] = [Fe^{2+}]. The two factors
of the product are, therefore, the same, for the first moment, and we
may put [Fe^{2+}] × [S^{2−}] = [Zn^{2+}] × [S^{2−}] = P.

Since P is smaller than K_{FeS} and larger than K_{ZnS}, it is
clear that the ‹solubility-product constant for zinc sulphide must
be smaller than that for ferrous sulphide›. The solubility-product
constants, for similar salts, are a measure of their solubilities in
water. We may obtain their values by determining the solubilities
of salts in pure water, whenever the solubility is not affected by
other chemical changes. In the present instance, the quantitative
measurements, that have been made in this way, are open to question,
owing to the considerable hydrolysis which sulphides, as salts of a
very weak acid, undergo in solutions of such extreme dilution.[408]
Until such relations have been taken into account quantitatively, it
is better to limit ourselves for the present to the more accessible
question of ‹relative› solubility.

It is a comparatively easy matter to determine the ‹relative
solubility› of zinc and ferrous sulphides. If equal quantities of the
equivalent solutions are mixed and a precipitant, ammonium sulphide,
‹which would precipitate either sulphide, if its salt were present
alone›, is carefully and gradually added to the mixture, it will
precipitate first the less soluble one (see p. 163); and that one
alone can be present permanently (‹i.e.› in equilibrium) in contact
with the solution containing the two salts. As a matter of fact,[409]
[p206] ‹we find that zinc sulphide is precipitated first, under
conditions permitting the precipitation of ferrous sulphide if no
zinc sulphate were present›, and the precipitate of zinc sulphide
remains unchanged in the presence of a mixture of the composition
indicated (‹exp.›).

It is clear, therefore, that the prediction, based on the
conclusion drawn from the application of the principle of the
solubility-product, is verified by experiment.

Now, closer examination of the solution of zinc sulphate, from
which zinc sulphide has been precipitated by the action of hydrogen
sulphide, shows, after the hydrogen sulphide has precipitated as
much sulphide as it can and the solution has been passed through a
filter, that a very considerable proportion of zinc salt is still
present in the filtrate, and we must ask why hydrogen sulphide
fails to precipitate the zinc completely. The concentration of the
zinc-ion has grown somewhat smaller, but that is not the cause of
the nonprecipitation of zinc sulphide under the new conditions,
since hydrogen sulphide will precipitate the sulphide, if it is
passed into a solution of zinc sulphate which contains even a smaller
concentration of zinc-ion than the filtrate, in which it fails to
give any further precipitate. If the filtrate is examined, it is
found to be ‹strongly acid›, since sulphuric acid has been liberated
by the action of hydrogen sulphide on zinc sulphate: ZnSO_{4} +
H_{2}S → ZnS ↓ + H_{2}SO_{4}. Sulphuric acid is a strong acid, which
is very highly ionized, much more so than the exceedingly weak acid
hydrogen sulphide, and consequently, as the precipitation of zinc
sulphide proceeds, the ‹concentration of hydrogen-ion in the solution
rapidly grows larger and larger›. But, the greater the concentration
of the hydrogen-ion, the smaller is that of the sulphide-ion, since
the product [H^{+}]^2 × [S^{2−}] is a constant [equation (IV), p.
201] for a solution kept saturated with hydrogen sulphide. The
sulphide-ion is reduced in concentration very much more rapidly
than is the zinc-ion.[410] As [S^{2−}] is a factor in the [p207]
solubility-product of zinc sulphide, it is clear that the value of
this product must grow rapidly smaller during the precipitation of
zinc sulphide from the solution, and that it may well, eventually,
grow too small to surpass the value of the solubility-product
constant K_{ZnS}. Precipitation of zinc sulphide will then cease.
Obviously, the suppression of the sulphide-ion may be accomplished
by the addition of hydrochloric, sulphuric or any other strong acid
to the zinc sulphate solution in the first place, and then hydrogen
sulphide should fail to precipitate any zinc sulphide at all. In
fact, if to 50 c.c. of the 0.1 molar zinc sulphate solution 2 c.c. of
hexamolar hydrochloric acid is added,[411] hydrogen sulphide does not
precipitate even a trace of zinc sulphide (‹exp.›).

We have found, then, that 0.1 molar zinc sulphate solution,
acidified with a small excess of hydrochloric acid, fails to
produce a precipitate of zinc sulphide, when it is saturated
with hydrogen sulphide. We must conclude that, under these
circumstances, the product of the ion concentrations is smaller
than the solubility-product constant for zinc sulphide:
([Zn^{2+}] × [S^{2−}] / ‹x›) < K_{ZnS}, the new concentration of the
sulphide-ion being represented by the symbol [S^{2−}] / ‹x›.

It would follow, from these considerations, that the action of
hydrochloric or sulphuric acid, in preventing the precipitation
of zinc sulphide, depends on their producing a sufficiently high
concentration of the hydrogen-ion, to keep the concentration of the
sulphide-ion, in a mixture of zinc sulphate and hydrogen sulphide,
below the point where the solution could become supersaturated with
zinc sulphide. [p208] ‹For exactly similar reasons, none of the
sulphides of the zinc group is precipitated by hydrogen sulphide in
(sufficiently) acid solutions.›

It is evident, further, that, if a solution of zinc acetate (without
the addition of any acid) is substituted for the zinc sulphate
solution and is treated with hydrogen sulphide, an entirely different
result, quantitatively considered, must be obtained. By the action of
hydrogen sulphide on the acetate, acetic acid is liberated, according
to Zn(CH_{3}CO_{2})_{2} + H_{2}S ⥂ ZnS ↓ + 2 CH_{3}COOH. As a ‹weak›
acid, acetic acid produces much less hydrogen-ion than is formed
in equivalent solutions of sulphuric acid. Consequently, ‹a much
slighter suppression of the sulphide-ion› and a much more ‹complete
precipitation of zinc sulphide› from the acetate, than from the
sulphate solution, must result. Such is the case. Zinc sulphide is,
indeed, precipitated ‹quantitatively› by hydrogen sulphide from the
‹acetate› solution.

This behavior of zinc acetate[412]—and zinc salts of other ‹weak
acids› show, of course, the same behavior—represents one of the
pitfalls, into which the unwary analytical chemist is liable to fall,
when he uses hydrogen sulphide. The separation of groups by hydrogen
sulphide depends, as stated, on the fact, that, in the presence
of a certain concentration of hydrogen-ion, hydrogen sulphide
will not precipitate zinc sulphide and the remaining sulphides
of the zinc group. To secure this concentration of hydrogen-ion,
some hydrochloric acid is added to solutions, from which hydrogen
sulphide is expected to precipitate none but sulphides of the copper
and arsenic groups—and, as a rule, the purpose is accomplished, as
desired. It is evident, however, that if a solution contains an
acetate, say sodium acetate, or the salt of any other weak acid,
‹e.g.› a borate or a phosphate, the addition of hydrochloric acid
will result, at least at first, in the ‹liberation› of the ‹weaker
acid› and will not produce the excess of hydrogen-ion, required
for the analysis. Zinc sulphide, and possibly nickel and cobalt
sulphides,[412] may, under such conditions, be precipitated with
the sulphides of the groups mentioned. Unless provision is made,
therefore, ‹to insure a certain excess of hydrogen-ion› (p. 213),
or unless we are on our guard and look for zinc, nickel and cobalt
in [p209] the analysis of the precipitate formed by hydrogen
sulphide,[413] serious errors obviously could result. To add an
inordinately large excess of hydrochloric acid to mixtures, in order
to avoid this pitfall, will, as we shall presently see, only throw us
more certainly into still another error, to which we are exposed in
the use of this important reagent, hydrogen sulphide.

«III. Precipitation of Cadmium Sulphide.»—Now, if a 0.1 molar
solution of cadmium sulphate (22.6 grams of the salt,[414]
CdSO_{4}, H_{2}O, ‹per› liter) is prepared, equivalent, in
concentration, to the solutions of ferrous and zinc sulphates used
previously, we may consider that the concentration of cadmium-ion
is, approximately, the same as the concentrations of the ferrous-ion
and zinc-ion in the solutions of their sulphates. If the solution
of cadmium sulphate is added to the acidified solution of zinc
sulphate, which was saturated with hydrogen sulphide but from which
no zinc sulphide could be precipitated (‹exp.›, p. 207), a heavy
precipitate of cadmium sulphide is at once obtained (‹exp.›). Or,
if 2 c.c. of hexamolar hydrochloric acid is added to 50 c.c. of
the cadmium sulphate solution and the mixture is saturated with
hydrogen sulphide,[415] cadmium sulphide is precipitated readily
(‹exp.›) and, in fact, quantitatively. We would decide, on the basis
of the principle of the solubility-product, that, in this mixture,
precipitation results because ([Cd^{2+}] × [S^{2−}] / ‹x›) > K_{CdS}.

By the conditions of the experiment we started with a concentration
of the cadmium-ion, [Cd^{2+}], equal to the concentration, [Zn^{2+}],
of the zinc-ion in the zinc sulphate solution, and with the same
concentration,[415] [S^{2−}] / ‹x›, of sulphide-ion as was used
when hydrogen sulphide failed to precipitate zinc sulphide. The
corresponding factors of the products of the ion concentrations
are equal, at the beginning of the two experiments, and we may put
([Cd^{2+}] × [S^{2−}] / ‹x›) = ([Zn^{2+}] × [S^{2−}] / ‹x›) = P′.
We recall the fact, that we have already concluded, on the basis
of the principle of the solubility-product, that ([Zn^{2+}] ×
[S^{2−}] / ‹x›), or P′, is ‹smaller› than K_{ZnS} (p. 207), and that
([Cd^{2+}] × [S^{2−}] / ‹x›), or P′, is ‹greater› than K_{CdS}.

P′ being smaller than K_{ZnS} and larger than K_{CdS}, it is clear
that [p210] K_{CdS} is smaller than K_{ZnS} and that cadmium
sulphide must be the ‹less soluble› of the two sulphides. As a
matter of fact, if ammonium sulphide is carefully added to a mixture
of equal quantities of the two salt solutions, cadmium sulphide
is precipitated first, and when practically all of the cadmium
is precipitated, a final precipitate of white zinc sulphide is
obtained (‹exp.›; see note, p. 205). Or, if zinc sulphide is first
precipitated by the addition of a little ammonium sulphide to 25
c.c. of the 0.1 molar zinc sulphate solution, care being taken
to have zinc sulphate in excess, and if 25 c.c. of the 0.1 molar
cadmium sulphate solution is then added to the mixture, the white
zinc sulphide immediately gives way to the less soluble yellow
cadmium sulphide (‹exp.›; see p. 165). Cadmium sulphide is thus
proved to be the ‹less soluble› of the two sulphides, a result which
confirms the prediction made above with the aid of the principle
of the solubility-product, and we may indeed conclude that the
solubility-product constant K_{CdS} of cadmium sulphide must be
smaller than the constant K_{ZnS} of zinc sulphide (see pp. 163–168,
on fractional precipitation). We are, therefore, also justified
in deciding that CdS may well be precipitated from acidulated
solutions by hydrogen sulphide, when ZnS is not thus precipitated,
simply because K_{CdS} is ‹sufficiently small› (CdS is sufficiently
insoluble) ‹to make the product of the ion concentrations›
[Cd^{2+}] × [S^{2−}] / ‹x›, ‹in spite of the extremely small value
of› [S^{2−}] / ‹x›, ‹greater than the constant› K_{CdS}, whereas
the same small value of [S^{2−}] / ‹x› makes it impossible for the
product [Zn^{2+}] × [S^{2−}] / ‹x› to reach the value of the
‹larger constant› K_{ZnS}, required for the precipitation of ZnS.
Since cadmium sulphide may be precipitated quantitatively under the
conditions given, it is also evident that it may be precipitated even
when the concentration of the cadmium-ion also has a rather small
value. The relations, in regard to this point, will be discussed
presently.

«The Separation of the Copper and Arsenic Groups from the
Zinc Group.»—Ferrous-ion and zinc-ion may be taken as typical
representatives of the ions of the ‹zinc group, whose sulphides are
not precipitated by hydrogen sulphide in the presence of a definite
concentration of hydrogen-ion›, cadmium-ion as a representative of
the ‹copper›, ‹silver› and ‹arsenic› groups, ‹whose sulphides are
precipitated under the same conditions›. The separation of the groups
depends, therefore, on the different solubilities of the sulphides of
these [p211] groups, the sulphides of the zinc group being the most
soluble. Since even these sulphides are precipitated quantitatively
by ammonium sulphide and are very difficultly soluble, the separation
is a kind of fractional precipitation of difficultly soluble salts,
in which the fractionation is made possible and convenient by the
use of an agent, hydrogen sulphide, the concentration of whose
active precipitating component, the sulphide-ion, S^{2−}, is easily
regulated and readily made sufficiently small, not to precipitate
even the difficultly soluble sulphides of the iron group.

Solubilities vary from salt to salt, and we have already found that,
in the zinc group, zinc sulphide is less soluble than the sulphide
of a second member of the group, ferrous sulphide, and that the
difference is revealed in a somewhat different behavior of their
salts toward hydrogen sulphide, when the action is studied in some
detail. Similar differences must be expected to exist among the
sulphides of the groups that hydrogen sulphide precipitates even in
the presence of an excess of hydrochloric acid. As these differences
are the sources of some of the most common and most serious errors
which analysts are liable to commit, the detailed study of the action
of hydrogen sulphide must be continued a little further.

«The Effect of a Large Excess of Acid.»—The precipitation of cadmium
sulphide depends on the relation of the product of the concentrations
of the cadmium-ion and the sulphide-ion to the solubility-product
constant for cadmium sulphide (see the equation, p. 209). Now, it
is clear that if a ‹larger› and ‹larger excess of hydrogen-ion› is
introduced by the addition of more concentrated hydrochloric acid to
the cadmium sulphate solution, the concentration of sulphide-ion is
correspondingly ‹reduced›.[416] The point might be reached, where the
sulphide-ion factor becomes so small, that the product of the ion
concentrations remains smaller than the value K_{CdS}, required for
precipitation of cadmium sulphide.

In fact, if a large excess[417] of hydrochloric acid is added to 50
c.c. [p212] of the 0.1 molar solution of cadmium sulphate, hydrogen
sulphide fails to precipitate any of the sulphide (‹exp.›).

But, if a few cubic centimeters of a 0.1 molar solution of cupric
sulphate (25.0 grams of CuSO_{4}, 5 H_{2}O, per liter) are added
to the solution from which hydrogen sulphide fails to precipitate
cadmium sulphide, cupric sulphide is at once precipitated. And, if
15 c.c. of concentrated hydrochloric acid are added to 50 c.c. of
the 0.1 molar cupric sulphate solution, there results a mixture
corresponding to the cadmium sulphate solution from which hydrogen
sulphide fails to precipitate CdS; we find that hydrogen sulphide
will ‹precipitate› the ‹sulphide of copper› very readily, even under
these adverse conditions (‹exp.›). Cupric sulphide must be even
less soluble in water than cadmium sulphide,[418] and there is no
difficulty in showing that such is the case. If ammonium sulphide,
or hydrogen sulphide, is gradually introduced into a mixture of
25 c.c. each of the 0.1 molar sulphate solutions, cupric sulphide
is precipitated first, and, if the precipitate is collected in
fractions, [p213] pure yellow cadmium sulphide is precipitated
last.[419] Or, if 25 c.c. of 0.1 molar cupric sulphate is added to
the mixture in which a precipitate of cadmium sulphide displaced the
more soluble zinc sulphide (p. 210), the yellow sulphide will, in
turn, give way to the less soluble black sulphide of copper (‹exp.›).

We find thus that the precipitation of cadmium sulphide, by hydrogen
sulphide in acid solution, ‹can be prevented by the presence
of an excess of hydrochloric acid›, which does not prevent the
precipitation of the less soluble cupric sulphide.[420] The fact,
then, that, in an analysis of some unknown mixture, hydrogen sulphide
produces a precipitate in acid solution, must not be considered as
evidence that the conditions are such as to insure the precipitation
of all the sulphides of the groups, which we intend to precipitate.
To avoid error, conditions must be such as to insure the complete
precipitation of the more soluble as well as the less soluble
sulphides. The sulphides of ‹cadmium› and ‹lead›, in particular,
and, to a lesser degree, the sulphides of antimony and tin, are
most liable to remain unprecipitated and thus escape detection in
systematic analysis. This is a matter of special importance, also,
in detecting traces of the ions of these metals, especially of lead,
which is a slow cumulative poison, even when absorbed in minute
amounts, and which analysts must therefore be able to detect, even in
traces, with absolute certainty. It is clear, from a consideration of
the product of the ion concentrations, as affecting the precipitation
or nonprecipitation of such a sulphide, that a much smaller excess
of acid will prevent the precipitation of the last traces of lead
sulphide, and, therefore, of all of it, if only traces are present,
than will interfere with the precipitation of the sulphide in bulk.

«The Desirable Concentration of Acid (of Hydrogen-ion) and an
Indicator for Correct Acidification.»—Summarizing the conclusions
reached in regard to the conditions necessary for a successful
separation of the copper and arsenic groups, by means of hydrogen
sulphide, from the zinc and aluminium groups, we find [p214] that
the concentration of the hydrogen-ion, in the solution to be treated
with hydrogen sulphide, is the most important factor. Too great a
concentration, as has just been shown, will prevent the precipitation
of all, or part, of the more soluble sulphides of the former groups,
notably of the sulphides of cadmium and lead, which is a common
error in the laboratory. Too small a concentration, which may result
when a salt of a weak acid, such as an acetate, borate or phosphate
is present, may lead, as was shown above, to the precipitation of
part of the zinc group, notably of zinc and possibly of nickel
and cobalt, with the copper and arsenic groups, and thus lead to
other errors. For the ordinary purposes of analysis, requiring the
precipitation of say one milligram of any ion from 100 c.c. solution
(one-tenth per cent, if one gram of substance is used for analysis),
a concentration of hydrogen-ion of 0.1 to 0.3 gram-ion per liter
forms a good basis for work.[421] The presence of this concentration
of hydrogen-ion, irrespective of the possible presence of weak
organic or inorganic acids, may be readily insured by a simple test
with an appropriate indicator. ‹Methyl-violet›[422] is suitable for
such a purpose, because it is sensitive only to the rather high
concentrations of hydrogen-ion required: 0.1 c.c. or two drops of
0.05 to 0.1 molar hydrochloric acid, added to an equal volume of a
very dilute solution (1 : 12,500) of the indicator, changes its color
to a ‹pure blue›; 0.2 to 0.25 molar acid, used similarly, turns the
indicator to a ‹blue-green› tint, and 0.33 molar acid produces a
‹yellow› or ‹yellow-green› hue. The ‹blue-green tint›, with which one
becomes easily familiar, and which can, indeed, always be prepared
for matching tints, may be used to recognize speedily, and with
sufficient accuracy, a concentration of the hydrogen-ion of the
strength desired, irrespective of its source.[423]

If an analyst aims to find even smaller quantities of a particular
metal ion, ‹e.g.› traces of lead, the ordinary method of analysis
[p215] may be modified, the source of error in the precipitation of
traces of lead sulphide being kept in mind.[424]

Besides the complications mentioned, and provided against in the
way discussed, there is still one more complication in the use
of hydrogen sulphide: this is in the matter of the precipitation
of ‹arsenic› sulphide from solutions containing ‹arsenic in the
pentavalent condition›. Since the interpretation of this complication
and the explanation of the methods for avoiding the errors, which
may arise therefrom, are necessarily intimately connected with the
chemical behavior of arsenic acid, this subject will be considered in
the discussion of the arsenic group (Chapter XIII).


  FOOTNOTES:

  [395] Auerbach, ‹Z. phys. Chem.›, «49», 220 (1904).

  [396] See footnote 1, p. 201.

  [397] Knox (in Abegg's laboratory), ‹Trans. Faraday Soc.›, «4», 44
  (1908).

  [398] The concentration of the hydrogen-ion is really a little
  greater than that of the hydrosulphide-ion, as a result of the
  ionization of the latter, but the amount of hydrogen-ion formed in
  this way (about 1E−15) is so minute, compared with that formed by
  the primary ionization, that it is negligible.

  [399] We can obtain the relation, directly, from H_{2}S ⇄ 2 H^{+} +
  S^{2−} and [H^{+}]^2 × [S^{2−}] / [H_{2}S] = K = 1.1E−22. For
  a given pressure of the hydrogen sulphide, [H_{2}S], expressing
  its solubility (about 0.1 molar at 25°), is constant, and
  therefore [H^{+}]^2 × [S^{2−}] = a constant, as given in equation
  (IV). Putting [H_{2}S] = 0.1, we have [H^{+}]^2 × [S^{2−}] =
  0.1 × 1.1E−22 = 1.1E−23.

  [400] On account of the great mass of water, we compare (see
  equation, p. 176) [H^{+}] × [HO^{−}] = 1.2E−14 (at 25°) with
  [H^{+}] × [S^{2−}] / [HS^{−}] = 1.2E−15.

  [401] The calculation was made by the method used by Knox (‹loc.
  cit.›) for a molar solution. The degree of ionization of the
  salt was not considered and the correct ionization constant for
  ammonium hydroxide was used, 1.8E−5 in place of 2.3E−5. The
  latter, evidently, was used by Knox as the result of overlooking a
  correction, which Bredig made in his (Bredig's) first calculations
  of the constant; ‹cf.› Bredig, ‹Z. phys. Chem.›, «13», 293,
  footnote. The same erroneous constant is found in Kohlrausch and
  Holborn, ‹loc. cit.›, p. 194.

  [402] For further values and for the method of calculation, see
  Knox, ‹loc. cit.›

  [403] [S_{2−}] = 1.1E−23 / [H^{+}]^2, according to equation (IV),
  p. 201.

  [404] Knox's work leads to that conclusion.

  [405] The precipitation of sulphides, from a solution containing
  much more of the hydrosulphide-ion than of the sulphide-ion, is
  comparable with the precipitation of mercuric oxide, HgO, and of
  silver oxide, Ag_{2}O, by sodium or potassium hydroxide.

  [406] On account of the presence of a small, unknown amount of
  sulphuric acid in the original solution, resulting from the
  hydrolysis of ferrous sulphate, the exact value of [S^{2−}] in the
  first solution cannot be calculated without further examination;
  but, according to the values given in the table on page 202, the
  value of ‹x›, indicating the growth in the concentration of S^{2−},
  is ‹at least› 10^{12}, if 2 equivalents of NaOH, and 10^9, if 2
  equivalents of NH_{4}OH are used to convert the 0.1 molar hydrogen
  sulphide into the corresponding sulphide Me_{2}S, of 0.1 molar
  concentration.

  [407] [S^{2−}] is exactly the same in the two products, when equal
  volumes of the zinc and ferrous sulphate solutions are mixed and
  the mixture is saturated with hydrogen sulphide; ‹zinc sulphide› is
  precipitated.

  [408] The difference in the values obtained, when hydrolysis is
  considered or neglected, is very considerable. ‹Vide› Bodländer,
  on the solubility of calcium carbonate, ‹Z. phys. Chem.›, «35», 23
  (1900), and Stieglitz, ‹Carnegie Institution Publications›, No.
  «107», 249 (1909).

  [409] In carrying out this ‹fractional precipitation› a very
  dilute solution of ammonium sulphide is used, so as to prevent
  the mechanical enclosure of black ferrous sulphide, which would
  discolor the white sulphide. The ammonium sulphide solution should
  be saturated with hydrogen sulphide, to prevent the precipitation
  of green ferrous-ferric oxide by an excess of free ammonia. It
  is best to prepare a set of the precipitates and to preserve
  them in well-stoppered vessels, and not to try to take the
  time and care necessary to effect a perfect fractionation as a
  lecture experiment. The presence of the ferrous sulphate, in the
  supernatant liquid above the first precipitate of zinc sulphide,
  may be readily demonstrated by pouring off some of the solution
  and adding an excess of ammonium sulphide to it. Of course, it is
  also perfectly legitimate, and easier, to precipitate first zinc
  sulphide from a pure zinc sulphate solution and then to add ferrous
  sulphate solution to the mixture and to preserve the mixture. If
  the zinc sulphide were not the less soluble, it would be rapidly
  converted into the black ferrous sulphide. (See p. 165, and see
  below, pp. 210, 213, where similar transformations are carried out
  as lecture experiments.)

  [410] When 10% of the zinc in a 0.1 molar solution has been
  precipitated, 0.01 molar sulphuric acid has been formed. For
  the sake of a rough approximation, the acid may be considered
  completely ionized and then [H^{+}] = 0.02, which is 200 times the
  value of [H^{+}] in a saturated H_{2}S solution (p. 200); if the
  presence of a little sulphuric acid in the original zinc sulphate
  solution, resulting from a slight hydrolysis of the salt, is
  ignored, the concentration of the sulphide-ion is decreased roughly
  (200)^2 or forty thousandfold, while the concentration of zinc-ion
  falls 10%. The corrections, that have been indicated, would change
  the quantities involved, but they would not modify the character of
  the result.

  [411] This proportion of acid, making the concentration of the
  hydrogen-ion, approximately, [H^{+}] = 0.2, is used, not because
  it represents the minimum concentration of the hydrogen-ion, which
  will prevent the precipitation of zinc sulphide in 0.1 molar
  zinc sulphate solution, but because it represents the practical
  conditions under which the precipitation of zinc sulphide is
  avoided, when the copper and arsenic groups are precipitated in
  qualitative analysis (see p. 213).

  [412] Nickel and cobalt sulphides are also precipitated by
  hydrogen sulphide in the presence of free acetic acid, if sodium
  or potassium acetate is added, to suppress the hydrogen-ion of the
  acetic acid (p. 112).

  [413] They would be found in the copper group.

  [414] The sulphate, of this composition, is obtained by drying the
  crystallized sulphate in an air bath at 100–105°.

  [415] ‹Cf.› the corresponding experiment with zinc sulphate, p. 207.

  [416] [S^{2−}] = ‹k› / [H^{+}]^2. See equation (IV), p. 201.

  [417] Any immediate precipitation of cadmium sulphide will be
  prevented by the addition of 10 c.c. of concentrated acid (sp.
  gr. 1.19) to 50 c.c. of the 0.1 molar solution, and 15 c.c. will
  completely prevent any precipitation of the sulphide. Of course, a
  smaller excess would prevent the precipitation of small quantities
  of the sulphide (‹e.g.› a half milligram of cadmium), which should
  easily be found in 50 c.c. (see p. 214).

  [418] The value of the solubility-product constant for cupric
  sulphide, at 25°, was determined by Knox (‹loc. cit.›): [Cu^{2+}] ×
  [S^{2−}] = 1.2E−42, corresponding to a concentration of 1.1E−21
  of cupric-ion. Mercuric sulphide was found even less soluble:
  [Hg^{2+}] × [S^{2−}] = 2.8E−54, and its behavior agrees with such
  a relation (Lab. Manual, p. 50, § 2). The solubility-product
  constant for lead sulphide, which resembles cadmium sulphide in
  the fact that a large excess of acid prevents its precipitation,
  was found to be [Pb^{2+}] × [S^{2−}] = 2.6E−15, the constant
  being about 10^{27} times as large as the constant for cupric
  sulphide. This value for the solubility-product constant for
  lead sulphide must either be considerably larger than the true
  value or lead must be easily precipitated as a hydrosulphide,
  Pb(SH)_{2}, since solutions in which the product of the ion
  concentrations, [Pb^{2+}] × [S^{2−}], is very much smaller
  than the constant given, readily precipitate lead sulphide.
  Thus Noyes and Bray [‹J. Am. Chem. Soc.›, «29», 137 (1907)]
  report it possible to precipitate 1 to 2 milligrams of lead-ion
  in 100 c.c. of solution (say [Pb^{2+}] = 1E−4) with hydrogen
  sulphide in the presence of 4 c.c. of hydrochloric acid (sp. gr.
  1.12), for which, approximately, [H^{+}] = 0.25. Then (equation
  (IV), p. 201) [S^{2−}] = (1.1E−23) / (0.25)^2 = 1.8E−22, and
  [Pb^{2+}] × [S^{2−}] = 1E−4 × 1.8E−22 = 1.8E−26, which is a much
  lower value than that given by Knox, and which still is not claimed
  to represent the limit of insolubility. Experiments, made in this
  laboratory, confirm this result and show further, that lead-ion in
  a concentration of 1E−5 is precipitated in the presence of 0.25
  molar hydrochloric acid ([H^{+}] = 0.22). Then [S^{2−}] = 2.3E−22
  and [Pb^{2+}] × [S^{2−}] = 2.3E−22 × 10^{−5} = 2E−27, which does
  not yet express the limit of insolubility.

  [419] The fractions are not prepared in the lecture, but the first
  fraction is kept suspended in part of the solution of the two
  sulphates and may be kept so for years. The last fraction is kept
  in a separate container.

  [420] A large excess of acid is liable to interfere with the
  precipitation of the ‹last traces› of cupric sulphide and is
  avoided in exact work.

  [421] Noyes and Bray use, approximately, [H^{+}] = 0.25 [‹J. Am.
  Chem. Soc.›, «29», 137 (1907)]. Tests in this laboratory showed
  that 1 milligram of cadmium-ion, or of lead-ion, in 100 c.c., is
  readily precipitated by hydrogen sulphide in the presence of 0.25
  molar hydrochloric acid, ([H^{+}] = 0.22).

  [422] Kahlbaum's "Krystallviolett,"
  [(CH_{3})_{2}NC_{6}H_{4}]_{2}C : C_{6}H_{4}N(CH_{3})_{2}Cl, is
  referred to.

  [423] An indelible ink pencil (violet) may, in most cases, be used
  in place of the solution. The details for the application of the
  indicator are given in the instructions for laboratory practice,
  Lab. Manual, pp. 31, 102, 103.

  [424] See Blyth, ‹Poisons, etc.›, p. 608 (1895), in regard to the
  detection of traces of lead.

[p216]




 CHAPTER XII

 «THE COPPER AND SILVER GROUPS» (‹Continued›).—«THE THEORY OF COMPLEX
 IONS»


We will now turn to the consideration of a series of reactions
involving the behavior of so-called "complex ions," which are very
frequently met with in the various analytical groups and which
offer valuable methods of separation and identification of ions.
The behavior of silver nitrate solution towards ammonia forms a
convenient point of attack in taking up the general subject.

«Action of Ammonia on Silver Nitrate.»—Addition of ammonium hydroxide
solution to silver nitrate (‹exp.›) results in the formation of a
brown precipitate of silver oxide (and silver hydroxide). We may
consider the supernatant liquid to be saturated with silver hydroxide
(this is in equilibrium with silver oxide), and for the saturated
solution we may put [Ag^{+}] × [HO^{−}] = K_{AgOH}.

If more ammonium hydroxide is added to the mixture, the precipitate
dissolves readily. The excess of ammonium hydroxide must increase the
concentration of hydroxide-ion and, if no other action occurred, we
should, according to the principle of the solubility-product, expect
that the precipitate would thereby be slightly increased (p. 145),
rather than that it should be dissolved so readily. Since solution
results even when the value of the one factor, [HO^{−}], of the
product is increased, we must suspect that the value of the other
factor, the concentration [Ag^{+}] of silver-ion, is in some way made
much smaller by the addition of the excess of ammonium hydroxide.
Recalling the fact that aluminium hydroxide is soluble in excess
of sodium hydroxide, as the result of its amphoteric character, a
solution of sodium aluminate NaAlO_{2} being obtained, we might
suspect that silver hydroxide also has amphoteric properties, ‹i.e.›
that it might be capable of ionizing into "argentate ions," AgO^{−},
and hydrogen ions, AgOH ⇄ AgO^{−} + H^{+}. If such be the case, the
nonionized silver hydroxide is in equilibrium, not only with the
solid phase, [p217] but also with two sets of ions,

 Ag^{+} + HO^{−} ⇄ AgOH

 AgOH ⇄ AgO^{−} + H^{+}

 AgOH ⇄ AgOH ↓,

and we must have ‹two› solubility-product constants, one corresponding
to the basic ionization (see above) and the other corresponding to
the acid ionization, and [AgO^{−}] × [H^{+}] = K′_{AgOH}.

If silver hydroxide have acid properties, the addition of an alkali
must suppress the hydrogen-ion and the hydroxide will go into
solution as an argentate, MeAgO. We find, however, that sodium or
potassium hydroxide, which would form an argentate very much more
readily than ammonium hydroxide, has no solvent action on silver
hydroxide (‹exp.›); on the contrary, quantitative experiments show
that the alkali makes the hydroxide still less soluble than in pure
water—as demanded by the solubility-product for the basic ionization.
It is thus evident, that the solvent action of ammonium hydroxide is
not due to its basic functions. We would suspect that we have here
an action, in which ‹ammonia› is the active component, the product
of a form of dissociation of ammonium hydroxide, of which the fixed
alkalies are incapable.

«The Complex Silver-Ammonium[425]-Ion.»—For a solution of
ammonia, in water, we have the reversible reactions: [p218]
HO^{−} + H^{+} + NH_{3} ⇄ NH_{4}^{+} + HO^{−} ⇄ NH_{4}OH, and we
note that a molecule of ammonia appears to combine first with a
hydrogen ion, to form an ammonium ion, and this then forms ammonium
hydroxide with the hydroxide ion. This suggests that ammonia may have
the capacity to combine with positive ions other than hydrogen ion,
and with metal hydroxides other than water. For an analogous reaction
of ammonia with silver ion and with silver hydroxide, we would have:

 NH_{3} + Ag^{+} + HO^{−} ⇄ (NH_{3}Ag)^{+} + HO^{−} ⇄ (NH_{3}Ag)OH.

For the condition of equilibrium between ammonia, the silver-ion and
the silver-ammonium-ion, we would have[426]:

 [NH_{3}] × [Ag^{+}] / [NH_{3}Ag^{+}] = K.

Experimental investigations of the quantitative relations, obtaining
in ammoniacal solutions containing silver compounds, show that ‹no
constant› value is obtained for the ratio, as just developed. But the
experimental data show equally conclusively,[427] that a constant is
obtained, ‹when the concentration of the ammonia is raised to the
second power, in the mathematical statement›.

The significance of this change in the mathematical relation, it will
be recalled (p. 94), is that two molecules of ammonia must combine
with one silver ion to form an ion [(NH_{3})_{2}Ag]^{+}, whereas
in the formation of the ammonium ion, NH_{4}^{+}, we have a single
molecule of ammonia combining with one hydrogen ion. We have then

 2 NH_{3} + Ag^{+} + HO^{−} ⇄ [(NH_{3})_{2}Ag]^{+} + HO^{−} ⇄
   [(NH_{3})_{2}Ag]OH.

We would thus have a silver-ammonium ion, [(NH_{3})_{2}Ag]^{+},
and its hydroxide, silver-ammonium hydroxide, corresponding to the
[p219] ammonium ion and its hydroxide, ammonium hydroxide. The
properties of ammoniacal solutions of silver oxide are in entire
agreement with this conception. The hydroxide is a stronger base than
barium hydroxide.[428] It forms salts, [(NH_{3})_{2}Ag]X, in which
silver appears as part of a so-called positive "complex ion." The
hydroxide, like ammonium hydroxide, is unstable and is only known
in solution and in the presence of free ammonia, exactly as is the
case for ammonium hydroxide. The mathematical equation expressing the
equilibrium conditions for the complex ion,

 [NH_{3}]^2 × [Ag^{+}] / [(NH_{3})_{2}Ag^{+}] = K_{Instability},

gives a ‹definite measure› of the ‹stability› of this complex ion.
It is clear, that the ‹larger› the constant, the more ‹unstable› the
complex ion would be, and so the constant is called the ‹Instability
Constant›[429] of the complex silver-ammonium-ion. Bodländer found
the value of the constant to be 6.8E−8 at 25°.[430]

According to the composition of the complex ion, two molecules of
ammonia should be required for every molecule of silver nitrate,
to produce a solution containing the nitrate of the complex ion:
Ag^{+} + NO_{3}^{−} + 2 NH_{3} ⇄ [(NH_{3})_{2}Ag]^{+} + NO_{3}^{−}.
As a matter of fact, 20 c.c. of a molar solution of ammonium
hydroxide (= 200 c.c. of a 0.1 molar solution) must be added to
100 c.c. of a 0.1 molar solution of silver nitrate, to convert the
silver nitrate into the salt of the complex silver-ammonium-ion.
If the ammonium hydroxide solution is allowed to flow slowly, from
a pipette, into the silver nitrate solution, we find that the last
trace of the precipitated silver hydroxide redissolves just as the
‹last› drop or two of the 20 c.c. is added to the mixture (‹exp.›).
Working more exactly, Reychler[431] found that the addition of
ammonia to a silver nitrate solution, in the proportion of two
molecules of the former to one of the nitrate, does not change the
freezing-point of the solution, and therefore [p220] does not
increase the total number of molecules in the solution. This result
agrees with the conception that two molecules of ammonia combine with
one silver ion to form a complex ion.

«Application in Analysis.»—Turning now to the consideration of
the bearing of these relations on the detection of silver-ion in
analysis, we may conclude, in the first place, from the value of
the constant as given, that only a ‹small proportion› of the total
silver in such ammoniacal solutions is present in the form of
silver-ion; but, in the second place, there is, at least, a ‹portion›
of the silver present in the form of its ion—it is ‹not entirely›
suppressed; and, in the third place, it is clear, from the form of
the equilibrium equation, that any ‹excess› of ‹ammonia› must very
rapidly reduce the ‹concentration of silver-ion› in such solutions.

The bearing of these relations, which, it will be noted, concern
‹concentrations of silver-ion›, can best be seen by working with
solutions of definite concentrations.

If the solution we have just prepared is diluted with water to 200
c.c., a 0.05 molar solution of [(NH_{3})_{2}Ag]NO_{3} is formed. In
such a solution, the concentration, [Ag^{+}], of the silver-ion is
only 0.0009,[432] whereas in 0.05 molar silver nitrate solution it
is 0.0435. It is clear that the reactions of the silver-ion will
not be observed as readily in such an ammoniacal solution as in a
solution of silver nitrate, which contains the same concentration of
‹total silver›. That such is the case, may be readily demonstrated as
follows: the addition of 1 c.c. of molar sodium bromate to 10 c.c.
of 0.05 molar silver nitrate immediately forms a heavy precipitate
of the moderately difficultly soluble bromate, AgBrO_{3}, while the
same addition to 10 c.c. of the 0.05 molar silver-ammonium nitrate
solution produces no precipitate whatever (‹exp.›). [p221]

 A liter of water dissolves 0.025 mole (6 grams) of silver
 bromate[433] at 18°. If the same degree of ionization be assumed
 for it as for a 0.025 molar solution of the analogous salt, silver
 nitrate, AgNO_{3}, 90% of the silver bromate in the saturated
 solution is ionized. The solubility-product constant then is
 [Ag^{+}] × [BrO_{3}^{−}] = (0.025 × 0.9)^2 = 0.0005.

 When 1 c.c. of molar sodium bromate is added to 10 c.c. of 0.05 molar
 silver nitrate, each salt is ionized 80% in the mixture, and
 [Ag^{+}] = 0.05 × 0.8 × 10 / 11 = 0.037 and [BrO_{3}^{−}] =
 (1 × 1 / 11) × 0.8 = 0.072. Then the product of the ion
 concentrations, [Ag^{+}] × [BrO_{3}^{−}] = 0.037 × 0.072 = 0.0027, is
 considerably larger than the constant 0.0005 and precipitation
 follows.

 But, when 1 c.c. of molar sodium bromate is added to 10 c.c. of
 a 0.05 molar silver-ammonium nitrate solution, the concentration
 of silver-ion[434] is 0.00085 and the product of the ion
 concentrations, [Ag^{+}] × [BrO_{3}^{−}] = 0.00085 × 0.072 = 6E−5,
 is smaller than the constant; the solution will not be saturated
 with silver bromate and no precipitate is formed.

On the other hand, if 1 c.c. of a 0.1 molar solution of sodium
chloride is added to 10 c.c. of 0.05 molar silver-ammonium nitrate
solution, a very decided precipitate of silver chloride is formed
(‹exp.›). The difference in the action of the sodium bromate and
the chloride lies in the fact that silver chloride is 2500 times as
insoluble as is silver bromate, and the chloride may be precipitated
from solutions containing a ‹very much smaller concentration of the
silver-ion› than is required for the precipitation of silver bromate.

 The quantitative relations for the chloride are as follows: a
 liter of water dissolves 0.002 gram, or 1.4E−5 mole, of silver
 chloride at 25°,[435] and the solubility-product constant at
 25° is [Ag^{+}] × [Cl^{−}] = (1.4E−5)^2 = 2E−10. Now, if 1
 c.c. of 0.1 molar sodium chloride is added to 10 c.c. of 0.05
 molar silver-ammonium nitrate, we have,[436] for the first
 moment, [Ag^{+}] = 8.9E−4 and [p222] [Cl^{−}] = 0.008, and
 [Ag^{+}] × [Cl^{−}] = 8.9E−4 × 0.008 = 7E−6, which is much larger
 than the solubility-product constant, and precipitation must take
 place. The precipitate will be quite a heavy one: as silver-ion is
 removed from solution, the complex ion must decompose and furnish
 a new supply of silver-ion, and precipitation must continue until
 the excess of ammonia, which is liberated by the decomposition of
 the complex ion (Ag(NH_{3})_{2}^{+} + Cl^{−} → AgCl ↓ + 2 NH_{3}),
 suppresses the silver-ion sufficiently to satisfy, with the
 diminished concentration of chloride-ion, the solubility-product
 constant of silver chloride.

It is clear that, while the reactions of silver-ion are not obtained
‹as readily› in the ammoniacal solution as in an equivalent solution
of silver nitrate (bromate experiment), nevertheless more sensitive
tests show that a ‹small portion› of the silver still is present as
‹silver-ion› in the ammoniacal solution (chloride experiment).

This brings us to our third point, the influence of an excess of
ammonia on the concentration of silver-ion and on its reactions. It
is evident, from the form of the equilibrium equation (p. 219), that
any excess of ammonia must very rapidly reduce the concentration of
silver-ion. We may ask ‹what excess will be required to prevent the
precipitation of silver chloride› in the experiment just tried.

 The question may be answered as follows: The concentration of
 chloride-ion, when 1 c.c. of 0.1 molar sodium chloride is added
 to 10 c.c. of 0.05 molar [Ag(NH_{3})_{2}]NO_{3}, no precipitate
 being formed, will be 0.1 × (1 / 11) × 0.87, the solution being
 diluted 1 to 11 and the percentage of ionization of a salt MeX
 being approximately 87% in 0.05 to 0.06 molar concentration. For
 a solution containing this concentration of chloride-ion, the
 concentration [Ag^{+}] of silver-ion, ‹which may just be present›
 «without» ‹leading to the precipitation of silver chloride› (‹i.e.›
 for the saturated solution) is, according to the principle of the
 solubility-product,

 [Ag^{+}] = K_{S.P.} / [Cl^{−}] = (2E−10) / (0.1 × 0.87 × 1 / 11).

 Further, in the presence of an excess of ammonia, practically
 all of the silver is present in the complex form, and,
 [Ag(NH_{3})_{2}^{+}] = 0.05 × 0.87 × 10 / 11 the 0.05 molar solution
 being diluted 10 parts to 11 and the salt being 87% ionized.

 If we call ‹x› the concentration of free ammonia required to reduce
 the concentration of silver-ion to the small value indicated, we may
 put

 [NH_{3}]^2 × [Ag^{+}] / [Ag(NH_{3})_{2}^{+}] =
 [‹x›^2 × 2E−10 / (0.1 × 0.87 × 1 / 11)] / (0.05 × 0.87 × 10 / 11) =
   6.8E−8.

 Solving for ‹x›, we obtain ‹x› = [NH_{3}] = 0.33. The concentration
 of free ammonia, necessary to prevent precipitation of silver
 chloride in this system, is then [p223] 0.33, instead of 0.0018,
 present in the original solution. Now, 11 c.c. of 0.33 molar ammonia
 is equal to 11 × 0.33 / 6, or 0.61 c.c. hexamolar ammonia.[437]

Calculations, based on the solubility-product constant of silver
chloride and on the instability constant of silver-ammonium-ion,
lead, thus, to the conclusion that an excess of 0.61 c.c.
of hexamolar ammonia is required, in 10 c.c. of 0.05 molar
[Ag(NH_{3})_{2}]NO_{3}, to prevent the precipitation of silver
chloride by 1 c.c. of 0.1 molar sodium chloride. Conversely, this
excess of ammonia will be required to ‹redissolve the precipitate›
of silver chloride, formed when 1 c.c. of 0.1 molar sodium chloride
solution is added to 10 c.c. of 0.05 molar [Ag(NH_{3})_{2}]NO_{3}.
The following experiment shows that such is the case.

 EXP. 1 c.c. of 0.1 molar sodium chloride is added to 10 c.c. of
 0.05 molar silver-ammonium nitrate, prepared as described on p.
 220; hexamolar ammonia is slowly added to the mixture from a 1
 c.c. pipette, graduated in twentieths of a cubic centimeter. The
 precipitate will be seen to be just about ‹completely dissolved›
 when 0.6 to 0.65 c.c. of the ammonia solution has been used.

We find, in this way, that the equilibrium equation for the
instability constant of the complex silver-ammonium-ion, together
with the principle of the solubility-product, allows a ‹quantitative
interpretation› of the problem of the behavior of ammoniacal silver
solutions, as far as the detection of silver by the precipitation of
its salts is concerned.

If a still larger excess of ammonia is used (‹exp.›), even the
addition of a 10% solution of sodium chloride fails to precipitate
the chloride, and, ‹vice versa›, ammonia in excess will readily
redissolve a heavy precipitate of silver chloride (‹exp.›). Advantage
is taken of this fact in the separation and identification of
silver-ion (Laboratory Manual, ‹q. v.›).

It is interesting to note that the addition of potassium bromide,
iodide or sulphide to the ammoniacal solution, in which sodium
chloride fails to precipitate any silver chloride, will still
precipitate silver bromide, iodide or sulphide readily (‹exp.›).
Judged by the line of argument used above, in contrasting the
behavior of silver bromate and silver chloride, these silver salts
[p224] must be still less soluble than the chloride. Experiment
proves, that such is, indeed, the case.[438]

 Silver iodide is so insoluble, that ammonia[439] may be used to
 separate it, with a considerable degree of accuracy, from silver
 chloride, and this separation forms the basis of a method to detect
 chloride-ion in the presence of an iodide. If a solution with a
 ‹limited concentration of ammonia› is used, the method may be
 extended also to the separation of chlorides from bromides (see
 Chap. XVI).[440]

«Complex Metal-Ammonium Ions of Copper, Cadmium, etc.»—Quite a number
of metal ions are capable of forming more or less stable complex
ions with ammonia. For analytical purposes, the most interesting of
such complex ions, aside from the silver-ammonium-ion, are those
formed by cupric, cadmium, zinc and nickel ions, the most important
of which represent bivalent complex ions of the composition[441]
Me(NH_{3})_{4}^{2+}. The following instability constants have been
determined:[442] At 21°,

 [Cd^{2+}] × [NH_{3}]^4 / [Cd(NH_{3})_{4}^{2+}] = 1E−7

 [Zn^{2+}] × [NH_{3}]^4 / [Zn(NH_{3})_{4}^{2+}] = 2.6E−10.

Cupri-ammonium-ion is far more intensely blue than cupric-ion and
its color is used as one of the tests to identify copper in its
salts. Nickel-ammonium-ion is also blue, a much paler blue, and its
color must not be mistaken as indicating the presence of a dilute
solution of cupric-ammonium-ion. The same kind of relations obtain
for these complex ions as for silver-ammonium-ion. For instance, a
salt like cupric phosphate, which is readily precipitated from cupric
sulphate solutions, is not precipitated from the ammoniacal solutions
containing an excess of ammonia (‹exp.›), while the very much less
soluble[443] cupric sulphide is readily precipitated even from the
ammoniacal solutions (‹exp.›). It may [p225] easily be shown, in the
usual way,[444] that the sulphide of copper is very much less soluble
than its phosphate (‹exp.›).

«The Complex Cyanide Ions.»—Metal ions are capable of forming complex
ions, of importance in analytical work, with a number of components
other than ammonia. Among the most important of these are the complex
ions formed with cyanide-ion. The theory of the complex cyanide ions
is entirely analogous to that of the complex metal-ammonium ions,
but there is a difference in stability that makes their special
consideration desirable, both for practical and for theoretical
purposes. The complex ions of silver-ion and cyanide-ion will be
discussed first.

«The Argenticyanide-Ion.»—When potassium cyanide is added to a
solution of silver nitrate, a very insoluble precipitate of silver
cyanide is obtained, but an excess of potassium cyanide readily
redissolves the precipitate (‹exp.›). Since solution is effected in
spite of the presence of an excess of the precipitating cyanide-ion,
one is led to suspect that the other ion, the silver-ion, which is
needed to form the precipitate, is suppressed by entering into some
kind of complex with the excess of cyanide. As a matter of fact,
the solution contains a salt, potassium argenticyanide KAg(CN)_{2},
in which the silver forms a part of a ‹negative argenticyanide-ion›
(Ag(CN)_{2}^{−}).[445] If a current of electricity is passed through
such a solution, the silver (all but traces), together with the
cyanide groups, moves towards the positive electrode.[446] The
complex has been formed, then, by the combination of a positive
silver-ion with two negative cyanide ions,[447] which produce a
univalent negative argenticyanide-ion, Ag(CN)_{2}^{−}. Recalling
the fact that the complex silver-ammonium-ion is not perfectly
stable, one might suspect that the complex cyanide-ion, in
turn, is not absolutely stable, and that the action, by which
it is formed, is balanced, when equilibrium is reached, by a
reverse action of decomposition. We would have, then, [p226]
K^{+} + Ag^{+} + 2 (CN)^{−} ⇄ K^{+} + [Ag(CN)_{2}^{−}] or, more
simply, Ag^{+} + 2(CN)^{−} ⇄ [Ag(CN)_{2}^{−}].

For the condition of equilibrium between the complex and its
components, the relation

 [Ag^{+}] × [CN^{−}]^2 / [Ag(CN)_{2}^{−}] = K_{Instability}

would hold. Bodlaender[448] determined the value of this constant by
measuring the concentrations of the three components under varying
conditions. The value found is 1E−21. The value of the instability
constant for [Ag(NH_{3})_{2}^{+}], of analogous composition,
is 6.8E−8, a very much larger value than the constant of the
[Ag(CN)_{2}^{−}] complex. The latter is, therefore, by far the more
stable. It must, consequently, be much more difficult to obtain
reactions, such as precipitations, of silver-ion in cyanide than
in ammoniacal solutions. In fact, it is impossible to precipitate
silver chloride by the addition of sodium chloride to KAg(CN)_{2}
solution (‹exp.›).[449] Silver sulphide was found to be a much less
[p227] soluble salt than the chloride (p. 224), and ammonium or
sodium sulphide solution, when added to the cyanide solution, readily
precipitates silver sulphide (‹exp.›). (The sulphide is ‹capable› of
‹existence› in the solid phase, therefore, under these conditions.)
In view of the extremely small concentrations of silver-ion in the
cyanide solution, we have here a striking illustration of the extreme
insolubility of the sulphide.

According to the equilibrium equation given above, the larger the
excess of cyanide-ion in the solution, the smaller must be the
concentration of silver-ion which is capable of existence in its
presence. In agreement with this conclusion, we find that the
addition of an excess of potassium cyanide readily redissolves
the precipitated silver sulphide (‹exp.›).[450] In other words,
even the minute concentration of silver-ion, that must be present
in the supernatant liquid above a precipitate of silver sulphide
([Ag^{+}]^2 × [S^{2−}] = K_{Sol. Prod.}, for a saturated liquid),
cannot be permanently present with an excess of potassium cyanide.
Consequently, ‹the solid phase is incapable of existence in the
system›.

The equilibrium equations give us, thus, a comprehensive basis for
the interpretation of the behavior of cyanide solutions containing
silver. First, in accordance with the small value of the constant,
we find it very much more difficult to obtain precipitates of silver
salts in cyanide, than, say, in ammoniacal solutions; secondly,
in accordance with the fact that a very small, but definite,
concentration of the silver-ion may still persist in the [p228]
system, we find it possible, in the absence of an excess of cyanide,
to precipitate such an extremely insoluble silver salt as silver
sulphide represents; and finally, in accordance with the form and
constant of our equation, we find it possible, by using an excess of
potassium cyanide, to suppress the silver-ion to the point where even
this extremely insoluble salt can no longer exist.[451]

«Cuprocyanide and Cadmicyanide Ions.»—Very many of the metal ions
are capable of forming complexes with cyanide-ion, of greater or
smaller degrees of stability, and, as is the case for the complex
ions formed by metal ions with ammonia, a metal ion is frequently
able to form more than one complex with cyanide-ion.[452] A number of
these complex cyanide ions are of particular interest in qualitative
analysis. For instance, we make use of the difference in the
stability of the cuprocyanide and the cadmicyanide ions as offering
us the most convenient method of recognizing cadmium in the presence
of copper. Excepting for the sulphide and the oxide, cadmium does not
form salts and compounds of characteristic colors, and, except in
color, the salts resemble the corresponding copper salts very much in
their physical and chemical behavior. Copper and cadmium consequently
show the same group reactions in systematic analysis. The more
intense colors of the copper compounds—the black sulphide, the
intensely blue cupric-ammonium-ion—mask the cadmium reactions. But
cupric-ion may be converted, by potassium cyanide, into a complex ion
of extreme stability, from the solutions of which hydrogen sulphide
and alkali sulphides ‹fail to precipitate any sulphide of copper,
while cadmium sulphide may be precipitated from the solutions of the
much less stable complex cadmicyanide-ion›.

 When potassium cyanide is added to the deep blue ammoniacal
 solution of cupric-ammonium sulphate [Cu(NH_{3})_{4}]SO_{4}, the
 cupric-ion is reduced[453] [p229] to cuprous-ion, and the latter
 is converted, by an excess of cyanide, into the extremely stable
 complex ion Cu(CN)_{3}^{2−} and its salt, potassium cuprocyanide
 K_{2}[Cu(CN)_{3}]. The instability constant of the complex ion
 is: [Cu^{+}] × [CN^{−}]^3 / [Cu(CN)_{3}^{2−}] = 0.5E−27, and
 the concentration of cuprous-ion, in a 0.1 molar solution, is
 approximately[454] 3.7E−8. Without an excess of cyanide, traces of
 cuprous sulphide may still be precipitated, but ‹a few drops excess
 will prevent the precipitation entirely›.[455]

 With an excess of potassium cyanide, cadmium forms the salt
 K_{2}[Cd(CN)_{4}], yielding the ion [Cd(CN)_{4}^{2−}]. The
 instability constant[456] of the complex ion is [Cd^{2+}] ×
 [CN^{−}]^4 / [Cd(CN)_{4}^{2−}] = 1.4E−17. The concentration of
 cadmium-ion, in a 0.1 molar solution of the salt, is then
 approximately[457] 8E−5.

If potassium cyanide is added to an ammoniacal solution, containing
both cadmium and copper, until the color of the solution is just
discharged, and if two or three drops excess of the cyanide is then
used, the addition of ammonium sulphide will precipitate pure cadmium
sulphide (‹exp.›), while ammonium sulphide, added to a portion of
the original ammoniacal solution, will precipitate a dark mixture
of cupric and cadmium sulphide (‹exp.›), in which the yellow color
of cadmium sulphide is masked by the black precipitate of cupric
sulphide.

«Cobalticyanide and Nickelocyanide Ions.»—In much the same way, in
the identification of nickel in the presence of cobalt, advantage
may be taken of the fact that cobalt forms an extremely stable
cobalticyanide[458] ion, [Co(CN)_{6}^{3−}], which does not permit of
the precipitation of cobaltic hydroxide, whereas nickel does not form
such an ion, but only forms a not very stable nickelocyanide ion,
[Ni(CN)_{4}^{2−}], which is readily decomposed by bromine and alkali,
nickelic hydroxide being precipitated. [p230] The following are the
chief actions involved in the precipitation of the latter:[459]

 Ni(CN)_{4}^{2−} ⥂ Ni^{2+} + 4 CN^{−}

 2 Ni^{2+} + Br_{2} ⥂ 2 Ni^{3+} + 2 Br^{−}

 Ni^{3+} + 3 HO^{−} ⥂ Ni(OH)_{3} ↓

«Applications and Precautions in Analysis.»—The complex cyanide
ions thus give us a convenient means of ‹interfering› with the
precipitation of certain metal ions, and of enabling us, thereby,
to detect other, closely related, ions in their presence. At the
same time, we must be careful ‹to identify the ions›, which we wish
to suppress, before converting them into these extremely stable
complexes. Potassium cuprocyanide and potassium cobalticyanide
solutions would not give any of the ordinary tests for ions of copper
and cobalt, and to find the latter in such solutions, by these tests,
we would have to take the trouble of destroying the complexes. Should
the destruction of such complexes become necessary (‹e.g.› when
complex cyanide ions are present in the original substance under
examination), evaporation with sulphuric acid, with due precautions
against inhaling poisonous hydrocyanic acid fumes, fusion with
alkali carbonates, and perhaps most conveniently, electrolysis with
sufficiently high potentials,[460] are the methods most frequently
employed for the purpose. It will be recalled that we have used the
method of fusion with potassium carbonate to find iron in potassium
ferrocyanide (p. 89).

«Ferrocyanide and Ferricyanide Ions.»—The ferro- and ferricyanide
ions may also be treated as complex ions. For instance, for the
ferricyanide-ion, we would expect a condition of equilibrium to exist
between the complex ion and the simple ions according to:

 Fe(CN)_{6}^{3−} ⇄ Fe^{3+} + 6 CN^{−} and

 [Fe^{3+}] × [CN^{−}]^6 / [Fe(CN)_{6}^{3−}] = K.

[p231]

If the fact is recalled that the extremely sensitive tests for the
ferric-ion fail to reveal the least trace of it in a potassium
ferricyanide solution, one must conclude that the ferricyanide-ion
must be extremely stable. The conception of the ferricyanide-ion
as a complex ion, subject to the above equilibrium conditions,
suggests that if a considerable excess of hydrogen-ion is added to
its solutions, the concentration of ferric-ion must be increased:
since hydrocyanic acid is an extremely weak acid (p. 104), the
ratio [H^{+}] × [CN^{−}] / [HCN] having the value 7 / 10^{10},
the addition of some concentrated hydrochloric acid must decidedly
suppress the cyanide-ion in a ferricyanide solution and thus lead
to an increase in the concentration of the ferric-ion. Under these
conditions, direct evidence of the presence of the ferric-ion, and
of the fact that the complex ion is a component in a reversible
reaction, may, indeed, be obtained, as well as further evidence of
the extreme stability of the complex. The presence of traces of
ferric-ion may be detected, namely, in the acid solution by the
thiocyanate test, applied in its most sensitive form, in which any
ferrithiocyanate produced is taken up in ether.

 EXP. Potassium ferricyanide, treated with a thiocyanate and ether,
 does not show the least trace of color; when some concentrated
 hydrochloric acid is added to the mixture, a perfectly plain,
 although noticeably faint, pink tint is imparted to the ether
 solution.

 Mercuric cyanide, as we have seen (p. 115), is exceptional in its
 exceedingly small capacity for ionization. Sherrill[461] has found
 that the dissociation constant for [Hg^{2+}] × [CN^{−}]^4 /
 [Hg(CN)_{4}^{2−}] has the extremely small value 0.4E−41.
 Consequently, mercuric-ion must be even more effective than
 hydrogen-ion (strong acids), in suppressing the cyanide-ion and
 liberating the ferrous- or ferric-ion, in solutions of ferrocyanides
 or ferricyanides. In fact, when a solution of potassium ferrocyanide
 is warmed, for a moment, with some mercuric oxide, the ferrocyanide
 complex is to some extent decomposed; the liberated ferrous-ion is
 oxidized, by the excess of mercuric oxide,[462] to ferric-ion, and
 the presence of the latter, in quantity, is shown by the abundant
 precipitation of ferric ferrocyanide or Prussian blue, when the
 mixture is acidified with hydrochloric acid (‹exp.›). [p232]

«The Aurocyanide-Ion.»—Gold forms a particularly stable complex ion
with cyanide-ion. The constant[463] for the ratio [Au^{+}] ×
[CN^{−}]^2 / [Au(CN)^{−}_{2}] has the value 10^{−28}. This makes
potassium cyanide an excellent solvent for insoluble gold compounds,
such as gold sulphide, and the cyanide process for the extraction of
gold ores makes use of this property.

«The Reacting Components in Solutions of the Complex Cyanide
Ions.»—The extraordinary values, obtained for the constants
expressing the condition of equilibrium between cyanide ions and
some of the simple metal ions, such as gold and silver ions, and
their complex ions, have led to inquiries concerning a question
of fundamental interest in the theory of complex ions and in
the theory of ionization itself. In a 0.05 molar solution of
KAg(CN)_{2}, containing an excess of 0.1 mole of CN^{−}, per liter,
the concentration of silver-ion is only 5E−21. And yet, the addition
of potassium hydrosulphide (sufficient to make [KSH] = 0.1 molar)
will precipitate silver sulphide practically instantaneously from
the solution.[464] In solutions containing a larger excess of
cyanide, the concentration of the silver-ion is enormously reduced,
and yet, while we can no longer precipitate silver sulphide from
such a solution, metallic silver may be precipitated by zinc or
by the action of an electric potential at the cathode (Chapter
XV). The question may be asked, ‹whether we must consider that in
these actions the minute quantity of free silver ions, present at
any moment, is alone capable of the reactions› indicated, and that
the ‹decomposition of the complex› into its ‹components›—as one of
these, the silver-ion, is removed by precipitation—takes place with
‹sufficient speed› to account for the ‹rapid actions, wholly, as
direct actions of the silver ions›. The alternative to an affirmative
answer to this question is, that silver sulphide or silver ‹may be
precipitated by direct action of the precipitant› on the ‹complex›
ions, rather than on the ‹silver ions›. We may indicate the first
course suggested for the action, as follows:

 2 Ag(CN)_{2}^{−} + S^{2−} ⇄ 4 CN^{−} + 2 Ag^{+} + S^{2−} ⇄
   Ag_{2}S ↓ + 4 CN^{−}.                                             I

The second, suggested, course of the action would be the following:

 2 Ag(CN)_{2}^{−} + S^{2−} ⇄ Ag_{2}S ↓ + 4 CN^{−}.                  II

This second action would mean that we could obtain reactions of
silver ions, such as the precipitation of silver sulphide, ‹without
the intermediate formation of the free ions themselves›.

The consequences of the first, the ordinary, conception of such
actions ‹as direct actions of silver ions›, have been analyzed by
Haber[465] from the point of view of the velocities of the actions,
by which the complex must be formed from its components and be
decomposed into them, in order to satisfy the facts concerning the
precipitations. [p233]

 We may consider, with Haber, a liter of a 0.05 molar solution of
 K_{2}Ag(CN)_{3}, containing an excess[466] of 0.95 mole potassium
 cyanide. In such a solution, the concentration of silver-ion
 is reduced to 8E−24 gram-ion per liter. Now, according to the
 best determinations of the ultimate dimensions of molecules,
 about 10^{24} molecules are estimated to be contained in a mole
 (gram-molecule), and 10^{24} ions, therefore, in a gram-ion (‹e.g.›
 in 108 grams of silver-ion there would be 10^{24} individual silver
 ions). Then a liter of the solution we are considering would
 contain, at any moment, only eight individual silver ions, which are
 different ones from moment to moment, since the reversible reactions
 Ag^{+} + 3 CN^{−} ⇄ Ag(CN)_{3}^{2−}, are going on continually. Thus
 100 c.c. of the solution would not contain even one silver ion all
 the time, but the requirements of the equilibrium conditions could
 be met[467] by silver ions "flashing up and disappearing" in such
 a way, that the required average concentration in unit time is
 maintained. There is nothing irrational in such a conception.

 One may ask, however, what must be the velocities, with which the
 complex is formed from the components, and is resolved into them,
 in order to satisfy an instability constant[466] 10^{−22} and still
 enable us to obtain a practically instantaneous precipitation, say
 of silver sulphide, the action being analyzed on the basis of the
 ordinary conception that only the silver-ion itself, and not the
 complex ion, is directly active in the formation of the silver
 sulphide. A condition of equilibrium, in a reversible action,
 implies that the velocities of the two continuous, opposed reactions
 are equal (p. 94). For the action Ag^{+} + 3 CN^{−} → Ag(CN)_{3}^{2−}
 the ‹velocity› of ‹formation› of the ‹complex› is proportional to
 a characteristic constant, K_{Formation}, to the concentration,
 [Ag^{+}], of the silver-ion, and to the third power (see p. 94) of
 the concentration, [CN^{−}], of the cyanide-ion. The ‹velocity›
 of the ‹opposed reaction› of ‹decomposition› of the complex is
 proportional to another characteristic constant, K_{Decomposition},
 and to the concentration, [Ag(CN)_{3}^{2−}], of the complex ion.
 For the condition of equilibrium, the velocities of the opposed
 reactions are equal, and we derive the relation:

 [Ag^{+}] × [CN^{−}]^3 / [Ag(CN)_{3}^{2−}] =
   K_{Decomposition} / K_{Formation} = 1 / 10^{22}.

 The equilibrium constant of the complex ion is, then, the ratio of
 the velocity constants of its decomposition and formation (see p.
 94). Now, the ‹velocity constant›, K_{Formation}, represents the
 concentration, in moles, of the complex ion [Ag(CN)_{3}^{2−}],that
 is formed in unit time from unit concentrations of its components
 Ag^{+} and CN^{−}, and it may be considered as the ‹reciprocal›
 of a ‹time constant›, T_{Formation}, the ‹time› required ‹to form
 unit concentration› of the complex ion, while the components are
 maintained at unit concentration. The analogous reciprocal relation
 holds for the velocity constant, K_{Decomposition}, and a time
 constant, T_{Decomposition}. The equilibrium equation, therefore,
 expresses also the following relations:[468] [p234]

 [Ag^{+}] × [CN^{−}]^3 / [Ag(CN)_{3}^{2−}] =
   T_{Formation} / T_{Decomposition} = 1 / 10^{22}.

 In words, the time required for the spontaneous decomposition of one
 mole of the complex is 10^{22} times as long as the time required
 to form one mole of the complex, from uniformly unit concentrations
 of the components. If the concentration of silver-ion is reduced
 to 1 / 10^{22} and the concentrations of the cyanide-ion and the
 complex ion are maintained at 1, the formation of the complex takes
 place 10^{22} times as slowly as when [Ag^{+}] = 1, and a condition
 of equilibrium is produced, the time required to decompose and to
 form the same amount of the complex being now equal.

 This ‹relation› of ‹time constants› may be used to obtain some idea
 of the consequences of assuming certain limiting values for one or
 the other, the ratio being maintained at the value 1 / 10^{22}. If
 the time constant T_{Formation} for the ‹formation of the complex›
 be taken as one ten-thousandth of a second,[469] then, according
 to Haber, a molar solution of potassium argenticyanide would not
 be able to form in thousands of years sufficient silver ions to be
 discovered by any direct test, a result which is not compatible with
 the precipitation of silver sulphide and of metallic silver in a few
 minutes, since silver ions could not be ‹supplied rapidly enough›.
 It is evident, thus, that the ratio 1 / 10^{22} must indicate an
 exceedingly small value for T_{Formation}, if only silver ions form
 silver sulphide and silver.

 If we assume that the complex is decomposed so fast as to supply
 new silver ions rapidly enough, to allow us to consider the
 precipitation of silver and silver sulphide as direct actions of the
 silver ions, then we may, conservatively, consider T_{Decomposition}
 to be about 1 / 100 second. Then T_{Formation} would be only
 1 / 10^{24} second. Considering the limiting results for the
 dimensions of atoms (and ions) and taking account of the fact that
 the formation of the complex ‹involves electrical changes›, that
 is, in modern terms, changes in position of electrons,[470] Haber
 finds, that to satisfy the above value for the time constant, such
 changes must involve a motion of electrical charges at a speed
 about a million times as great as the velocity of light. Such a
 velocity is, unquestionably, incompatible with our knowledge of the
 velocities of light and of electrical charges. We must draw the
 conclusion that ‹the complex argenticyanide-ion probably cannot
 decompose fast enough into its ions›, to enable the latter to be
 the ‹only› components which make it possible to precipitate silver
 sulphide or metallic silver from its solutions[471] (see above,
 p. 232). That would make it necessary to assume ‹direct action›
 [p235] (as given in equation II, p. 232) ‹between the complex› and
 the ‹precipitating agent›, to some extent, at least, the extent
 being dependent on the concentrations involved in a given case. If
 further investigations should confirm such a view, we would probably
 find that ‹both› the actions under consideration (equations I and
 II, p. 232) must proceed ‹simultaneously›. The second one would
 have the advantage of enormously greater concentrations of the
 reacting components, ‹e.g.› of the complex ion; the first one would,
 probably, be found to have the advantage of an enormously greater
 velocity constant. The actual velocities of the two reactions have
 never been measured[472] and no final explanation of the relations
 can be offered. The problem is a very important one, involving
 the whole question of the mode of ionic action (‹cf.› Chap. V,
 especially p. 83).

 Aside from the theoretical value of the problem that has been
 raised, the question of immediate moment to us, from the point
 of view of analytical chemistry, is the question whether such
 conclusions would invalidate, in any way, the use we have made of
 the theory of complex ions, in elucidating the question of the
 precipitation and nonprecipitation of salts of simple ions from
 solutions of their complex ions.

 The existence of a precipitate in contact with a solution is a
 question of a ‹condition› of ‹equilibrium›; the question raised, as
 the result of Haber's calculations, deals simply with the ‹problem
 of the path, the mechanism by which equilibrium is reached›, but
 the answer to it ‹does not affect the conditions, on which the
 maintenance of equilibrium depends›. All the conclusions, drawn in
 our discussions of precipitation from solutions of complex ions,
 are concerned with ‹final conditions for equilibrium›, ‹i.e.› with
 the conditions under which a ‹precipitate can exist›, and not with
 the mechanism of its formation. The conclusions reached are valid,
 therefore, irrespective of what the decision may ultimately be in
 the question, whether the simple ions alone are acted upon, when
 their salts are precipitated, or whether the complex ions are also
 immediately concerned in the action. The precipitation of silver
 chloride from an ammoniacal solution[473] may serve to illustrate
 this point.

 In the first place, the precipitation of silver chloride from an
 ammoniacal solution, say by sodium chloride, may be considered to be
 the result of the direct interaction of chloride ions with the small
 quantity of silver ions present, ‹the complex serving only to renew
 the supply of silver ions›, as the latter are removed from solution,
 by the precipitation. The course of the action would be expressed by
 the equations

 [Ag(NH_{3})_{2}]Cl ⇄ [Ag(NH_{3})_{2}^{+}] + Cl^{−} ⇄
   2 NH_{3} + Ag^{+} + Cl^{−} ⇄ AgCl + 2 NH_{3}.                   (1)

 AgCl ⇄ AgCl ↓

 When the precipitation is ended and equilibrium established, a
 trace of silver chloride is in solution, in contact with the
 precipitate, and, according [p236] to the principle of the
 solubility-product, we must have [Ag^{+}] × [Cl^{−}] = K_{AgCl}.
 Bodländer's experiments,[474] on the solubility of silver chloride
 in ammonia, prove that this relation is in perfect agreement with
 the facts. For the silver-ammonium-ion, the free ammonia and the
 silver-ion present in the solution, we must have the relation
 [Ag^{+}] × [NH_{3}]^2 / [Ag(NH_{3})_{2}^{+}] = K_{Instab. Const.}.
 This relation, according to the experimental evidence, is also found
 to hold.

 Now, we might, on the other hand, assume that the primary or main
 action, leading to the precipitation of silver chloride, is the
 interaction of the chloride ions ‹with the complex ions›, rather
 than with silver ions. Silver-ammonium chloride, [Ag(NH_{3})_{2}]Cl,
 might first be formed, for instance, and then decompose ‹directly›
 into silver chloride and ammonia. This is the simplest assumption we
 can make for this kind of action and is sufficiently illustrative of
 any kind of direct action between the chloride ions and the complex
 ions. The path of the action would then be expressed by the equations

 [Ag(NH_{3})_{2}^{+}] + Cl^{−} ⇄ [Ag(NH_{3})_{2}]Cl ⇄
   2 NH_{3} + AgCl ⇄ 2 NH_{3} + Ag^{+} + Cl^{−}.                   (2)

 AgCl ⇄ AgCl ↓

 It is clear, from a comparison of this series of equations with
 equations (1), that they represent the same reversible reactions in
 a somewhat different order. ‹Since equilibrium conditions for any
 reversible reaction› (‹e.g.› for A + B ⇄ C + D) ‹are independent
 of the order in which the components› (‹e.g.› A, B, C, D) ‹are
 brought into the system› (p. 94), the difference of order, indicated
 by equations (1) and (2), cannot affect the final condition of
 equilibrium in the system under discussion. For instance, since we
 again have silver chloride in contact with its saturated solution,
 we again must have [Ag^{+}] × [Cl^{−}] = K_{AgCl}, and ‹the
 experimental confirmation› of this relation (and similarly of the
 relation [Ag^{+}] × [NH_{3}]^2 / [Ag(NH_{3})_{2}^{+}] = K) ‹agrees
 as well with this second path of the action as with the first›.
 Conversely, since the path, by which the equilibrium is reached,
 does not affect the condition of equilibrium, it is perfectly
 legitimate to draw conclusions from equilibrium constants, ‹without
 assuming to know anything at all about the path by which the
 condition is reached›.[475]

 For analytical work, the vital point is the ‹ultimate condition of
 equilibrium, which determines whether a precipitate may exist and be
 formed in a given system or not›. The instability constants of the
 complex ions and the solubility-product constants of precipitates
 are the constant factors involved in the ultimate conditions for
 equilibrium, and they do not depend on the path by which equilibrium
 is reached. Consequently, we find that the application of [p237]
 the theory of complex ions to analytical problems of precipitation
 has been in no wise invalidated by the problems presented by Haber.
 The theory forms now, as before, in fact, the best quantitative
 basis for the expression of the experimental results. The stability
 constants, and the concentrations of the components used, determine
 the limiting concentrations in which a given metal ion is capable of
 continued existence, and determine, therefore, the question whether
 an ionogen, of a given solubility, is capable of existence as a
 solid phase in a given system.

 «The Structure of Complex Ions.»—The ability of ammonia to form
 complex ions with simple metal ions is commonly ascribed to the
 unsaturated condition of ammonia (see p. 65). It is interesting
 to recall the fact, that the marked power of the cyanide-ion to
 form complexes of extraordinary stability, is also associated with
 a similarly unsaturated condition of the cyanide-ion (p. 66).
 According to the results of Nef's researches,[476] we have, in
 hydrocyanic acid and the cyanides, unsaturated or bivalent carbon;
 potassium cyanide, for instance, has the structure K—N=C<. The two
 free valences of the carbon atom may, according to the electrical
 theory of valence, be again considered to consist of one negative
 and one positive charge. The possibility of the formation of
 complexes is then self-evident, and we can readily see, how silver
 cyanide, Ag—N=C±, should absorb cyanide-ion,[477] ∓C=N^{−}, and
 form a complex (Ag—N=C=C=N^{−}) or Ag(CN)_{2}^{−}, whose potassium
 salt would be potassium argenticyanide, K[Ag(CN)_{2}]. For the
 potassium salt K_{2}Ag(CN)_{3}, of the second complex ion[478]
 [Ag(CN)_{3}^{2−}] of silver and cyanogen, the most likely structure
 is

 Ag—N=C—C=N—K.
      \ /
       C=N—K

 The other complex cyanide ions, ferrocyanide, ferricyanide,
 cobalticyanide, etc., are considered to have structures entirely
 similar to those given to the argenticyanide ions.[479]

 «Complex Halide, Sulphide, Oxide and Oxonium Ions.»—In conclusion,
 there are other elements besides nitrogen (in ammonia and its
 derivatives) and carbon (in cyanides), which form complex ions
 with simple ions; notably the halogens form such complexes.
 Chloroplatinic acid, H_{2}PtCl_{6}, and its salts (Lab. Manual, ‹q.
 v.›), fluorosilicic acid, H_{2}SiF_{6}, potassium-mercuric iodide,
 [p238] KHgI_{3} and K_{2} HgI_{4},[480] which forms a most sensitive
 reagent for the detection of traces of ammonia,[481] are instances
 of complexes of the halogens that are of importance in analysis.
 It is worthy of note that the most likely structure[482] for these
 compounds, ‹e.g.› Cl_{2}=Pt=(Cl=Cl—H)_{2}, bears a very striking
 analogy to the structures frequently assigned to the cyanide and
 ammonia complex ions. Oxygen and sulphur form complex ions, of great
 stability, with many elements, and we shall presently have occasion
 to discuss in detail some of the complex ions formed by sulphur. All
 of the oxygen acids may be treated as containing complex ions of
 oxygen and some other element, and their instability constants[483]
 are factors in determining their chemical behavior. For instance,
 such is the case, most likely, for their behavior as oxidizing and
 reducing agents (see Chapter XVI). The unsaturated condition of
 oxygen in water, (H_{2}O±), makes possible, also, the formation of
 complex ions, [(H_{2}O)_{‹x›}Me]^{+}, etc., called oxonium ions
 and comparable with metal-ammonium ions. They form a most inviting
 field for rigorous investigation. It is altogether probable that
 the hydrogen-ion is intimately related, in aqueous acid solutions,
 to the complex oxonium-ion, [(H_{2}O)_{‹x›}H]^{+}, comparable with
 the ammonium-ion, (NH_{3}H)^{+}, and, possibly, the greater part
 of the hydrogen-ion, in aqueous solutions, exists in this form of
 combination.[484]

«Complex Ions of Organic Oxygen Derivatives.»—A further group of
complex ions, derived from organic derivatives of oxygen, are of
particular importance in analytical work. Many organic compounds,
such as sugars, glycerine, tartrates, citrates, interfere, more or
less, with the precipitation of metal hydroxides and certain of their
salts. For instance, the addition of cane sugar or of rochelle salt
(sodium potassium tartrate) to a solution of [p239] cupric sulphate
prevents the subsequent precipitation of cupric hydroxide by alkali
(‹exp.›). In place of a precipitate of the hydroxide, a clear,
intensely blue, solution is formed. In an analogous way, the same
substances and similar compounds interfere with the precipitation
of the hydroxides of aluminium and chromium, and since aluminium
and chromium should be precipitated as hydroxides in systematic
analysis (Chap. X), the presence of such organic compounds must be
most carefully considered, to avoid error.[485] The precipitation of
moderately difficultly soluble salts, such as phosphates, is also
rendered, appreciably, more difficult. Only extremely insoluble
salts, such as the sulphides of the arsenic, copper and zinc groups,
are precipitated, from solutions of organic substances of the
character indicated, without any appreciable interference.[486]

These relations clearly recall the characteristic behavior of
ammoniacal and cyanide solutions, in which complex ions are formed,
and the interference of the organic compounds with precipitation
is of a similar nature—complex ions are formed by metal ions with
these organic compounds, and the complexes are, in many instances,
sufficiently stable to reduce the concentrations of the metal ions
to the point, where only very difficultly soluble salts can be
precipitated.

The relations may be illustrated by the discussion of the complex
formed by the cupric-ion with tartrates. The structure of sodium
tartrate is expressed by NaO_{2}C—CH(‗OH‗)—CH(‗OH‗)—CO_{2}Na. The
underscored hydroxide groups ‗OH‗ are known in organic chemistry
as ‹alcohol groups›.[487] Now, alcohols resemble water in very
many properties and, among others, in the capacity to form metal
derivatives or ‹alcoholates›, in which the hydrogen (ion) of
the hydroxide group is replaced by metal ions. The alcoholates
correspond, thus, to the metal hydroxides, which are the analogous
[p240] derivatives of water. Exactly as there is a vast difference
in the readiness with which the various metal hydroxides, or bases,
ionize, many of them being only slightly ionizable (the weakest
bases), so certain alcoholates are much less readily ionizable than
others. The alkali alcoholates are most readily ionized.

When sodium tartrate is mixed with an excess of sodium hydroxide,
some of the ‹readily ionizable› sodium salt of the ‹alcohol› groups
of the sodium tartrate is formed and we have:

 (CHONa)_{2}(CO_{2}^{−})_{2} + 2 Na^{+} ⇄
   (CHO^{−})_{2}(CO_{2}^{−})_{2} + 4 Na^{+}.

When cupric sulphate is added to this mixture, a ‹slightly ionizable
complex cupri-tartrate-ion› is formed by the union of the cupric-ion
with the "alcoholate-tartrate-ion":

 (CHO^{−})_{2}(CO_{2}^{−})_{2} + Cu^{2+} ⥂
   [(CHO)_{2}Cu](CO_{2}^{−})_{2}.

The complex ion is not perfectly stable and so the action is a
reversible one, as indicated in the equation. The greater portion of
the copper, however, is present ‹as part of the complex negative ion›
of cupric-tartaric acid and its salts. This may be demonstrated by
subjecting the solution to electrolysis in a U-tube (p. 45). It is
readily seen (‹exp.›) that ‹a deep blue ion›, obviously containing
copper, ‹migrates to the positive pole›.[488] The concentration of
cupric-ion is so small that its hydroxide and its phosphate are not
precipitated from the solution by the addition, respectively, of
alkali or of a soluble phosphate (‹exp.›). Cupric sulphide, however,
is so insoluble that it may be precipitated completely from the
solution by the addition of a sulphide (‹exp.›), the concentration
of cupric-ion being much smaller in the saturated solution of the
sulphide than in the solution of sodium cupri-tartrate.

Citrates, sugars, glycerine, contain alcoholic groups of the same
nature as found in the tartrates, and they are capable of forming
similar complexes, or little ionizable ‹alcoholates›, with metal ions.

Certain organic acids, which contain no alcohol groups,[489] are
[p241] also capable of forming fairly stable complexes with
metal ions: thus, acetates form a complex with lead-ion, that is
sufficiently stable to render lead sulphate, which is difficultly
soluble in water, readily soluble in ammonium acetate solution[490]
(‹exp.›). Soluble oxalates readily combine with ferric, ferrous,
cupric and other oxalates and interfere, more or less, with the
detection of the metal ions, as the result of complex formations.

All of these complexes are ‹decomposed› rather readily ‹by the
addition of strong acids›, whose hydrogen-ion breaks up the complex
ions, by suppressing the anions[491] of the much weaker organic
acids and alcohols. Consequently, these organic compounds do not
interfere with tests which may be carried out in strongly acid
solution. For instance, the addition of potassium ferrocyanide to a
solution of ammonium ferrioxalate (NH_{4})_{3}Fe(C_{2}O_{4})_{3},
to which an excess of ammonium oxalate has been added, gives only
a slight indication of the presence of ferric-ion (a greenish blue
solution is obtained); when hydrochloric acid, in excess, is added
to the mixture, Prussian blue, ferric ferrocyanide, is immediately
precipitated in quantity (‹exp.›).


  FOOTNOTES:

  [425] The naming of the complex ions, which ammonia forms
  with metal ions, has not yet been satisfactorily settled.
  English writers frequently speak of "ammonio-argentic" ion
  and "ammonio-argentic" nitrate. German writers speak of
  "Silber-ammoniak" ion (Abegg, ‹Handb. der anorg. Chem.›, II, 728),
  which would read "silver-ammon‹ia›" ion in English terms. The
  terminology "silver-ammoni‹um›" ion, used in this book, is based on
  the idea, that all these complex ions are essentially ‹of the same
  nature› as the well-known ‹ammonium-ion›, NH_{4}^{+}, the positive
  charge being, almost certainly, carried by ‹nitrogen› in these
  complex ions, as it is in ammonium-ion. The latter is a ‹complex
  ion of ammonia› with ‹hydrogen›-ion. The name "ammonio-argentic"
  ion does not bring out this close relationship and puts the
  emphasis on the silver, which is probably little concerned in the
  reactions of the complex as such. The names "silver-ammon‹ia›" ion
  and "silver-ammon‹ia›" nitrate sound badly and do not emphasize
  the relation to ammoni‹um›, potassi‹um›, sodi‹um› and similar
  positive ions and their salts. The term "‹ammonium›" is, for the
  reasons given, used here in a ‹generic› sense for all complex ions
  of ammonia with simple metal ions (such as H^{+}, Ag^{+}, Cu^{2+},
  Zn^{2+} etc.), and the number of ammonia molecules, entering into
  the composition of a complex ion, is not indicated in the names.
  A similar nomenclature has long been in vogue, and has worked
  well, for the complex ions of metal ions with the cyanide-ion
  (see below). We speak of ferro‹cyanide›, Fe(CN)_{6}^{4−},
  argenti‹cyanide›, Ag(CN)_{2}^{−} and Ag_{2}(CN)_{3}^{2−}, etc.,
  without indicating the number of cyanide groups, CN, in the
  complex, and we use the same generic ‹ending› "cyanide" as is used
  to designate the simple cyanide ion, ‹e.g.› to designate the ion
  formed from potassium cyanide, KCN ⇄ K^{+} + CN^{−}.

  [426] The hydroxide-ion appears with the same coefficient, 1, on
  both sides of the equilibrium equation and need not be included in
  the mathematical statement; it would appear as a factor in both
  terms of the ratio given and would cancel out.

  [427] Bodländer and Fittig, ‹Z. phys. Chem.›, «39», 602 (1903).

  [428] Bonsdorff, ‹Ber. d. chem. Ges.›, «36», 2324 (1903).

  [429] It is also frequently called the ‹dissociation constant› of
  the complex ion, indicating the tendency of the complex ion to
  dissociate into its components.

  [430] Two independent experimental methods were used and gave
  concordant results—one having as its basis the solubility of silver
  salts (chloride, bromide), the other the electrolytic potentials of
  silver against ammoniacal silver solutions (see Chap. XV).

  [431] ‹Bull. de la Soc. Chim. de Paris›, (3), «13», 386 (1895).

  [432] We may consider the salt to be ionized to about the same
  extent as ammonium or potassium nitrate in 0.05 molar solutions,
  or, approximately, 87%. If we call ‹x› the concentration of
  silver-ion, formed by the decomposition of the silver-ammonium-ion,
  then 2 ‹x› is the concentration of the free ammonia, and
  (0.05 × 0.87 − ‹x›) is the concentration of the complex ion. Since
  ‹x› is a small number in comparison with 0.0435, we may write, with
  sufficient accuracy for our purposes,

   [NH_{3}]^2 × [Ag^{+}] / [(NH_{3})_{2}Ag^{+}] =
     (2 ‹x›)^2 × ‹x› / 0.0435 = 6.8E−8.

  Then, ‹x› = [Ag^{+}] = 0.0009.

  [433] Kohlrausch and Holborn, ‹loc. cit.›, p. 202.

  [434] The dilution of the silver-ammonium nitrate (10 c.c.
  to 11 c.c.) and the decrease in ionization due to the added
  salt reduce the concentration of silver-ion from 0.0009 to
  0.00085. [Ag(NH_{3})_{2}^{+}] = (0.05 × 10 / 11) × 0.8 = 0.0364
  and 4 ‹x›^3 = 6.8E−8 × 0.0364 (see footnote, p. 220). Then
  ‹x› = [Ag^{+}] = 0.00085.

  [435] Thiel (‹cf.› Bodländer and Fittig, ‹loc. cit.›). The
  solubility given in the table at the end of the laboratory manual
  refers to 18°. The constant for the complex ion was determined at
  25°.

  [436] The combined concentration of the salts is 0.055
  and their degree of ionization may be taken as 87%, the
  same as the degree of ionization of 0.05 to 0.06 molar
  KNO_{3}. Then [Cl^{−}] = (0.1 × 1 / 11) × 0.87 = 0.008.
  [Ag(NH_{3})_{2}^{+}] = (0.05 × 10 / 11) × 0.87 = 0.04 and
  ‹x› = [Ag^{+}] = 0.00089 (see the method of calculation in the
  footnote, p. 220).

  [437] The strong solution of ammonia is used in order to avoid
  unnecessary dilution, and in the experiment, described below,
  the dilution of the liquids by the added ammonia is considered
  negligible.

  [438] The following solubilities have been determined at 25°:

  [Ag^{+}] × [Cl^{−}] = 2E−10; [Ag^{+}] = 1.4E−5.

  [Ag^{+}] × [I^{−}] = 1E−15; [Ag^{+}] = 1E−8.

  [Ag^{+}]^2 × [S^{2−}] = 4E−50; [Ag^{+}] = 4.3E−17.

  [439] 100 c.c. molar ammonia dissolves at 25° only 0.6 milligram of
  silver iodide (Bodländer, ‹loc. cit.›, p. 606).

  [440] Fresenius, ‹Qualitative Analysis›, p. 378.

  [441] In regard to Cu(NH_{3})_{4}^{2+} see Locke and Forssall,
  ‹Am. Chem. J.›, «31», 268, 297 (1904), and Dawson, ‹J. Chem. Soc.›
  (London), «89», 1674 (1906).

  [442] Euler, ‹Ber. d. chem. Ges.›, «36», 3403 (1903).

  [443] See footnote, p. 212.

  [444] See pp. 165, 210 and 213.

  [445] The acid HAg(CN)_{2}, corresponding to the salt, is
  crystallizable and is a strong acid. It is largely decomposed, by
  water, into silver cyanide and hydrocyanic acid.

  [446] See the experiments described on pp. 45 and 89.

  [447] In solutions containing an excess of potassium cyanide
  greater than 0.05 molar, the salt K_{2}[Ag(CN)_{3}] is formed.
  The dissociation or instability constant for the complex ion
  Ag(CN)_{3}^{2−} is 1E−22.

  [448] ‹Z. anorg. Chem.›, «39», 222 (1904).

  [449] The solubility-product constant for silver chloride at
  25° is 2E−10. If the concentration of chloride-ion be made
  1.0 by the addition of potassium chloride to a 0.05 molar
  solution of KAg(CN)_{2}, then the concentration of silver-ion,
  necessary for the precipitation of the chloride, would be
  K_{S.P.} / [Cl^{−}] = 2E−10 gram-ion. Neglecting the fact
  that the complex salt is not completely ionized and putting
  [Ag(CN)_{2}^{−}] = 0.05, and calling ‹x› the concentration of the
  cyanide-ion just necessary to prevent the precipitation of the
  chloride, we have:

   [Ag^{+}] × [CN^{−}]^2 / [Ag(CN)_{2}^{−}] =
     2E−10 × ‹x›^2 / 0.05 = 10^{−21}.

  We find ‹x› = 5E−7 mole, or approximately 0.03 milligram potassium
  cyanide (cyanide-ion) per liter. This minute quantity of free
  cyanide, if not originally present in the solution used, would be
  formed by the liberation of potassium cyanide from the complex
  (according to KAg(CN)_{2} + KCl → AgCl + 2 KCN) as soon as 2.5E−7
  mole, or 0.036 milligram, of silver chloride per liter have been
  formed, a quantity too small to be perceptible.

  When potassium cyanide is added to a silver nitrate solution,
  the precipitate formed is found to be silver argenticyanide,
  Ag[Ag(CN)_{2}], the silver salt of the extremely stable complex,
  rather than the simple salt, silver cyanide, AgCN [‹cf.› Bodländer,
  ‹Z. anorg. Chem.›, «39», 223 (1904)]. Ag[Ag(CN)_{2}] is even less
  soluble than silver chloride, the solubility-product constant for
  [Ag^{+}] × [Ag(CN)_{2}^{−}] being 2.25E−12. An excess of only 2E−6
  mole, or about 0.15 milligram, of potassium cyanide (cyanide-ion)
  per liter is sufficient to prevent the precipitation of silver
  cyanide (silver argenticyanide) from a 0.1 molar solution of
  KAg(CN)_{2}, and, conversely, at least this minute excess of
  potassium cyanide is used in the preparation of a clear 0.1 molar
  solution of KAg(CN)_{2}, by the addition of potassium cyanide to
  silver nitrate, until the silver cyanide, first precipitated, is
  just redissolved (Bodländer, ‹loc. cit.›). This excess, as just
  explained, is more than sufficient to prevent the precipitation of
  silver chloride from the cyanide solution, even by a large excess
  of potassium or sodium chloride. Unless one takes into account, in
  the manner indicated, this marked influence of a minute excess of
  cyanide-ion in decidedly reducing the concentration of silver-ion
  in these solutions, one could be led, wrongly, to infer from the
  value of the instability constant of the complex ion and that of
  the solubility-product constant of silver chloride, that silver
  chloride should still be precipitated by the addition of sodium
  chloride to a solution of KAg(CN)_{2}.

  [450] For this reason potassium cyanide is an excellent cleansing
  agent for stained silverware (sulphide stains), and, since it is an
  intense poison, cleaning powders should be examined for it.

  [451] For the quantitative relations see Lucas, ‹Z. anorg. Chem.›,
  «41», 192 (1904).

  [452] See Bodlaender, ‹Z. phys. Chem.›, «39», 597 (1902); ‹Ber. d.
  chem. Ges.›, «36», 3933 (1903).

  [453] Potassium cyanide is a powerful reducing agent (see p.
  89) and is readily oxidized to potassium cyanate. The action,
  presumably, takes the following course (see Chapters XIV and XV):

   2 Cu^{2+} + 4 HO^{−} + KNC^{±} → 2 Cu^{+} + 4 HO^{−} + KNC^{2+} →
     2 Cu^{+} + 2 HO^{−} + KNCO + H_{2}O.

  [454] Put [Cu^{+}] = ‹x›, and [CN^{−}] = 3 ‹x›, and, neglecting
  the degree of ionization, [Cu(CN)_{3}^{2−}] = 0.1, ‹x› being
  so small that it need not be subtracted from 0.1. Then
  ‹x› × (3 ‹x›)^3 = 0.1 × 0.5E−27, and ‹x› = 3.7E−8.

  [455] Treadwell and Girsewald, ‹Z. anorg. Chem.›, «38», 92 (1904).

  [456] Euler, ‹Ber. d. chem. Ges.›, «36», 3404 (1903).

  [457] Putting [Cd^{2+}] = ‹y›, we have ‹y› × (4 ‹y›)^4 = 0.1E−17,
  and ‹y› = 8E−5. In view of the values of the constants, a ‹small›
  excess of potassium cyanide will have a much smaller suppressing
  effect on the cadmium-ion than on the cuprous-ion. For the
  excess [CN^{−}] = 0.01, [Cu^{+}] = 5E−23, [Cd^{2+}] = 10^{−10}
  as compared with [Cu^{+}] = 4E−8 in a 0.1 molar solution of the
  salt K_{3}[Cu(CN)_{3}], and with [Cd^{2+}] = 8E−5 in a 0.1 molar
  solution of K_{2}Cd(CN)_{4}.

  [458] Bromine water is a convenient agent for oxidizing cobaltous
  to cobaltic ions (see Chapter XV).

  [459] The heavy arrows «→» [See Transcriber's Note] indicate the
  main course the reversible actions take, ‹under the influence of
  the reagents used›. Since the oxidation of nickel-ion by bromine
  is accomplished only after the bromine has oxidized any excess of
  cyanide used—potassium cyanide is a powerful reducing agent (p.
  89)—the addition of cyanide, beyond a very small excess, must be
  avoided (see laboratory instructions).

  [460] ‹E.g.› for the precipitation of silver, copper, nickel,
  cobalt and certain other metals from cyanide solutions; ‹cf.› Edgar
  F. Smith, ‹Electro-Analysis› (1907).

  [461] ‹Z. phys. Chem.›, «43», 705 (1903). ‹Vide› also Haber, ‹Z.
  Elektrochem.›, «11», 847 (1905).

  [462] 2 Fe^{2+} + Hg^{2+} → 2 Fe^{3+} + Hg ↓. If the treatment
  with mercuric oxide is carried to completion the final products of
  the reaction are ferric hydroxide, mercuric cyanide, mercury and
  potassium hydroxide (Rose, ‹Z. anal. Chem.›, «1», 300 (1862)):

   2 K_{4}[Fe(CN)_{6}] + 7 HgO + 7 H_{2}O →
     3 Hg[Hg(CN)_{4}] + 8 KOH + 2 Fe(OH)_{3} ↓ + Hg ↓

  [463] Bodlaender, ‹loc. cit.›

  [464] The solubility-product constant of silver sulphide at 25°
  is 0.5E−51; for [S^{2−}] = 0.8E−5 (p. 202), we would have in the
  present case [Ag^{+}]^2 × [S^{2−}] = 2E−46, which is greater than
  the constant. ‹Vide› quantitative data by Lucas, ‹loc. cit.›

  [465] ‹Z. f. Elektrochem.›, «10», 433 and 773 (1904).

  [466] See footnote 4, p. 225.

  [467] Ostwald, ‹Allgem. Chemie›, Vol. II, part 1, p. 881 (1893).

  [468] Haber, ‹loc. cit.›

  [469] Then T_{Decomposition} = 10^{−4} × 10^{22} = 10^{18}
  seconds, and, since there are 3.15E7 seconds in a year,
  T_{Decomposition} = 3E10 years.

  [470] See p. 42.

  [471] Since there are still smaller "instability constants" than
  that of the argenticyanide-ion (‹e.g.› for the gold-cyanide-ion the
  constant is 1 / 10^{28}), there is a large margin of safety for the
  plausibility of Haber's argument. For full details, his articles
  (‹loc. cit.›), and the discussion (by Abegg, Bodlaender, Danneel,
  ‹ibid.›) aroused by them should be consulted.

  [472] See Le Blanc and Schick, ‹Z. phys. Chem.›, «46», 213 (1903),
  on measurements of the speed of ionic actions. The values obtained
  agree, in general, with Haber's contention.

  [473] The concentrations of silver-ion are large, in comparison
  with those in cyanide solution, and the action is, most likely,
  essentially an ionic one; but the argument applies with equal force
  to cyanide systems.

  [474] ‹Loc. cit.›

  [475] An equilibrium constant, as we have seen, is a ‹ratio› of
  velocity constants of balanced reactions (pp. 94, 233) and involves
  therefore at least ‹two unknown› velocity constants. By determining
  the actual ‹rate› of ‹change› with known concentrations of
  reacting components, ‹i.e.› by determining the velocity constants
  themselves, rather than their ratio, a definite conclusion as to
  the mechanism or path of a given reaction can often be reached (see
  p. 80).

  [476] ‹Proceedings Amer. Academy›, 1892.

  [477] In the absence of any added cyanide, it combines with
  itself. Silver cyanide, according to Bodländer's results, is, in
  saturated solutions, chiefly (AgCN)_{2} or Ag[Ag(CN)_{2}], ‹i.e.›
  Ag—[N=C=C=N—Ag].

  [478] See p. 225, footnote 4.

  [479] Werner has developed quite a different theory of the
  structure of complex ions. (‹Cf.› Nernst, ‹Theoretical Chemistry›,
  p. 374 (1904).)

  [480] Sherrill, ‹Z. phys. Chem.›, «43», 721 (1903).

  [481] In Nessler's reagent, Fresenius' ‹Qualitative Analysis›, p.
  141.

  [482] ‹Cf.› Remsen, ‹Am. Chem. J.›, «11», 291 (1899); «14», 81
  (1892) («Stud.»).

  [483] For instance, for arsenious acid we have

   3 H^{+} + AsO_{3}^{3−} ⇄ H_{3}AsO_{3} ⇄ As^{3+} + 3 HO^{−}

  and, therefore, [As^{3+}] × [HO^{−}]^3 / ([AsO_{3}^{3−}] ×
  [HO^{+}]^3) = ‹k›_{1}. Since [H^{+}] = ‹k′›_{HOH} / [HO^{−}] (p.
  176), we have further, [As^{3+}] × [HO^{−}]^6 / [AsO_{3}^{3−}] =
  ‹k›_{2}. And since we may derive the relation [HO^{−}]^2 =
  ‹k›_{3} × [O^{2−}], by considering the primary and the secondary
  ionization of water (see pp. 246, 278), we have, finally,
  [As^{3+}] × [O^{2−}]^3 / [AsO_{3}^{3−}] = ‹K›. The constants for
  the primary and the secondary ionization of water are included in
  the value of ‹K›.

  [484] Fitzgerald and Lapworth, ‹J. Chem. Soc.› (London), «93»,
  2163 (1908); Lapworth, ‹ibid.›, 2187. ‹Vide› also Franklin on the
  characteristics of the NH_{4}^{+} ion in liquid ammonia, ‹Am. Chem.
  J.›, «23», 305 (1900).

  [485] See the laboratory instructions, in regard to the precautions
  used, to avoid errors from this source.

  [486] On the other hand, ‹colloidal› organic substances, such as
  casein, glue or albumen, interfere with the precipitation of even
  the most insoluble sulphides, by producing ‹colloidal suspensions›
  of the latter (see Chap. VII; ‹cf.› Müller, ‹Allgemeine Chemie der
  Kolloide›, p. 56 (1907)).

  [487] In alcohols the hydroxide group is held by a carbon atom,
  whose remaining valences are satisfied by hydrogen or carbon atoms,
  as in ordinary or ethyl alcohol, H_{3}C—CH_{2}(OH).

  [488] Küster, ‹Z. Elektrochem.›, «4», 117 (1897).

  [489] The most common organic acids contain the acid group
  —CO(‗OH‗), as in acetic acid, CH_{3}CO(‗OH‗). The hydroxide group
  ‗OH‗ of the alcohols, ‹e.g.› in CH_{3}CH_{2}(‗OH‗), is still found
  in these organic acids, but its tendency to form hydrogen-ion is
  very much increased by the replacement of two hydrogen atoms of the
  alcohols by the oxygen atom, as found in the acids. To a certain
  degree, the properties of the alcohol hydroxide are maintained in
  the properties shown by the acid hydroxide group. Thus, the organic
  acids, on the whole, are still rather weak acids, and their salts,
  in many instances, are appreciably less ionizable than the salts of
  strong inorganic acids. The organic acids, further, may combine,
  to a certain extent, with water and thus form hydrates (‹e.g.›
  CH_{3}COOH + H_{2}O ⇄ CH_{3}C(OH)_{3}) containing a number of
  hydroxide groups: the second and third hydroxide groups must have
  a very much smaller tendency to form hydrogen ions and ionizable
  salts, than has the first hydroxide group (p. 102), and the former,
  thus show, more nearly, the behavior of alcoholic hydroxide groups.
  Finally, organic acids also show a tendency to combine with
  themselves, forming complex acids (‹e.g.›, (CH_{3}COOH)_{2} or
  CH_{3}C(OH)_{2}OOCCH_{3}), from which complex salts may be derived,
  which may be little ionizable. The power of the organic acids to
  form complex ions—which they share with many inorganic acids—is
  most likely intimately connected with the relations described.

  [490] Lead acetate, itself, is less ionized than most salts and
  this property contributes to the solubility of lead sulphate in
  acetate solutions. (‹Cf.› Noyes and Bray, ‹loc. cit.›)

  [491] On p. 231, the same effect is discussed, in detail, in
  connection with the ferricyanide-ion.

[p242]




 CHAPTER XIII

 «THE ARSENIC GROUP. SULPHO-ACIDS AND SULPHO-SALTS»


The analytical groups, which we have heretofore discussed, contain
elements, whose oxides are preëminently ‹base-forming›. The methods
of separation of these groups, from each other, involve, primarily,
physical[492] differences between the groups—in the matter of the
relative insolubility of analogous salts. Thus, barium, strontium
and calcium carbonates are precipitated, and separated from the
alkalies, by means of ammonium carbonate, not because the alkalies do
not form carbonates when their salts, in solution, are treated with
ammonium carbonate, but wholly because barium, strontium and calcium
carbonates are very difficultly, the alkali carbonates easily,
soluble in water. The hydroxides of the aluminium group and the
sulphides of the zinc group are less soluble than the hydroxides and
sulphides of the alkaline earths and alkalies. The sulphides of the
copper and the arsenic groups, again, are still less soluble than the
sulphides of the zinc group, and thus the former may be precipitated
by hydrogen sulphide, even when its precipitating power is reduced
by the suppression of its sulphide (and hydrosulphide) ions by the
addition of a strong acid.

On the other hand, the separation of the arsenic group (arsenic,
antimony, tin, gold and platinum) from the copper group, with
which it is precipitated by hydrogen sulphide from acid solutions,
depends, essentially, on a ‹chemical› difference between the
groups. The oxides, especially the ‹higher› oxides, of the arsenic
group, are preëminently ‹acid›-forming; the higher oxides form such
acids as arsenic acid, H_{3}AsO_{4}, antimonic acid, H_{3}SbO_{4},
stannic acid, H_{2}SnO_{3}, platinic acid, H_{2}PtO_{3}, and auric
acid, HAuO_{2}. These [p243] hydroxides are, however, all more
or less ‹weakly basic› in character ‹as well›. The hydroxides of
the lower oxides of the metals are, as one must expect, much more
strongly basic, but most of them—arsenious, antimonous and stannous
hydroxides—still show sufficient acid character to be distinctly
amphoteric in behavior. But, with the exception of arsenious acid,
the basic ionization of the hydroxides of the lower oxides is more
pronounced than their acid ionization.

The basic ionization of the hydroxides of their lower and higher
oxides brings these elements into the plan of analysis for the
metal or positive ions in systematic analysis. In the presence of
hydrochloric acid they form chlorides, which yield positive ions in
sufficient quantity[493] to allow their extremely insoluble sulphides
to be precipitated by hydrogen sulphide in acid solution, together
with the, likewise, very insoluble sulphides of the copper group.

The acid-forming properties of the oxides of the arsenic group are
maintained in their sulphides. Again, this is especially evident
in the ‹higher› sulphides. The element sulphur is substituted for
the closely related element oxygen without any profound change
in the chemical behavior of the compounds. Advantage is taken of
this acid-forming power to separate the sulphides of the arsenic
group from the sulphides of the copper group, which either are not
acid-forming at all, or exhibit this property only to a very slight
degree.[494]

«Sulpho-Salts.»—The similarity in the behavior of oxygen and sulphur
derivatives, in this respect, is general and is not restricted to the
metal sulphides we are discussing. For instance, the acid-forming
power of carbon dioxide is shown also by carbon disulphide, the
corresponding sulphur derivative of carbon. Just as the former
combines with potassium hydroxide to form a carbonate, so carbon
disulphide dissolves in solutions of potassium hydrosulphide and
potassium sulphide to form potassium sulpho-carbonate:

 CO_{2} + 2 KOH ⇄ K_{2}CO_{3} + H_{2}O.                            (1)

 CS_{2} + 2 KSH ⇄ K_{2}CS_{3} + H_{2}S.                            (2)

 CS_{2} + K_{2}S ⇄ K_{2}CS_{3}.                                    (3)

[p244]

The higher sulphides of the arsenic group, and arsenious and
antimonious sulphides among the lower ones, combine with the alkali
sulphides to form soluble alkali ‹salts› of sulpho-acids, in the same
way as carbon bisulphide does. In the case of arsenious sulphide, for
instance, we have the action

 As_{2}S_{3} + (NH_{4})_{2}S ⇄ 2 NH_{4}AsS_{2}.                    (4)

The salt, ammonium sulpharsenite, is ionized as follows:

 NH_{4}AsS_{2} ⇄ NH_{4}^{+} + AsS_{2}^{−}.

«Sulpho-Acids.»—The free ‹sulpho-acids› are liberated, from their
salts, by any stronger acid, such as hydrochloric acid; the acids are
extremely unstable and revert rapidly to the sulphides, from which
their salts were originally obtained. We have, for instance,

 2 HAsS_{2} ⥂ As_{2} S_{3} ↓ + H_{2}S ↑.

This instability of the sulpho-acids is entirely analogous to
the instability of the metal hydrosulphides (p. 203) and to the
instability of certain oxygen acids, notably of carbonic acid.
Sulpho-carbonic acid, H_{2}CS_{3}, is the best-known free acid of
this type. It may be precipitated, undecomposed, as an oil, and its
gradual decomposition into hydrogen sulphide and carbon disulphide
may be observed.

«Sulpho-Bases.»—Since one meets, in this group, ‹sulpho-acids› and
‹sulpho-salts›, corresponding to the oxygen acids and their salts,
one is naturally led to inquire,[495] whether the third great
class of oxygen compounds is not found duplicated among sulphur
compounds, whether ‹sulpho-bases›, as well as sulpho-acids and
salts, are known. One would look for such bases, with the most
pronounced basic character, among the compounds obtained by the
substitution of sulphur for oxygen in the strongest oxygen bases. To
a certain extent potassium and sodium hydrosulphides and sulphides
show, in fact, properties, which are akin to those fundamentally
characteristic of ordinary bases. They combine with acid sulphides to
form sulpho-salts, as the oxygen bases combine with acid oxides. To
a very considerable extent they neutralize all but the very weakest
acids; hydrogen sulphide, itself a very weak acid, is driven out of
its salts by all stronger acids, and the latter are almost completely
neutralized. For instance, we have: [p245] KOH + HCl ⥂ KCl + H_{2}O,
and KSH + HCl ⥂ KCl + H_{2}S and K_{2}S + 2 HCl ⥂ 2 KCl + H_{2}S. The
concentration of the hydrogen-ion is reduced most decidedly in each
of these reactions.

 EXP.—A solution of potassium hydrosulphide is saturated with
 hydrogen sulphide, in order to prevent hydrolysis and the formation
 of potassium hydroxide[496] (p. 180), as far as possible, and the
 solution is added to an acid (hydrochloric) solution of methyl
 orange;[497] the acid color is changed to orange, as a result of
 the almost complete neutralization of the acid. The potassium
 hydrosulphide (the hydrosulphide-ion HS^{−}) neutralizes the
 hydrogen-ion (of hydrochloric acid), that converts methyl orange
 into its pink salt, and hydrogen sulphide is formed, which is too
 weak an acid to affect the color of the indicator (p. 79).

The objection that potassium sulphide and hydrosulphide are salts,
the salts of hydrogen sulphide, might be raised against the
conception of their possessing a certain measure of basic functions;
but the common oxygen base, potassium hydroxide, is also a salt,
the salt of a still weaker acid, water. Indeed, the characteristic
properties of ordinary bases are due essentially to the fact, that
they are the more or less readily ionizable salts of an extremely
weak acid, water, and these properties may well be duplicated by
salts of other ‹weak› acids, duplicated in a ‹very much weaker› way,
in proportion as the acids are stronger than water. The difference
is, then, really one of ‹degree› and not of kind.[498]

 Owing to the fact that hydrogen sulphide is a much stronger
 acid than water, the action of potassium hydrosulphide on an
 acid sulphide, like carbon disulphide (equation (2), p. 243),
 is reversed to a correspondingly greater degree than the action
 of potassium hydroxide on carbon dioxide[499] (equation (1), p.
 243). The dissociation constant for the secondary ionization
 of hydrogen sulphide (HS^{−} ⇄ H^{+} + S^{2−}) is very much
 smaller than the constant for the primary ionization (HS^{−} is
 a much weaker acid than HSH), and so we find that a sulphide
 like K_{2}S exhibits very much stronger basic functions than
 do the hydrosulphides, as, for instance, in forming salts with
 acid-forming sulphides [p246] (equation (3), p. 243) and in
 neutralizing acids. There can be no question that, if we could have
 an aqueous solution of potassium oxide, K_{2}O, it would show,
 similarly, the characteristic actions of strong bases ‹even more
 powerfully› than the hydroxide, KOH; for instance, in acting on
 acid-forming oxides (equation (1), p. 243), in neutralizing acids,
 in saponifying esters (p. 81), and so forth. It is, in fact, on
 account of this property, that potassium oxide is decomposed by
 water. It is a salt involving the ‹secondary ionization› of water,
 (HO^{−} ⇄ H^{+} + O^{2−}), which has a much smaller dissociation
 constant even than the primary ionization (H_{2}O ⇄ H^{+} + HO^{−}).
 The oxide, K_{2}O, is decomposed by ‹neutralizing hydrogen
 ions formed by the primary ionization of water›. We have
 2 K^{+} + O^{2−} + H^{+} + HO^{−} ⥂ 2 K^{+} + 2 HO^{−},
 which is entirely analogous, in principle, to K^{+} + HO^{−} +
 H^{+} + Cl^{−} ⥂ K^{+} + Cl^{−} + HOH.

 «Sulphoxy-Salts.»—The close relations between the oxygen and the
 sulphur series are seen also in the fact that an oxygen base may
 be combined with an acid sulphide, and ‹vice versa›; arsenious
 sulphide, for instance, dissolves even in the solution of so weak
 a base as ammonium hydroxide (‹exp.›). The salts produced by this
 "crossing" are usually "hybrid" salts, partly sulpho-, partly
 oxygen-salts. There is, for instance, a series of ‹arseniates›,[500]
 Me_{3}AsO_{4}, Me_{3}AsSO_{3}, Me_{3}AsS_{2}O_{2}, Me_{3}AsS_{3}O
 and Me_{3}AsS_{4}. In analytical work the pure types are ordinarily
 utilized, rather than the mixed types.

 «Complex Sulphide Ions.»—The ions of the sulpho-acids, like
 the ions of oxygen-acids (p. 238), may also be treated as
 ‹complex ions›—of the positive metal ions and the sulphide-ion,
 S^{2−}. Ammonium sulphide combines with stannic sulphide,
 forming ammonium sulphostannate: SnS_{2} + (NH_{4})_{2}S ⇄
 (NH_{4})_{2}SnS_{3}. If the action is considered to be the
 result of interactions of the ions of stannic and ammonium
 sulphides, we can resolve the equation into the following one:
 Sn^{4+} + 2 S^{2−} + 2 NH_{4}^{+} + S^{2−} ⇄ 2 NH_{4}^{+} +
 SnS_{3}^{2−}.

 The ammonium-ion, appearing with the same coefficient on both sides
 of the last equation, evidently takes no direct part in the action
 and we have more simply: Sn^{4+} + 3 S^{2−} ⇄ SnS_{3}^{2−}.

 For the condition of equilibrium between the complex and its
 components we have:[501][502]

 [Sn^{4+}] × [S^{2−}]^3 / [SnS_{3}^{2−}] = K.

[p247]

«Sulphurization of Sulphides.»—Since the solubility of the arsenic
group of sulphides in ammonium sulphide solution—the reagent commonly
used in analysis—depends on the formation of soluble sulpho-salts,
due consideration must be taken of the fact that some of the ‹lower›
sulphides—notably stannous, aurous and platinous sulphides—do not
possess acid-forming properties in any marked degree; even antimonous
sulphide is soluble only in a considerable excess of ammonium
sulphide. In order, then, to insure a more complete separation of the
arsenic from the copper group, precautions are taken to sulphurize
the lower sulphides to higher, stronger acid-forming, sulphides,
in the course of the separation. For this purpose so-called
"yellow" ammonium sulphide, containing persulphides of ammonium,
(NH_{4})_{2}S_{2}, etc., is used in place of a solution of ammonium
sulphide and ammonium hydrosulphide. Stannous sulphide, for instance,
is dissolved by the reagent as ammonium sulphostannate: SnS +
(NH_{4})_{2}S_{2} ⇄ (NH_{4})_{2}SnS_{3}.

«Behavior of Arsenic Acid toward Hydrogen Sulphide.»—In conclusion,
special consideration must still be given to the behavior of arsenic
acid, H_{3}AsO_{4}. As its name indicates, it is an acid, and,
in fact, a rather strong acid, of the order of strength[503] of
phosphoric acid, H_{3}PO_{4}, which it resembles in composition and
in many of its properties. As a strong acid, arsenic acid, when it is
ionized, yields chiefly negative arseniate ions, H_{2}AsO_{4}^{−},
HAsO_{4}^{2−} and AsO_{4}^{3−}. Any basic properties, which it may
and, most likely, does possess, must be extremely weak. It is,
therefore, not surprising to find that unusual difficulties are
experienced in precipitating arsenic sulphide, by hydrogen sulphide,
from arseniate [p248] solutions, in as much as hydrogen sulphide
is an agent for the precipitation of the sulphides of ‹cations›.
Arsenious acid, the hydroxide of the lower oxide, on the other hand,
is a much weaker acid and shows more pronounced basic (amphoteric)
properties, and arsenic trisulphide is precipitated, without
difficulty, from solutions of arsenious acid in hydrochloric acid.
We have: 2 As^{3+} + 3 S^{2−} ⥂ As_{2}S_{3} ↓. When arsenic acid is
reduced to arsenious acid by sulphurous acid, by iodides (see Chap.
XVI) or by hydrogen sulphide (see below), no further difficulty in
precipitating a sulphide (As_{2}S_{3}) is experienced.

When a solution of arsenic acid, containing the usual small amount of
hydrochloric acid (0.3 molar), is treated with hydrogen sulphide at
ordinary temperatures, the following three reactions take place, but
‹exceedingly slowly›:

 2 H_{3}AsO_{4} + 5 H_{2}S ⥂ As_{2}S_{5} ↓ + 8 H_{2}O         (1)[504]

 H_{3}AsO_{4} + H_{2}S ⥂ H_{3}AsO_{3} + S ↓ + H_{2}O          (2)[505]

 2 H_{3}AsO_{3} + 6 HCl + 3 H_{2}S ⇄ 2 AsCl_{3} + 3 H_{2}O +
   3 H_{2}S ⥂ As_{2}S_{3} ↓ + 6 HCl + 3 H_{2}O                     (3)

Even in the presence of a considerable amount of arsenic acid,
precipitation, either of the trisulphide or of the pentasulphide, may
not occur for some time, and, unless one takes account of that fact,
the dangerous element, arsenic, would ‹easily› be ‹overlooked›. ‹Heat
accelerates› both the precipitation of the pentasulphide and the
reduction of arsenic acid and the subsequent precipitation of arsenic
trisulphide.[506]

The interesting observation has also been made that, in the presence
of an unusually ‹large excess› of hydrochloric acid and of a rapid
stream of hydrogen sulphide, the precipitation of the ‹pentasulphide›
(equation (1)) is favored and accelerated.[507] For instance, if 100
c.c. of concentrated hydrochloric acid (sp. gr. 1.2) are added to
50 c.c. of a 0.1 molar solution of potassium arseniate and a rapid
stream of hydrogen sulphide is passed through the mixture at the
ordinary temperature, a copious precipitate is formed within a minute
(‹exp.›). The precipitate formed under these conditions [p249] is
the ‹pentasulphide›.[508] On the other hand, a mixture of 5 c.c.
of hexanormal hydrochloric acid and 50 c.c. of 0.1 molar potassium
arseniate fails, for a long time, to give a precipitate when treated
in the same way (‹exp.›).

 The acceleration of the precipitation of the pentasulphide by the
 presence of a large excess of hydrochloric acid forms a problem of
 peculiar interest and importance, and no complete explanation of
 it has yet been offered.[509] The following considerations lead
 to one explanation, that has been suggested. Arsenic acid, by
 virtue of its close relations to antimonic, stannic and arsenious
 acids, may be assumed to have extremely weak basic, as well as
 pronounced acid, properties. For its ionization, we would have
 3 H^{+} + AsO_{4}^{3−} ⇄ H_{3}AsO_{4} (+ H_{2}O) ⇄ As(OH)_{5} ⇄
 As^{5+} + 5 HO^{−}. Further, the precipitation of As_{2}S_{5}
 may be assumed to result, ultimately,[510] from the action
 of the sulphide-ion S^{2−} on the positive ion As^{5+}
 (2 As^{5+} + 5 S^{2−} ⇄ As_{2}S_{5} ↓). The favorable action of the
 hydrochloric acid might, consequently, be thought to result from
 the fact, that it ‹facilitates› the ‹ionization of arsenic acid›
 as a base and the formation of a salt[511] AsCl_{5}. It could thus
 greatly increase the concentration of the ion As^{5+} and facilitate
 its combination with the sulphide-ion.

 Treatment of a solution of arsenic acid with a concentrated acid,
 yielding a large concentration of hydrogen-ion, would carry the
 series of actions, represented in the above ionization equation
 for arsenic acid, decidedly toward the right—suppressing the
 arseniate-ion AsO_{4}^{3−} and increasing the concentration of
 the arsenic-ion As^{5+}. Since we cannot apply the equilibrium
 laws (or the principle of the solubility-product) to solutions
 as concentrated as the one under discussion, a quantitative
 theoretical treatment of the subject cannot be given. The following
 may be suggested: The action of the acid would be favorable to
 the precipitation of As_{2}S_{5} by suppressing the arseniate-ion
 AsO_{4}^{3−} and thus increasing the concentration of the hydroxide
 As(OH)_{5}, available for ionization as a base and for the
 production of the ion As^{5+}. But the further favorable effect
 of the hydrochloric acid, in converting the hydroxide into a salt
 AsCl_{5} and increasing thereby the concentration of As^{5+}, would
 be ‹very largely offset› by the action of the acid in suppressing
 the [p250] sulphide-ion ([S^{2−}] = ‹k› / [H^{+}]^2; see p. 201).
 For systems to which the equilibrium laws could be applied, the
 concentration of As^{5+} (except for the suppression of the ion
 AsO_{4}^{3−}) would grow, approximately, with the fifth power[512]
 of the concentration of the hydrogen-ion, and the concentration of
 the sulphide-ion would decrease, approximately, proportionally to
 the square of the concentration of the hydrogen-ion. Further, the
 precipitation of As_{2}S_{5}, in a system to which the principle of
 the solubility-product were applicable, would depend on the relation
 of the product [As^{5+}]^2 × [S^{2−}]^5 to the solubility-product
 constant; it is evident that the value for [As^{5+}]^2 would
 ‹increase› proportionally to the tenth power of [H^{+}] and the
 value of [S^{2−}] ‹decrease› proportionally to the tenth power of
 the same factor [H^{+}]. The two effects would consequently offset
 each other under such conditions. However, the equilibrium laws
 cannot legitimately be applied to such concentrated solutions and
 the relation has been developed only to indicate opposing factors,
 which must be taken into account. An experimental study of the
 problem would be extremely interesting.[513] Since it involves the
 question of the ‹minute basic ionization of a moderately strong
 acid› (H_{3}AsO_{4}), which may be open to ‹measurement› (see Chap.
 XVI), the problem is one of particular interest and importance.

The analytical precautions, taken to insure the precipitation, by
hydrogen sulphide, of arsenic sulphide, when arsenic is present
in quinquivalent form, are based on the observations described;
in quantitative analysis, for the sake of securing a precipitate
of ‹uniform composition›, the aim is to precipitate the pure
‹pentasulphide› and a considerable excess of hydrochloric acid
is used. In qualitative analysis, where the composition of the
precipitate is a matter of indifference and a large excess of acid
would seriously interfere with the precipitation of certain sulphides
(‹e.g.› CdS, see p. 211), a smaller excess of acid is used and the
precipitation of arsenic sulphide is insured by prolonged treatment
of a solution with hydrogen sulphide ‹at a high temperature›.


  FOOTNOTES:

  [492] The ‹weak basic properties› of the hydroxides of the
  aluminium group, as compared with those of the zinc group, ‹a
  chemical difference›, and the resulting great instability of
  the carbonates of the former group, are used in the separation
  of the aluminium from the zinc group, by barium carbonate; but
  the physical element of extreme insolubility of the trivalent
  hydroxides enters also as an important factor (see footnote 3, p.
  194).

  [493] See p. 247, in regard to the behavior of arsenic acid in this
  respect.

  [494] See p. 246, footnote 3, in regard to the action of sodium
  sulphide on mercuric and bismuth sulphide.

  [495] ‹Vide› Nilson, ‹J. prakt. Ch.›, «14», 150 (1876).

  [496] Such a solution does not react alkaline to phenolphthaleïn.

  [497] Hydrogen sulphide rapidly destroys the indicator and the
  experiment is best carried out by preparing 50 c.c. of a saturated
  aqueous solution of hydrogen sulphide, containing 1 or 2 c.c. of
  normal hydrochloric acid, and by adding a considerable excess of
  methyl orange to the solution immediately before the addition
  of potassium hydrosulphide solution, which has been prepared as
  described in the text.

  [498] See the discussion on p. 177. See also the discussion by
  Remsen on acidic and basic halides, ‹Am. Chem. J.›, «11», 300
  (1889) Stud.

  [499] In both cases acid salts, KHCO_{3} and KHCS_{3}, are also
  formed.

  [500] McCay, ‹Z. anorg. Chem.›, «29», 36 (1901).

  [501] On p. 238 the analogous equation for the condition of
  equilibrium of the anion of an oxygen acid with its components was
  developed. Applying the result to the ion SnO_{3}^{2−} of stannic
  acid, H_{2}SnO_{3}, we have:

   [Sn^{4+}] × [O^{2−}]^3 / [SnO_{3}^{2−}] = K.

  It is evident, from the form of the equation, that for the stronger
  oxygen acids, ‹which are most stable as acids and ionize as bases
  at most in traces›, the value of the constant must be extremely
  small.

  [502] Mercuric sulphide is somewhat soluble in potassium and
  sodium sulphides, forming the salts Me_{2}HgS_{2}, and the
  complex ion HgS_{2}^{2−}. A liter of 0.1 molar Na_{2}S dissolves,
  at 25°, 1.9 grams (0.0082 mole) of HgS [Knox, ‹Trans. Faraday
  Society›, «4», 36 (1908)]. While the oxide (hydroxide) shows no
  perceptible tendency toward acid ionization, mercuric salts, it
  will be recalled, show in many cases an abnormally small tendency
  to form the mercuric-ion (see p. 115), and the latter also
  shows a particularly great tendency towards forming very stable
  complex ions of all kinds (‹e.g.› HgI_{4}^{2−}, in K_{2}HgI_{4},
  HgCl_{4}^{2−} in K_{2}HgCl_{4}, Hg(CN)_{4}^{2−}, etc.). Knox found
  for [Hg^{2+}] × [S^{2−}]^2 / [HgS_{2}^{2−}] = ‹k›, the approximate
  value of ‹k› to be 1 / 10^{53}. Bismuth sulphide is also very
  sparingly soluble in sodium or potassium sulphide, but not in
  ammonium sulphide. Solid salts, KBiS_{2} and NaBiS_{2} are known
  [Knox, ‹J. Chem. Soc.› (London), «95», 1760 (1909)].

  [503] See the table, p. 104.

  [504] See the discussion of the reaction, given below.

  [505] See Chap. XVI, for the interpretation of the reduction as an
  ionic reaction.

  [506] Bunsen, ‹Ann.› (Liebig), «192», 305 (1878). Brauner and
  Tomicek, ‹J. Chem. Soc.› (London), «53», 145 (1888). Usher and
  Travers, ‹ibid.›, «87», 1370 (1905).

  [507] Neher, ‹Z. anal. Chem.›, «32», 45 (1893).

  [508] Neher, ‹loc. cit.›

  [509] The theory of the relations favoring the precipitation
  expressed in equation (1) as against the reduction expressed in
  equation (2), forms a second interesting problem.

  [510] Intermediate derivatives, such as H_{3}AsSO_{3} (p. 246),
  could be the result of the ionization of As(OH)_{5}, or of
  AsCl_{5}, in stages (see p. 106). Neher, ‹loc. cit.›, McCay, ‹loc.
  cit.›

  [511] Neher (‹loc. cit.›) suggested that the favorable action
  of the large excess of hydrochloric acid might well be due to
  the formation of AsCl_{5}. McCay, ‹J. Am. Chem. Soc.›, «24», 661
  (1902), discusses the ionization of arsenic acid as a base, in
  connection with the precipitation of As_{2}S_{5}.

  [512] As(OH)_{5} is considered to be an ‹extremely weak› base and
  AsCl_{5} to be an ionizable salt.

  [513] To a certain extent, the effect of the acid may be to
  coagulate and precipitate the ‹colloidal› sulphide. Possibly, also,
  the concentrated acid renders inactive a considerable portion of
  the water present (forming oxonium salts OH_{3}Cl, etc., see p.
  238), which tends, by hydrolysis, to reverse the formation of the
  chloride As(OH)_{5} + 5 HCl ⇄ AsCl_{5} + 5 H_{2}O. Possibly, the
  formation of the pentasulphide is not wholly an ‹ionic reaction›,
  its precipitation being always a more or less ‹slow process›,
  and there may be intermediate products whose formation could be
  ‹accelerated› by the presence of acids (see Bredig and Walton, ‹Z.
  Elektrochem.›, «9», 114 (1903) for the study of a simple inorganic
  action involving such ‹catalytic› effects of acids).

[p251]




 CHAPTER XIV

 «OXIDATION AND REDUCTION REACTIONS. I»


Oxidation and reduction reactions are frequently met with in
analysis, and we shall turn now to the consideration of such
reactions, from the point of view of the modern theory of solution
and the laws of equilibrium.

Leaving until later the discussion of the most important and most
common oxidizing agents, such as oxygen, nitric acid, permanganate,
etc., we shall, in order to develop the subject most simply, confine
ourselves, for the moment, to the ‹qualitative› study of some
oxidations and reductions met with early in the study of analytical
reactions. One such reaction is the reduction of ferric salts by
hydrogen sulphide, and the simultaneous oxidation of the latter to
sulphur (‹exp.›). The reaction may be expressed by the equation

 2 FeCl_{3} + H_{2}S → 2 FeCl_{2} + 2 HCl + S ↓.

If the action is considered to be the result of the interaction
of the ionized ferric chloride and hydrogen sulphide, it would be
represented by the equation

 2 Fe^{3+} + 6 Cl^{−} + 2 H^{+} + S^{2−} →
   2 Fe^{2+} + 6 Cl^{−} + 2 H^{+} + S ↓.

It is then clear that the reacting components, according to such a
conception, are the ferric and the sulphide ions, whose electrical
charges mutually discharge each other. Considering only those
components whose charges are changed, we have

 2 Fe^{3+} + S^{2−} → 2 Fe^{2+} + S ↓.

The reduction of a ferric to a ferrous salt would then be
accomplished by the discharge of one of the three positive charges on
the ferric ions; the oxidation of hydrogen sulphide to sulphur would
be accomplished by the complete discharge of the sulphide ions.

Ferric salts are reduced, much in the same way, by iodides (‹exp.›),
iodine being liberated: 2 Fe^{3+} + 2 I^{−} → 2 Fe^{2+} + I_{2}.

Reduction then appears to involve a loss of positive charges by ions,
oxidation a loss of negative charges. [p252]

Conversely, we frequently have occasion to oxidize ferrous salts to
the ferric condition, and among the most convenient reagents for the
purpose are chlorine and bromine water (‹exp.›). For instance, we
have 2 FeCl_{2} + Cl_{2} → 2 FeCl_{3}, or, considering the action
from the point of view of the theory of ionization,[514] 2 Fe^{2+} +
Cl_{2} → 2 Fe^{3+} + 2 Cl^{−}. In this case the oxidation of the
ferrous to the ferric ion consists in the assumption of an additional
positive charge; reduction of chlorine to the chloride-ion consists
in the assumption of negative charges by the chlorine atoms.

«Definitions of Oxidation and Reduction in Electric Terms.»—The
definitions must then be amplified and ‹oxidation be considered
to involve ultimately the assumption of positive, or the loss of
negative, electrical charges by ions or atoms, reduction to involve
ultimately the assumption of negative, or the loss of positive,
charges›. According to the electron theory of electricity a unit
negative charge is an electron, the unit positive charge, probably,
the charge left on an atom when it has lost an electron; and, thus,
oxidation may simply be defined, according to the electric theory of
oxidation and reduction, as consisting, fundamentally, in the ‹loss
of electrons by atoms or ions›, reduction as consisting in a ‹gain
of electrons›. For instance, when hydrogen sulphide reduces a ferric
salt, 2 Fe^{3+} + S^{2−} → 2 Fe^{2+} + S, ‹the sulphide ions transfer
their electrons to the ferric ions›.

«Oxidations and Reductions by Electric Currents.»—All of the
oxidation and reduction reactions which have been discussed may, in
fact, be effected by the use of an ‹electric current› in the place of
chemical agents. Ferrous salts, for instance, are ‹oxidized›, at the
positive pole, by the current to ferric salts:[515]

 Fe^{2+} + ⊕ → Fe^{3+}, or Fe^{2+} − ε^{−} → Fe^{3+}.

Ferric salts are ‹reduced›, at the negative pole, to ferrous salts:

 Fe^{3+} + ⊖ → Fe^{2+}, or Fe^{3+} + ε^{−} → Fe^{2+}.

[p253]

 EXP.—A solution of ferrous chloride, freshly prepared from iron
 wire, or a freshly prepared solution of ferrous-ammonium sulphate,
 is placed in a very small beaker; a solution of ferric chloride,
 acidulated with hydrochloric acid to prevent subsequent complete
 reduction of the ferric-ion to iron, is brought into a similar
 beaker. A small amount (5 c.c.) of each solution is tested, the
 former with potassium thiocyanate and the latter with ferricyanide
 solution, to show the absence of perceptible quantities of ferric
 and ferrous ions in them, respectively. Platinum electrodes,
 consisting best of cylinders of platinum gauze, are introduced into
 the solutions, the solutions are connected by means of a "salt
 bridge" (a U-tube filled with a solution of sodium chloride and
 closed at both ends by plugs of filter paper), and a current of 0.2
 ampere is passed through the system, the positive current entering
 the solution containing the ferrous salt. After the current has
 been allowed to pass for a minute or two, 5 c.c. is withdrawn, by a
 pipette, from the meshes of the positive electrode and tested with
 thiocyanate, and 5 c.c., withdrawn in the same way from the negative
 electrode, is tested with potassium ferricyanide.

«Production of Electric Currents by Means of Oxidation and Reduction
Reactions.»—Not only may all the oxidations and reductions which we
have discussed be accomplished with the aid of the electric current,
but ‹vice versa›, an electric current may readily be produced by a
proper arrangement of the components of any one of these reactions.
Care need only be taken to have the simultaneous loss and gain of
electrons, characteristic of all oxidation and reduction reactions,
occur in separate localities, which must be connected, however,
in such a way as to make the transfer of electrons, a flow of
electricity, possible.

 EXP. For instance, some ferric chloride and sodium chloride solution
 may be put into a small beaker, some sodium chloride solution
 into a second beaker of the same size, and the two solutions
 connected, first by means of a "salt-bridge," and then by means of
 two platinum electrodes dipping into the solutions and connected
 with the terminals of a sensitive voltmeter.[516] If [p254] all
 of the connections are made, the introduction of the "salt-bridge"
 being left to the last, a momentary slight motion of the needle is
 observed, when the bridge is introduced. The needle then falls back
 to the zero point (see p. 276). If now some hydrogen sulphide water
 is poured into the beaker containing sodium chloride, a decided, and
 continuing, deflection of the needle of the voltmeter is immediately
 observed, showing the passage of an electric current, and it is
 in the direction anticipated by the consideration of the reaction
 equation: 2 Fe^{3+} + S^{2−} → 2 Fe^{2+} + S ↓. The positive current
 passes into the voltmeter from the ferric chloride solution, where
 ferric ions are giving up their charges; the negative current enters
 the voltmeter from the solution containing the hydrogen sulphide,
 where sulphide ions are being discharged. The "salt-bridge" is
 necessary to complete the electrical circuit and prevent any local
 accumulation of positive or negative electricity (polarization). For
 instance, as the ferric ions are discharged, an excess of chloride
 ions would remain in the beaker, rendering the solution negative and
 preventing the flow of electricity from the electrode, if negative
 ions did not move off, through the "salt-bridge," into the beaker
 containing hydrogen sulphide and, simultaneously, positive ions
 migrate into the beaker containing the ferric salt. Similarly,
 the accumulation of positive electricity in the hydrogen sulphide
 solution, on account of the hydrogen ions left free by the discharge
 of sulphide ions, is prevented by the flow of positive ions (sodium
 and hydrogen) through the U-tube into the beaker containing the
 ferric chloride and the flow of negative (chloride) ions into the
 hydrogen sulphide solution. Thus a current of electricity passes
 through the whole circuit.

It is thus possible to reduce ferric chloride in one vessel by
hydrogen sulphide poured into another vessel,[517] and an electric
current may be obtained from the simultaneous discharge of the
sulphide and ferric ions in the action.

«Effects of Ion Concentrations on the Current.»—Hydrogen sulphide,
it will be recalled, is an extremely weak acid (p. 199), only a very
small proportion is ionized and, consequently, the concentration
of the discharging (reducing) sulphide-ion must be minute in this
solution. Its salts, however, are highly ionized, and by the
addition of an alkali to the solution containing the hydrogen
sulphide, the concentration of the discharging ion would be very
greatly increased and the current should therefore be intensified
most decidedly—provided the hydrogen sulphide really reduces ‹by
means of its negative ion and not by the action of the nonionized
acid›. As a matter of fact, the anticipated decided increase in the
intensity of the current is observed, when alkali is added to the
mixture containing the hydrogen sulphide (‹exp.›). Similarly, [p255]
we have assumed that the oxidizing agent is the highly charged
ferric-ion, not the nonionized ferric salt. Now iron forms rather
‹stable complex ions›[518] with the fluoride-ion, for instance,
FeF_{6}^{3−}, which yield ferric ions very much less readily than do
ferric salts. Hence the addition of a fluoride—potassium or ammonium
fluoride—should, according to this view, reduce the oxidizing power
of the iron solution by suppressing the ferric-ion and converting it
into the complex FeF_{6}^{3−}. In fact, the addition of potassium
fluoride immediately reduces the intensity of the current (‹exp.›),
and, simultaneously, the deep yellow-brown color of the ferric salt
solution gives way to the very pale yellow tint of the complex ion
and its salt.[519]

«Further Illustrations.»—If ferrous sulphate solution is put into
one beaker and sodium chloride solution into another, connections
being made similar to those used in the previous experiment, then a
vigorous current is instantly produced (‹exp.›), when some bromine or
chlorine water is added to the sodium chloride solution, the positive
current flowing into the voltmeter from the beaker containing the
bromine (chlorine); the bromine atoms (chlorine atoms) combine with
electrons lost by the ferrous ions and are reduced to bromide ions
(chloride ions) (see p. 252).

It would appear possible, in fact, to obtain an electrical current
from any oxidation-reduction reaction, if the oxidizing and reducing
agents can be, experimentally, properly arranged for this purpose.

«Summary.»—We find thus that there is a most intimate connection
between oxidation and reduction phenomena and electrical charges
on atoms or ions. In the first place, an electrical current may be
used as an oxidizing and reducing agent; indeed, a current cannot
be passed through any solution without simultaneous oxidation and
reduction at the positive and negative poles, respectively. And,
conversely, an electric current may, in turn, be produced by a proper
combination of the reagents in oxidation and reduction reactions.

«Need of the Study of the Quantitative Relations.»—The interpretation
of such actions from the point of view of the theory [p256]
of ionization offers, then, no particular difficulties. But,
as far as we have developed the theory, that is, essentially
from its qualitative side, difficulty would be encountered in
understanding why certain other reactions, involving a similar
simultaneous discharge of positive and negative electricity by
ions, which might be expected to take place, do not seem to take
place. Thus, solutions of ferric sulphate do not appear to be
reduced appreciably by the hydroxide and oxide ions of the water
present. Although the possibility of such a reduction exists
through the simultaneous discharge of the positive electricity
of the ferric ions and the negative charge on the oxide ions (or
hydroxide ions) of water (4 Fe^{3+} + O^{2−} → 4 Fe^{2+} + O_{2} or
4 Fe^{3+} + 4 HO^{−} → 4 Fe^{2+} + O_{2} + 2 H_{2}O), comparable
with the reduction of ferric ions by sulphide ions, such a reduction
does not take place appreciably.[520] And, similarly, whereas the
iodide-ion, as we have seen, reduces the ferric-ion very readily, the
analogous chloride-ion does not appear to do so. Sodium chloride may
be added to ferric sulphate solution and potassium ferricyanide fails
to show that any ferrous salt is produced (‹exp.›).

The mere possibility of a transfer of charges, or electrons, is
therefore apparently[521] not sufficient to induce an oxidation and
reduction reaction—much in the same way as, for instance, the mere
presence, simultaneously, of the barium-ion and the carbonate-ion,
in itself, does not necessarily lead to the precipitation of barium
carbonate (p. 90), although the latter is difficultly soluble. In
order to understand the problem of precipitation or nonprecipitation
of salts, it was found necessary to examine the question from its
‹quantitative› side (p. 91), and, similarly, the solution of the
difficulty concerning the occurrence or nonoccurrence of oxidation
and reduction reactions, where the possibility of a transfer of
electrons is given, will be found in a study of the problem from its
quantitative side.

«Oxidation and Reduction Reactions as Reversible Reactions.»—In order
to reduce the development of the quantitative [p257] relations to
the simplest possible terms, we may turn to still simpler oxidation
and reduction reactions than those studied thus far. If a rod of zinc
is placed in a solution of copper sulphate, copper is deposited and
zinc sulphate is formed. If we consider the action to be an ionic
one, we have:

 Cu^{2+} + SO_{4}^{2−} + Zn ↓ → Zn^{2+} + SO_{4}^{2−} + Cu ↓,

or, since the sulphate-ion is not directly concerned in the action,
we have more simply:

 Cu^{2+} + Zn ↓ → Cu ↓ + Zn^{2+}.

Cupric-ion has been reduced, therefore, to metallic copper, the
metallic zinc oxidized to zinc-ion, each zinc atom transferring two
electrons to a cupric ion.

 Closer analysis of the action shows that this interpretation of
 the action, from the electrical point of view, is not at all in
 conflict with the older definitions and conceptions of oxidation
 and reduction: copper is deprived of the oxygen with which it is
 combined in nonionized copper sulphate,

    O
   ╱ ╲
 Cu   SO_{2}, and by evaporation of the solution,
   ╲ ╱
    O
                   O
                  ╱ ╲
 zinc sulphate, Zn   SO_{2},
                  ╲ ╱
                   O

 containing the zinc combined with oxygen, is obtained. We shall
 presently find, however, that it is just in the quantitative
 formulation of the relations, that the interpretation of the action
 from the point of view of the theory of ionization has proved its
 superiority over the older view.

If a strip of copper is placed in a solution of mercuric nitrate,
copper, in turn, is dissolved, being oxidized to the form of
cupric-ion, and mercury is deposited:

 Cu ↓ + Hg^{2+} → Cu^{2+} + Hg ↓.

We find, then, that cupric-ion has a tendency to give up its charges,
to be reduced to the metallic condition; metallic copper, in turn,
has a tendency to revert to the ionic condition, to be oxidized and
to form cupric-ion. We may consider the two opposed tendencies, shown
in these relations, as representing a ‹reversible› reaction:

 Cu ↓ ⇄ Cu^{2+}.

 EXP. If an electric current is passed through a copper sulphate
 solution, copper is ‹deposited› on the negative (platinum)
 electrode; if the current is reversed, the copper ‹vanishes› quite
 as rapidly at what is now the positive pole. [p258]

«Condition of Equilibrium.»—For such a reversible reaction we
might expect, if we may apply the law of equilibrium to it, that
the ratio of the concentrations of copper and of the cupric-ion
would be a constant for the ‹condition of equilibrium› at a given
temperature.[522] We would then have:

 [Cu^{2+}] / [Cu ↓] = ‹k›.

Since the concentration [Cu ↓] of a pure, dense[523] piece of copper
may be considered a constant at a given temperature, it would follow,
that the first term in our relation would also have a constant
definite value for the condition of equilibrium between the metal and
its ion. Consequently, ‹for the condition of equilibrium› we would
have:

 [Cu^{2+}] = K_{Cu^{2+}}.

Metallic copper would then be in equilibrium, at a given temperature,
with solutions containing cupric-ion only if the latter has a
perfectly definite, constant concentration. Nernst[524] discovered
this and similar relations, as a result of a more rigorous analysis
of the energy changes involved in the ionization and precipitation
of metals, and proved the validity of the relations. The value of
the constant,[525] which, according to Nernst's [p259] suggestion
is called the «electrolytic solution-tension constant», is 8E−22
for copper[526]; that is, copper is directly in equilibrium with
a solution containing cupric-ion only if the concentration of the
latter is 8E−22 gram-ion per liter.

We see, then, that copper would be directly in equilibrium with
solutions of cupric salts only if they contain this exceedingly
minute concentration of cupric ions. When such is the case, the
ionization of the metal and the formation of the metal, by the
deposit of discharging ions, may be considered to proceed ‹with the
same velocity› (p. 94).

But, if the metal is dipped into a solution of greater concentration
of cupric ions than that represented by the constant, say into a
solution of 0.1 molar copper sulphate, the velocity of deposition
of the metal would be proportionally increased (p. 92), while the
velocity of ionization and solution of the metal would remain
unchanged. We would consequently have the ions discharging and
forming metal more rapidly than they are formed. A condition of
change, not of equilibrium, exists. If we [p260] consider the
changes that must occur, we see that the ions, discharging on the
metal, would ‹charge› it with ‹positive electricity›, and the
positive charge would, in turn, repel from the metal the positive
cupric ions remaining in the solution. Equilibrium would be expected
to result when the charge on the plate becomes heavy enough to repel
from the film, immediately surrounding it, all the cupric ions
excepting those representing a concentration of 8E−22, as required
by the value of the equilibrium constant. The positive charge on the
plate would attract and hold negative sulphate ions, freed by the
discharge of cupric ions, in a kind of "double layer," the surface of
the metal holding positive charges and the film of liquid in contact
with it holding an excess of negative ions. An ‹electric potential›
would thus be established between the positive metal and the negative
solution, bathing it.[527] It is evident that the more concentrated
the solution of cupric ions, the heavier the charge must be that
will be required to repel the cupric ions sufficiently to establish
equilibrium.[528]

If copper is placed in a solution in which the concentration of the
cupric ions is smaller than the constant 8E−22, the velocity of
ionization will be greater than the velocity of the deposition of the
metal. The ions formed, having assumed positive charges, will leave
a negative charge on the metal, and, as a result of the electrical
attraction, a "double layer," surrounding the metal, will again be
formed, the positive ions clinging to the negative metal. Equilibrium
will be reached when the concentration of the cupric ions originally
present, increased by the new ions formed in this "double layer,"
will have reached, in the film bathing the plate, the concentration
demanded by the equilibrium constant. An electrical potential will
be established as before, the metal being negative, the solution, in
this case, positive.

By developing the quantitative relations between osmotic forces
and the electrical potential, Nernst[3] was able to show that, at
room temperature[529] (17°–18°), the following logarithmic relation
[p261] holds for the ‹potential difference› between a ‹metal›[530]
and a solution of its ‹ion›, which bathes it:

 ε_{Me, Me-salt} = (0.0575 / ‹v›) log(C / K).

In this equation ε_{Me, Me-salt} is the electrical potential, in
volts, existing between the metal Me and the solution of its salt,
Me-salt; ‹v› is the number of electrical charges transferred from
the metal to its ion, and ‹vice versa›, in the action Me ⇄ Me_{ion};
in the present case, it is identical with the ‹valence› of the
metal ion, which the metal forms. C is the concentration of this
ion in any given case, and K is the concentration represented by
the solution-tension constant, ‹i.e.› by the equilibrium constant.
The logarithm is the common one. In place of the concentrations,
K and C, the corresponding ‹osmotic pressures› of the metal ion
(P and ‹p›, as used by Nernst) may be used in the equation, and
for solutions in which osmotic pressure and concentration are not
strictly proportional, the osmotic pressure should be used by
preference (see footnote 4, p. 258). The ‹sign›[531] given to [p262]
ε_{Me, Me-salt}, in any given case, shows the ‹sign› of the ‹electric
charge› on the «first component named in the subscript», which is the
‹metal›, in the present instance.

For the relation between copper and cupric-ion we would have:

 ε_{Cu, Cu-salt} = (0.0575/2) log(C / K).

When the concentration of cupric-ion is equal to the constant, C = K,
the logarithm has the value 0 and the potential difference is 0. When
the concentration of cupric-ion is smaller than the constant, C < K,
the potential ε_{Cu, Cu-salt} is ‹negative›, ‹i.e.› the ‹metal›
receives a negative charge. This ‹negative› charge is the greater,
the smaller C is. When C > K, ε_{Cu, Cu-salt} is positive, the copper
plate receives a positive charge, and this ‹positive› charge is the
greater, the larger the value of C is.

«Applications.»—It should be clear, from these considerations, ‹that
an electric current will result, if copper plates are introduced into
solutions containing different concentrations of cupric-ion› and the
solutions and electrodes are connected in such a way as to allow the
flow of a current. If we call Cu′ the copper plate dipping into a
solution containing cupric-ion at a concentration C′, and Cu″ the
plate in a solution containing [Cu^{2+}] = C″, we have[532]: [p263]

 ε_{Cu′, Cu″} = ε_{Cu′, CuX} − ε_{Cu″, CuX} =
   (0.0575 / 2) [log(C′ / K) − log(C″ / K)]

and[533]

 ε_{Cu′, Cu″} = (0.0575 / 2) log(C′ / C″).

It is also clear, from this equation, that the greater the difference
in concentration of the cupric-ion in the two solutions, the greater
should be the potential difference produced. The following series of
experiments illustrates these relations and confirms the conclusions
reached. [p264]

If two electrodes of pure copper are introduced into solutions
of cupric sulphate of equal concentration,[534] no current is
produced, when the solutions are connected by a "salt bridge" and
the electrodes with a voltmeter (‹exp.›; the chemometer described on
p. 253 is used). If one of the beakers is partially emptied, only
a few drops of the solution being left in it, and is then filled
with a solution of sodium sulphate, we notice that the voltmeter
immediately indicates the establishing of a potential difference—a
current is produced. From the experimental arrangement and from the
manner of the deflection of the needle of the chemometer, we note,
too, that the plate dipping into the more concentrated solution
of the cupric-ion is the positive pole, and hence the cupric ions
are discharged on it; this solution is therefore growing less
concentrated in regard to cupric-ion. In the other vessel, copper
is dissolving and the concentration of cupric-ion is increasing.
Both changes tend toward equalizing the concentrations in the two
solutions and thus toward establishing equilibrium.

The ‹diffusion› of ions, from and to the plates, is a very slow
process (p. 8), and since the potential produced depends on the
momentary concentrations of the liquid films immediately next to
the plates, the potential difference, first observed, is seen to
disappear rapidly. More decided and lasting potential differences
are obtained by introducing reagents, which keep the concentration
of the cupric-ion, automatically, at very low values in the one
solution, and which thus make us less dependent on the slow diffusion
of the ions around the plates. We may add, for instance, sodium
hydroxide to a solution of copper sulphate to precipitate cupric
hydroxide; cupric hydroxide being a difficultly soluble compound,
its saturated solution contains only a very small concentration
of [p265] cupric-ion. If we connect, again, copper plates in
two equally concentrated solutions of copper sulphate, and add a
little more than the equivalent amount of sodium hydroxide to the
solution holding the plate connected with the ‹negative› post of the
voltmeter, cupric hydroxide is thereby precipitated, and we note that
a decided difference of potential is established and ‹maintained›
(‹exp.›). An excess of a concentrated solution of sodium hydroxide
should, according to the principle of the solubility-product, reduce
the concentration of cupric-ion still more, and the potential is,
in fact, thereby increased (‹exp.›). Cupric sulphide is much less
soluble than cupric hydroxide, and if we add sodium sulphide (a
little more than one equivalent) to the mixture containing the
hydroxide, we find that the hydroxide is converted into the less
soluble, black sulphide, leaving a still smaller concentration of
cupric-ion in this solution, and the potential is again increased
(‹exp.›). We found that the complex ions of copper with the
cyanide-ion are so extremely stable as to allow of the existence of a
concentration of cupric-ion so minute, that copper sulphide cannot be
precipitated from cyanide solutions (p. 228). If sufficient potassium
cyanide is added to the mixture containing the suspension of cupric
sulphide, the sulphide dissolves readily,[535] and the largest
potential difference, yet noted, is produced.[536] We find thus that
the behavior of the metal, in contact with these different solutions,
agrees with the demands of the theory.

«The Equilibrium Relations between Two Metals and Their Ions.»—The
tendency of a metal to ionize and of its ion to be reduced has been
aptly likened to the tendency of a liquid to form its vapor and of
the vapor to condense to its liquid (the name solution ‹tension›
expresses the analogy to vapor ‹tension›). As different liquids have
vastly different tendencies to vaporize at a given temperature,
so different metals, different elements, have vastly different
tendencies to ionize. We shall consider, briefly, this tendency also
in the case of zinc.

In aqueous solutions, the concentration of zinc-ion with which the
metal would be in equilibrium, as found by calculation from the
potential difference between zinc and zinc sulphate solutions [p266]
of realizable concentrations of zinc-ion, is 10^{17}, a value[537]
enormously larger than 10^{−21}, the value of the corresponding
constant for copper. A zinc rod, in contact with a solution of a
zinc salt, like zinc sulphate, will acquire a ‹negative charge›,
as the metal must ionize much more rapidly than the ion will be
discharged, since even a saturated solution would contain only a
relatively small concentration of the ion. Copper, as we have seen,
placed in a copper sulphate solution of moderate concentration, is
charged with ‹positive› electricity, the concentration of cupric-ion
being very much larger than that required for the condition of
equilibrium between the metal and its ion. When zinc, immersed in a
zinc sulphate solution, and copper, immersed in a copper sulphate
solution, are connected through a metal circuit, ‹e.g.› that of
a voltmeter, and the solutions are connected by a "salt-bridge"
(‹exp.›), a current is established, the positive current flowing
from the copper through the metal circuit to the zinc, metallic
copper being deposited and zinc going into solution. The combination
represents the well-known Daniell cell. We note that in each
solution the change in concentration of the ion is towards the
solution-tension constant, ‹towards a condition of equilibrium›. We
may inquire, a little more closely, what would be the condition for
equilibrium for such a system. If we imagine a copper plate dipping
into a solution containing a concentration of 10^{−21} of cupric-ion
(the solution-tension constant), the metal will be directly in
equilibrium with the solution and will not acquire any electrical
charge. If we imagine a zinc rod immersed, in the same way, in a
solution containing a concentration of zinc-ion of 10^{17} (this
is not practically feasible), the metal and its ion would also be
in equilibrium with each other and the metal would not assume any
charge. It is evident that, if the zinc and copper and the solutions
of their salts were connected, no current would be established,
[p267] ‹zinc would not be oxidized to zinc-ion, and cupric-ion
would not be reduced. In this condition of equilibrium, then, the
ratio of the concentrations of the respective ions in the solutions
bathing the metals would be, also, the ratio of the solution-tension
constants.› This is a ‹general relation› for these two metals—the
individual concentrations of the ions need not have the value of the
solution-tension constants, but ‹equilibrium will be established
whenever the ratio of the concentrations of the cupric-ion and the
zinc-ion has the same value as the ratio of the solution-tension
constants›.[538] The condition for equilibrium, in mathematical form,
is then

 [Zn^{2+}] / [Cu^{2+}] = K_{Zn} / K_{Cu} = K_{eq.}; and
   K_{Zn} / K_{Cu} = 10^{17} / 1E−21 = 10^{38} = K_{eq.}

The nearer the ratio is to the equilibrium constant, the smaller the
potential will be, until, when the constant is reached, it becomes
0. We cannot increase the concentration of zinc-ion indefinitely
in order to reach the condition of equilibrium, but we may reduce
the concentration of cupric-ion practically at will, as we have
seen (p. 265), and we may thus approach the constant. In fact, if
we add to the copper sulphate solution of the copper-zinc element,
described above, a solution of sodium hydroxide, and thus leave, in
the solution, only the small concentration of cupric-ion belonging
to the difficultly soluble cupric hydroxide, the potential of the
copper-zinc element is decidedly reduced (‹exp.›). If sodium sulphide
is added to the cupric hydroxide, to convert the hydroxide into
the less soluble sulphide, which yields a smaller concentration of
cupric-ion, the potential is again reduced most decidedly (‹exp.›).
It has now so small a value that we may readily anticipate that,
if the cupric-ion is suppressed so thoroughly, by the addition of
potassium cyanide, that even the sulphide cannot persist, the value
of the ratio [Zn^{2+}] : [Cu^{2+}] may grow even larger than the
[p268] equilibrium constant 10^{38}, and we would have a system
in which chemical change in the ‹opposite direction must result
from the tendency to establish equilibrium›. In fact, if potassium
cyanide is added to the mixture surrounding the copper plate,
in sufficient quantity to dissolve the sulphide, we find that a
current is established in the ‹opposite direction›[539]—‹zinc is now
precipitated at the expense of the solution of metallic copper; that
means, that the zinc-ion is being reduced by metallic copper, which
in turn is oxidized to cupric-ion› (‹exp.›).

We may apply the conclusions, reached, to the action of metallic
zinc when it is introduced into the solution of a cupric
salt. The oxidation of zinc to the zinc-ion and the reduction
of the cupric-ion to copper must be ‹reversible› reactions,
Zn ↓ + Cu^{2+} ⇄ Zn^{2+} + Cu ↓, which will come to a condition
of equilibrium, according to the laws of equilibrium, when
[Zn^{2+}] : [Cu^{2+}] = K = 10^{38}. The value of this ratio shows
that the cupric-ion will be ‹practically› completely reduced, and
precipitated as copper, by a sufficient quantity of zinc, the trace
of cupric-ion, required to maintain the equilibrium ratio, being too
minute to be detected. By the study of this oxidation and reduction
reaction with the aid of potential differences, as just described,
the validity of the relation is subject to demonstration, and the
value of the equilibrium constant is brought into definite relation
to the solution-tension constants of the metals.

Each element has its own characteristic solution-tension constant
(see the table at the end of Chapter XV), and the relation just
established for the reduction of cupric-ion, at the expense of the
oxidation of metallic zinc, may be applied to any pair of metals and
their ions.[540]

«General Principles Concerning Equilibrium in Reversible Oxidation
and Reduction Reactions.»—We may now extend the conclusions, reached
in the study of these particularly simple oxidations and reductions,
to oxidation and reduction reactions in general. We must expect
that, ‹when such an action is reversible› and subject to the laws of
equilibrium, its course will, as in all [p269] previous applications
of the equilibrium laws, depend, at a given temperature, in the
first place, ‹on the values of constants›. The (solution-tension)
constants, involved in this class of actions, measure what we
may call the affinity of atoms and ions for electric charges, or
electrons. In the second place, the course of the action will depend,
in each case, on the concentrations of the ions, concentrations which
are, to a considerable extent, ‹variable› at will, as we go from
case to case. In the third place, all such reversible reactions will
come ultimately to a ‹condition of equilibrium›, in which neither
action is absolutely completed, and the course of the action, in any
given system not in equilibrium, will always ‹proceed toward› this
condition of equilibrium.

The oxidation and reduction reactions, such as Zn ↓ + Cu^{2+} ⇄
Cu ↓ + Zn^{2+}, to which we have heretofore limited the discussion
of the quantitative relations, are particularly simple actions,
involving only ‹two› variables (in this case [Cu^{2+}] and
[Zn^{2+}]). But the knowledge of the general principles of the
quantitative relations will now enable us to answer questions,
in connection with more complicated cases, which the qualitative
relations alone did not put us into the position of answering (see p.
256).

«Applications; Reduction of Ferric Salts and Oxidation of Ferrous
Salts.»—It will not be difficult to arrive now at definite
conceptions as to why certain reactions of oxidation and reduction do
not seem to take place, although they are, qualitatively, entirely
analogous to reactions which take place readily. The study of one of
the questions previously raised (see p. 256), namely as to why ferric
ions apparently are not reducible by chloride ions, while they are
easily reduced by iodide ions, will be sufficient to illustrate the
application of the principles.

In considering the question of the possible reduction of ferric
to ferrous ions, at the expense of the oxidation of chloride ions
to chlorine, we must bear in mind the fact that the reduction of
the ferric ions is a ‹reversible process›, Fe^{3+} ⇄ Fe^{2+},
and that the oxidation of chloride ions to chlorine is also a
‹reversible process›, 2 Cl^{−} ⇄ Cl_{2}. We will deal first,
in some detail, with the action Fe^{3+} ⇄ Fe^{2+}. For this
reversible action we have an ‹equilibrium constant›[541]
[Fe^{2+}] : [Fe^{3+}] = K_{Ferro, Ferri} = 10^{17}, which must be
[p270] taken into account in all oxidation and reduction reactions
involving these ions.[542] In a system containing the two ions,
the tendency towards reduction of ferric-ion and the tendency
toward oxidation of ferro-ion ‹would be directly in equilibrium›
(‹i.e.› without the intervention of other opposed forces, such as
an electric potential, produced by an opposing cell or produced by
an opposing action[543] of other components in the solution) ‹only
when the concentration of ferro-ion is 10^{17} times as great as the
concentration of ferric-ion›.

If we connect a 0.1-molar solution of ferric chloride with a
0.1-molar solution of ferrous chloride, by means of a "salt bridge"
and a pair of platinum electrodes dipping into the solutions and
connected with the voltmeter (see p. 253), a current is produced, the
positive current entering the voltmeter from the electrode placed in
the ferric chloride solution (‹exp.›). It is evident that, in the
effort to establish equilibrium, ‹ferric ions› in the ferric chloride
solution ‹are reduced› at the expense of the ‹oxidation of ferrous
ions› in the ferrous chloride solution. If we consider only the ratio
of the concentration of the ferro-ion to that of the ferric-ion
in each of the salt solutions and leave out of consideration, for
the moment, other, secondary, electrical forces,[544] it is clear
that the ratio [p271] [Fe^{2+}]_{1} : [Fe^{3+}]_{1} in the ferrous
salt solution, considered by itself, is far closer to the point of
equilibrium[545] than the ratio [Fe^{2+}]_{2} : [Fe^{3+}]_{2} in the
ferric chloride solution, in which the concentration of ferric-ion is
enormously ‹greater› than that of ferro-ion, while the equilibrium
constant demands that the ferro-ion should be in great ‹excess›.
The strongest tendency to change must be toward a reduction of the
concentration of the ferric-ion in the solution of ferric chloride,
which is in agreement with the observed direction of the current.
Equilibrium, it may be added, will be reached when the ‹ratio› of the
concentration of ferro-ion to that of ferric-ion is the ‹same› in
both solutions.[546]

The addition of potassium fluoride to the ferric chloride
solution converts the ferric-ion into the rather stable complex
ferrifluoride-ion FeF_{6}^{3−}, whose potassium salt K_{3}FeF_{6} is
formed. The [p272] concentration of ferric-ion being ‹decidedly›
reduced, the system must be nearer to the condition of equilibrium,
the potential must fall (‹exp.›). It is again evident (p. 255) that
the ‹oxidizing agent› is clearly the ‹ferric-ion›, and not the total
quantity of the ferric salt in the solution.

«Intensity of Reactions.»—‹Vice versa›, any oxidizing agent, which
has the power to oxidize ferro-ion to ferric-ion, ‹does so the
more readily and vigorously›, the more completely any ferric-ion,
present or formed, is suppressed. If ferrous sulphate is added
to a solution of silver nitrate, a ‹slow›[547] reduction of the
silver-ion, and oxidation of the ferro-ion, takes place according
to Fe^{2+} + Ag^{+} → Fe^{3+} + Ag ↓. Now, if a little potassium
fluoride is added to the mixture, so as to suppress the ferric-ion,
which is always present, by contamination, in the original ferrous
sulphate solution, and which is formed in the action by the silver
nitrate, the oxidation of the ferrous salt and the precipitation of
metallic silver is very much ‹accelerated›,[548] and a heavy black
precipitate of silver is formed instantly (‹exp.›). The experiment
is an illustration of the rôle of potential in oxidation-reduction
reactions, the potential and the reducing power of ferro-ion being
decidedly diminished by the presence of its oxidation product, the
ferric-ion.[549] It is also a further illustration of the rôle the
‹ions› play in these actions, the total amount of ferric salts not
being changed by the introduction of the fluoride, which simply
suppresses ‹ferric ions›.

«Reduction of Ferric Salts by Iodides.»—In the study of the oxidation
of the ferro-ion and the reduction of the ferric-ion, we [p273]
have thus far considered only the reversible tendencies of the two
ions to change into each other, tendencies which would be ‹directly›
balanced, in a given solution, without the intervention of other
forces, when the ratio of the concentrations of the ions is that
of the equilibrium constant, 10^{17}. In reactions involving the
oxidation of a ferrous salt, we have to deal, however, in exactly the
same way, with the ‹reversible tendency› of the ‹oxidizing substance›
to act as oxidizing agent, and, similarly, in every reduction of a
ferric salt, we have to deal also with the ‹reversible tendency› of
the ‹reducing agent› to act as such. In order to reach some definite
conceptions as to the influences of these conflicting tendencies, we
shall consider, next, the reduction of ferric salts by iodides, and
then contrast this reduction with the action of chlorides on ferric
salts, and we shall thus complete the study of this action (see p.
269).

For the reduction of ferric salts by iodides (p. 251), we have
to consider the reversible tendency of iodide-ion to form iodine
and to be formed from iodine: 2 I^{−} ⇄ I_{2}. The constant[550]
K_{I^{−}, Iodine} for the equilibrium ratio [I^{−}]^2 / [I_{2}] is
5.6E29 at 25°. [p274]

The reduction of ferric salts by iodides is a ‹reversible› reaction:
2 Fe^{3+} + 2 I^{−} ⇄ 2 Fe^{2+} + I_{2}, and the ultimate condition
of equilibrium will depend on the values of the constants,
K_{Ferro, Ferri} and K_{I^{−}, Iodine}, and on the concentrations of
the components used. For the condition of equilibrium we have

 [Fe^{3+}]^2 × [I^{−}]^2 / ([Fe^{2+}]^2 × [I_{2}]) = K_{eq},

and for this constant the relation[551]

 K_{eq} = K_{I^{−}, Iodine} / (K_{Ferro, Ferri})^2 =
   5.6E29 / (10^{17})^2 = 5.6 / 10^5

[p275]

can be established. ‹It is evident, from the value of the
constant, that the chief tendency of the reversible reaction will
be toward the reduction of the ferric ions and the liberation of
iodine›, which is in accord with experience (‹exp.›, p. 251).

It is interesting to note, again, that the reduction of the ferric
salt depends on the reduction of the ‹ferric-ion›: the ferric-ion may
be ‹suppressed›, with the aid of potassium fluoride (see p. 255), and
the addition of potassium iodide to a mixture of ferric chloride and
potassium fluoride leads to the formation of ‹traces›, only, of free
iodine (‹exp.›).

«Action of Chlorides on Ferric Salts.»—Now, when a chloride is
used in place of an iodide, we have to do with an ion, Cl^{−},
which has an enormous affinity for its charge, as compared with
that of iodide-ion. The equilibrium relation for the reversible
reaction 2 Cl^{−} ⇄ Cl_{2} has the form [Cl^{−}]^2 : [Cl_{2}] =
K_{Cl^{−}, Chlorine}, and the value[552] of the constant is 2E60.

For the reaction of chloride-ion on ferric-ion we would have, as
in the case of the action of iodide-ion, 2 Fe^{3+} + 2 Cl^{−} ⇄
2 Fe^{2+} + Cl_{2} and

 [Fe^{3+}]^2 × [Cl^{−}]^2 / ([Fe^{2+}]^2 × [Cl_{2}]) = K_{eq}.

For this equilibrium constant we have the relation, as determined
above (p. 274),

 K_{eq} = K_{Cl^{−}, Chlorine} / (K_{Ferro, Ferri})^2 =
   (2E60) / (10^{17})^2 = 2E26.

[p276]

It is evident, from the value of the equilibrium constant,
that the action of chloride-ion on ferric-ion must result
quantitatively so differently from the action of the analogous
iodide-ion (p. 275), that the net qualitative results are entirely
dissimilar. Whereas in the case of the iodide, liberation of iodine
and reduction of the ferric-ion are bound to be the chief and obvious
actions, in the case of the chloride-ion, on the other hand, the
equilibrium constant demands that there should be no ‹appreciable›
reduction of the ferric-ion or liberation of chlorine—which is in
accordance with our experience (‹exp.›, p. 256).

It is noteworthy, however, that the equilibrium relations demand
that at least ‹traces› of chlorine be liberated, and ‹traces› of
ferrous salt be formed, since neither [Fe^{++}] nor [Cl_{2}] may
have the value 0. If we add some sodium chloride to a solution of
sodium sulphate, connected electrically, in the usual way, with a
solution of ferric sulphate, a very slight momentary current is
produced (‹exp.›). The liberation of the first traces of chlorine and
of ferro-ion on the electrodes is necessary, and also sufficient, to
satisfy the conditions for equilibrium as expressed by the constant,
until diffusion from the electrodes removes these traces.

«Summary.»—We find, thus, that the general principle of the
quantitative relations governing oxidation and reduction gives us the
means of interpreting ‹the differences in results› in (qualitatively)
similar combinations, which, qualitatively, might lead to an
oxidation-reduction reaction, and which, in certain cases, do produce
such reactions (ferric-ion with iodide-ion), and in other cases do
not (ferric-ion with chloride-ion).


  FOOTNOTES:

  [514] The oxidation by chlorine may also be represented on the
  basis of the conception that the chlorine molecule contains a
  positive and a negative chlorine atom, Cl^{+}Cl^{−}. (‹Vide›
  W. A. Noyes, ‹J. Am. Chem. Soc.›, «23», 460 (1901); Stieglitz,
  ‹ibid.›, «23», 796 (1901); Walden, ‹Z. phys. Chem.›, «43», 385
  (1903); J. J. Thomson, ‹Corpuscular Theory of Matter›, p. 130
  (1907)). We may consider the action to take place as follows:
  2 Fe^{2+} + Cl^{+} → 2 Fe^{3+} + Cl^{−}.

  [515] ε^{−} is used to indicate an electron.

  [516] The whole device is an adaptation of Ostwald's "Chemometer"
  [see ‹Z. phys. Chem.›, «15», 399 (1894)]. It has been found best
  to convert a Weston voltmeter into a lecture table apparatus by
  lengthening its index to 10 inches, with the aid of a very light,
  hollow aluminium wire carrying an index and playing over a scale
  10 inches wide, drawn on glass and divided into 150 divisions.
  The scale is illuminated by means of five small one-candle-power
  lamps. The whole is encased in a simple wooden frame. The voltmeter
  shows a range of 0.7 volt, but, on account of its low resistance
  (78 ohms), it is used only for qualitative purposes and does not
  register the true potentials, quantitatively. (Such adaptations
  of Weston voltmeters may be purchased from the Weston Electrical
  Instrument Co., or a similar instrument obtained from Hartmann and
  Braun, Frankfurt a/M, Germany.)

  [517] Chemical Action at a Distance, Ostwald, ‹Z. phys. Chem.›,
  «9», 540 (1892).

  [518] Peters, ‹Z. phys. Chem.›, «26», 229 (1898).

  [519] See below, in regard to the ‹quantitative› relations for
  reactions of this nature.

  [520] EXP. Ferric sulphate solution is tested with a ferricyanide.

  [521] Rigorous quantitative examination of the relations shows
  (p. 275) that these reductions and oxidations ‹do take place›,
  but equilibrium is reached when they have proceeded to so slight
  an extent, that, qualitatively, they are not always obvious or
  discernible.

  [522] A change in the nature of the solvent changes the value
  of the equilibrium constant, just as it changes the ionization
  constant of electrolytes. See p. 61 and see remarks by Sackur, ‹Z.
  Elektrochem.›, «11», 387 (1905).

  [523] For exceedingly thin films of copper we cannot make this
  assumption, and for such films the conclusions, that follow,
  are, in fact, found not to hold. (Overbeck. ‹Vide› Le Blanc,
  ‹Electrochemistry›, p. 252 (1896)).

  [524] ‹Z. phys. Chem.›, «4», 129 (1889).

  [525] The values of this and similar equilibrium constants
  are derived by means of Nernst's formula (see below) for the
  potential difference between an element and solutions of its
  ions. The derivation involves the assumption that this formula
  expresses correctly the relation between the potential change and
  the concentration change at all concentrations. This assumption
  appears to be justified by all experimental indications thus far
  observed. The constants are of importance, primarily, for the
  calculations which can be made with their aid (see below), and
  may, conservatively, be considered to be essentially "calculation
  factors" ("Rechengrössen," according to Haber. See pp. 232–7,
  Chapter XII). The constants may be expressed, as in the text,
  in terms of (molar) ‹concentrations› of the ions, or in terms
  of the ‹osmotic pressures› of the ions, a molar solution at 0°
  producing an osmotic pressure of 22.4 atmospheres. Where osmotic
  pressure and concentration are not strictly proportional (‹e.g.›
  for concentrated solutions), the osmotic pressure, rather than the
  concentration, is the determining factor and, when known, is used
  in exact calculations. The plan, pursued in the text, is adopted
  in order to express these constants in the terms used for all the
  other equilibrium constants. It should be recalled (‹e.g.› p. 30)
  that in calculations, in general, where pressure and concentration
  are not strictly proportional, the pressure is the determining
  factor. A third method of expressing the solution-tension relations
  consists in giving the ‹potential differences›, which exist
  ‹between elements› and solutions of their ‹ions, in which the ions
  have unit (molar) concentration›. These potential differences
  are ‹functions› of the solution-tension constants, as will be
  discussed below, and the constants, in terms of concentrations or
  osmotic pressures, may be easily calculated, from the potential
  differences, with the aid of this function (see below, and see the
  table at the end of Chapter XV).

  [526] According to Wilsmore's tabulation (‹Z. phys. Chem.›,
  «36», 92 (1901)), the potential difference ε_{Cu, Cu^{2+}}
  of copper against a 0.5 molar solution of cupric sulphate,
  in which [Cu^{2+}] = 0.11, is +0.584 volt. Inserting these
  values for [Cu^{2+}] and ε_{Cu, Cu^{2+}} in the equation
  ε_{Cu, Cu^{2+}} = (0.0575 / 2) log([Cu^{2+}] / K) (see below)
  and solving the equation for K, we find K = 8E−22. For
  [Cu^{2+}] = 0.24, ε_{Cu, Cu^{2+}} is +0.594 volt and K = 8E−22. In
  regard to the convention determining the signs used (in the present
  case ε_{Cu, Cu^{2+}} is ‹positive›), see the footnote below, p.
  262, and in regard to the definition of zero potential, to which
  the potential differences used in this book refer, see the table
  and summary at the end of Chapter XV.

  [527] Nernst, ‹loc. cit.›, p. 151.

  [528] In other words, the greater the concentration of cupric-ion,
  the greater its osmotic pressure must be, and the repelling
  electric force, required to overcome the pressure of the
  cupric-ion, would be correspondingly greater.

  [529] ‹Cf.› Nernst, ‹Theoretical Chemistry› (1904), pp. 720–723, in
  regard to the derivation and the general form of his formula.

  [530] For elements that form ‹negative ions›, ‹e.g.› for chlorine,
  bromine, oxygen, etc., the ‹equation reads› (see pp. 273, 275 and
  the table at the end of Chapter XV):

  ε_{Elem., Electrolyte} = −(0.0575 / ‹v›) log(C / K).

  Note the ‹changed› sign of the expression on the right. The
  difference in sign expresses the fact that, when negative ions
  discharge on an electrode, they render it negative, and when they
  are formed by an electrode, they leave the latter positive; for
  positive ions, it will be recalled, the conditions are just the
  ‹reverse› (see above).

  Where a ‹soluble› element (‹e.g.› chlorine) or a solution of
  a metal (‹e.g.› sodium amalgam) is used as an electrode, its
  concentration, in general, is not constant, as in the case of
  a pure, solid metal like copper (p. 258). In such cases, the
  quantity in the denominator of the ratio in the logarithm cannot
  be expressed by a constant K, but is expressed by K × C_{Element},
  C_{Element} being used to indicate the concentration of the element
  in the experiment in question.

  [531] The convention, adopted in the text, for the use of the
  positive and negative signs in expressing potentials, is that
  proposed by Luther (‹cf.› Le Blanc's ‹Lehrbuch der Elektrochemie›
  (third edition), p. 212). The ‹sign› always ‹denotes› the character
  of the ‹charge› on the ‹first component› written in the subscript
  to ε. Thus, for a copper plate in contact with a solution of
  cupric sulphate, when C > K, the logarithm, log(C / K), has
  a ‹positive› value and ε_{Cu, CuSO_{4}} is ‹positive›, which
  means that the ‹metal› will be ‹positive›, the electrolyte
  negative. For instance, for [Cu^{2+}] = 1, ε_{Cu, CuSO_{4}} is
  found to be +0.606 (see the table at the end of Chapter XV).
  ε_{Cu, CuSO_{4}} = −ε_{CuSO_{4}, Cu′}. By this use of the signs
  one is never in doubt as to their meaning. Unfortunately, widely
  different definitions of the signs have been used (‹cf.› Le
  Blanc, ‹Electrochemistry› (1896), pp. 209, 219, and Lehfeldt,
  ‹Electro-Chemistry› (1904), p. 159). Care must be taken, in using
  the data of original papers, to be informed as to the definition
  used.

  In accordance with the convention as to signs, adopted in this
  book, the ratio of concentrations (C / K), used in the logarithm
  of Nernst's formula, is the ‹reciprocal› of the ratio usually
  given. The change has been made in order that the algebraic signs
  of the values obtained from the application of the formula should
  be the same as those observed in the experimental arrangements, as
  demanded by the convention.

  [532] When two electrodes are combined to form an electric cell
  or couple, the potential difference of the couple is always
  the (algebraic) ‹difference› of the two individual electrode
  potentials, and hence these are ‹subtracted› from each other
  (algebraically). The electrode of the first term of the difference
  (the minuend) is named first in the subscript of the potential
  of the couple; then the sign of the difference represents the
  character of the charge on that electrode, in agreement with the
  convention (see footnote 2, p. 261). In illustration: two copper
  electrodes may be taken, each of which, considered by itself,
  carries a positive charge, because the concentrations of the
  cupric-ion in the solutions bathing them are both greater than
  K; when they are combined, each of the two electrodes will tend
  to send a positive current, in ‹opposite› directions, into the
  metal connecting them. But the potential of the electrode with the
  heavier charge (the one dipping into the solution containing the
  greater concentration of cupric-ion) will overcome the potential
  of the other electrode, and the current will flow, through the
  connecting metal, with a potential that represents the difference
  between the two values. If the electrode of the more concentrated
  solution is named first in the subscript of the potential of the
  couple, its individual electrode-potential appears as the first
  term of the difference (the minuend) and is reduced by the value
  of the electrode-potential of the second electrode; as this is
  numerically smaller than the value of the minuend, the difference
  will be positive, showing that the electrode in the stronger
  solution, named first in the subscript of the potential difference
  of the couple, carries a positive charge. Further, if the second
  electrode dips into a solution, in which the concentration of the
  cupric-ion is smaller than K, the logarithmic expression for its
  electrode-potential will be found to give a negative value; and
  the (algebraic) subtraction of this negative quantity from the
  electrode-potential of the first electrode will give a larger
  potential difference, for the couple, than that possessed by the
  first electrode alone—all of which agrees with the experimental
  results, when such combinations are made.

  Where negative elements are concerned, the same convention holds,
  but the ‹logarithmic expression for the potential of such an
  electrode carries a negative sign› (see footnote 1, p. 261), which
  must be inserted, algebraically, when the expression is used as a
  term in the difference under discussion.

  [533] If C′ > C″, the logarithm will be positive and ε_{Cu′, Cu″}
  will have a ‹positive› value, which means that the copper plate,
  Cu′, ‹which is named first in the subscript to ε›, will be charged
  positively, ‹when the system works›. If C′ < C″, the logarithm
  will be negative, which means that the first plate, Cu′, mentioned
  in the subscript, will receive a negative charge, ‹when the
  system works›. The sign is therefore intended, by the convention
  adopted (p. 261), to express any result for the ‹working system›,
  irrespective of the charge on the individual plates before they are
  combined. For instance, for C′ = 1 and C″ = 10^{−10}, both plates
  are positive, ‹before› they are connected with each other, since
  in each case C > K, and ε_{Cu, CuX} = (0.0575 / 2) log(C / K) = a
  positive value. When the plates are combined, we find from
  ε_{Cu′, Cu″} = (0.0575 / 2) log(C′ / C″) that the first plate,
  dipping in the more concentrated solution of cupric-ion, is
  ‹positive›, which is confirmed by experiment.

  [534] (1 / 10)-molar cupric sulphate, 100 c.c., containing some
  sodium sulphate or nitrate, to reduce the resistance, is a
  convenient concentration.

  [535] The copper plate is best freed from adhering sulphide by
  means of a strong cyanide solution, and re-introduced into the
  solution.

  [536] Küster, ‹Z. Elecktrochem.›, «4», 110 and 503 (1897).

  [537] In a solution of zinc sulphate in which [Zn^{2+}] = 0.114,
  the potential ε_{Zn, ZnSO_{4}}= −0.514 (the minus sign indicates
  that the metal named ‹first› in the subscript has a negative
  charge). Inserting the values for [Zn^{2+}] and ε_{Zn, ZnSO_{4}} in
  the general equation given on p. 261, and solving for K, we find
  K = 10^{17}. For [Zn^{2+}] = 0.022 and ε_{Zn, ZnSO_{4}} = −0.535,
  we find K = 10^{16.8}. (‹Cf.› Wilsmore's tables, ‹loc. cit.›)

  [538] Equilibrium will be established whenever the potential of the
  system is equal to 0. The potential of the system may be calculated
  according to the equation (see footnote 1, p. 262)

   ε_{Cu, Zn} = ε_{Cu, CuSO_{4}} − ε_{Zn, ZnSO_{4}} =
    (0.0575 / 2) (log(Cu^{2+} / K_{Cu}) − log(Zn^{2+} / K_{Zn})).

  The potential ε_{Cu, Zn} is 0 whenever [Cu^{2+}] / K_{Cu} =
  [Zn^{2+}] / K_{Zn}, ‹i.e.› when [Zn^{2+}] / [Cu^{2+}] =
  K_{Zn} / K_{Cu}.

  For ions of different ‹valence›, such as silver and cupric
  ions, the equilibrium equation assumes a somewhat less
  simple form. For Cu ↓ + 2 Ag^{+} ⇄ 2 Ag ↓ + Cu^{2+}, we have
  [Ag^{+}]^2 / [Cu^{2+}] = (K_{Ag})^2 / K_{Cu}.

  [539] ‹Vide› Ostwald's ‹Lehrbuch der allgemeinen Chemie›, 2d Ed.,
  Vol. II, p. 874, for the historical data on this action. ‹Vide›
  Küster's experiments, ‹Z. Elektrochem.›, «4», 503 (1897).

  [540] See the footnote, p. 267, in regard to the form the
  equilibrium ratio assumes when metals producing ions of different
  ‹valence› are used.

  [541] The value of the constant is calculated from the data given
  by Peters, ‹Z. phys. Chem.›, «26», 193 (1898).

  [542] The fact that this equilibrium relation has been proved to
  hold for the action Fe^{2+} ⇄ Fe^{3+} and that it must be taken
  into account in all oxidation-reduction reactions involving these
  ‹ions›, in no wise excludes the possibility that other equilibrium
  relations can also exist between ferrous and ferric compounds.
  For instance, ferrous hydroxide Fe(OH)_{2} may well have a
  characteristic tendency of its own to assume a further positive
  charge (lose an electron) according to Fe(OH)_{2} ⇄ Fe(OH)_{2}^{+},
  the potential of which action may, under given conditions, be a
  ‹main determining factor› in the course of an action, ‹e.g.› in
  alkaline mixtures. It is not impossible, even, that we also must
  consider negative ions FeO_{2}^{2−} and their tendency to be
  oxidized. Evidence would ‹suggest› that ferrous hydroxide, ‹or
  its negative ion› FeO_{2}^{2−}, may have, indeed, a very ‹great
  tendency› to be oxidized, possibly much greater than the tendency
  of Fe^{2+} to form Fe^{3+}. (‹Cf.› Manchot, ‹Z. anorg. Chem.›,
  «27», 419 (1901), and McCoy and Bunzel, ‹J. Am. Chem. Soc.›, «31»,
  370 (1909)). Closer investigations of these relations, from a
  quantitative viewpoint, would probably determine this question and
  bring exceedingly important relations to light.

  [543] ‹E.g.› by the potential of the action Cl_{2} ⇄ 2 Cl^{−}.

  [544] The potential of a solution of the iron salts is given by
  ε = 0.058 log(10^{17} × [Fe^{3+}] / [Fe^{2+}]). In a solution of
  a ferric salt, if [Fe^{2+}] = 0, the potential would obviously be
  ∞, which could not present a condition of equilibrium. Equilibrium
  is established in such a solution, as will be shown further on
  in the text, by the liberation of chlorine and the formation of
  ferro-salt, according to 2 Fe^{3+} + 2 Cl^{−} ⇄ 2 Fe^{2+} + Cl_{2},
  until the potential, resulting from the tendency of chlorine to
  form chloride-ion, just balances the tendency of the ferric-ion
  to form ferro-ion. But when a ferric chloride solution is used
  as the source of supply of positive electricity, as in the
  experiment described in the text, ‹both› the ferric-ion and the
  chlorine tend to charge the platinum electrode with positive
  electricity and to revert to a condition of equilibrium in
  reference to their individual constants. The relations are much
  like those between a cupric salt solution and a copper plate: if
  [Cu^{2+}] > K_{Cu^{2+}}, equilibrium will be established, as we
  have seen, by the positive charging of the plate in sufficient
  degree to oppose the tendency of the cupric-ion to discharge (see
  p. 259). But when the solution and plate are used as the source of
  supply for an electric current (p. 264), both the positive charge
  on the plate, and the tendency of the cupric-ion to discharge and
  acquire the concentration [Cu^{2+}] = K_{Cu^{2+}}, will supply
  the positive current. In calculations we ignore the positive
  charge already deposited on the plate and deal only with the
  concentration of Cu^{2+}. The chlorine, liberated in a solution of
  ferric chloride, plays practically the same rôle as does the copper
  plate in a cupric salt solution, and it can be ignored in the
  discussion of the combination described in the text. In a ferrous
  salt solution, in a similar manner, some ferric-ion must always be
  formed by liberation of hydrogen (see p. 282), until equilibrium
  is reached according to 2 Fe^{2+} + 2 H^{+} ⇄ 2 Fe^{3+} + H_{2}.
  Hydrogen plays here the same rôle as chlorine does in the ferric
  chloride solution.

  [545] The condition for equilibrium is [Fe^{2+}] : [Fe^{3+}] =
  10^{17}, in a solution considered for itself.

  [546] This ratio need not be 10^{17}, since we have two solutions
  combined with each other and the total potential will be expressed
  by:

   ε = ε_{1} − ε_{2} = 0.058 (log(10^{17} × [Fe^{3+}]_{1} /
     [Fe^{2+}]_{1}) − log(10^{17} × [Fe^{3+}]_{2} / [Fe^{2+}]_{2}))

   = 0.058 log([Fe^{3+}]_{1} × [Fe^{2+}]_{2} /
     ([Fe^{2+}]_{1} × [Fe^{3+}]_{2})).

  Equilibrium is reached when the total potential is 0. Then

   [Fe^{3+}]_{1} × [Fe^{2+}]_{2} / ([Fe^{2+}]_{1} × [Fe^{3+}]_{2}) = 1

   and [Fe^{2+}]_{1} / [Fe^{3+}]_{1} = [Fe^{2+}]_{2} / [Fe^{3+}]_{2}.

  [547] In order to have very decided differences in the speeds of
  the action in the absence and presence of fluoride, it is best to
  use an old ferrous sulphate, or ferrous ammonium sulphate, solution
  which contains considerable ferric salt.

  [548] ‹Vide› Peters, ‹loc. cit.›, p. 236.

  [549] Ostwald [‹Lehrbuch d. allgem. Chem.›, 2d Ed., II, 883
  (1893)], first emphasized the fact that potential differences are a
  ‹measure› of oxidizing and reducing powers.

  [550] The constant is calculated from the data of Küster and
  Crotogino on the potential of solutions of iodine in potassium
  iodide [‹Z. anorg. Chem.›, «23», 88 (1900)]. Owing to the formation
  of complex ions I_{3}^{−}, for which due allowance has not been
  made in the calculation, and owing to some uncertainty as to
  the vague definition of the concentration of iodine used, the
  estimation of the constant can only be considered a rough one.
  The value given expresses the order of the equilibrium ratio
  sufficiently well for our present purposes. In a recent paper, Bray
  and MacKay [‹J. Am. Chem. Soc.›, «32», 914 (1910)] have determined
  the constant for the formation of the complex ion according to
  I_{3}^{−} ⇄ I_{2} + I^{−}, which might be used to correct the data
  of Küster and Crotogino; but in view of other uncertainties and
  inaccuracies, the correction has not been considered advisable.

  Several related methods may be used to calculate the equilibrium
  constant for [I^{−}]^2 : [I_{2}] = K from the data of Küster and
  Crotogino. Perhaps the simplest method is the following: A solution
  of iodine ([I] = 1 / 32 normal, and therefore [I_{2}] = 1 / 64
  molar) in 1/8 molar potassium iodide, in which, the degree
  of ionization being taken into account, [I^{−}] = 0.109, was
  observed to show a potential ε_{I_{2}, I^{−}} = + 0.860 (the
  convention as to signs, discussed on p. 261, is used here and
  the potential, observed against a so-called "calomel electrode,"
  is reduced to the so-called "absolute potential"; ‹cf.› Le
  Blanc, ‹Lehrbuch der Elektrochemie›, p. 214). Now, ‹there must
  be a certain concentration of iodide-ion›, which we will call
  [C], ‹with which iodine› of the above concentration ‹would be
  directly in equilibrium› and would give no potential at all
  (‹cf.› pp. 261 and 258 in regard to copper). With a change in the
  concentration of the iodide-ion, a potential would be produced
  according to ε_{I_{2}, I^{−}} = 0.0575 log([C] / [I^{−}]).
  This relation is of exactly the same nature as that developed
  for the potential of copper plates, immersed in solutions of
  cupric-ion of different concentrations (but see footnote 1, p.
  261, concerning the ‹sign› of the new relation). In the present
  case, we are dealing with univalent ions, I^{−}, in place of
  bivalent ions Cu^{2+}, and the factor 0.0575 is used instead
  of 0.0575 / 2 (see p. 261). If we insert the observed values,
  [I^{−}] = 0.109 and ε = 0.860, of the experiment described above,
  into the equation ε_{I_{2}, I^{−}} = 0.0575 log([C] / [I^{−}])
  and solve the equation for [C], we find [C] = 10^{14}. ‹That
  means›, 1 / 64 molar iodine ‹would be directly in equilibrium
  with a concentration of iodide-ion› = 10^{14} (if this value
  is inserted for [I^{−}] in the logarithmic equation, the
  potential is found to be 0). For the condition of equilibrium for
  I_{2} ⇄ 2 I^{−}, according to [I^{−}]^2 : [I_{2}] = K, we have then
  (10^{14})^2 : (1 / 64) = K = 6.4E29. Similarly, for [I^{−}] = 0.109
  and [I_{2}] = 1 / 512 the potential ε = 0.831 is observed, and the
  equilibrium constant is found to be 5.1E29. When [I^{−}] = 0.109
  and [I_{2}] = 1 / 128, the potential is 0.850 and the constant is
  calculated to be 5.3E29. The mean value for K is 5.6E29. In these
  calculations, the formation of ions I_{3}^{−}, affecting the values
  for [I^{−}] and [I_{2}], has not been considered, and there is some
  doubt whether the concentrations of iodine, given by Küster and
  Crotogino, do not represent [I_{2}] rather than [I], as assumed in
  the calculations. If the former be the case, the mean value of the
  above experiments would be 2.8E29. The value, used in the text, is
  considered sufficiently accurate for the purposes of this book.

  [551] This relation of the equilibrium constant and the
  solution-tension constants may be deduced in a manner similar to
  that for the analogous equilibrium constant for the oxidation of
  zinc by the cupric-ion, as given in footnote 1, on page 267. The
  ‹exact› value of the equilibrium constant is uncertain, since
  K_{I^{−}, Iodine} has not yet been determined with a sufficient
  degree of accuracy; but the value, used, gives the order of the
  constant sufficiently well for our purposes, especially when it is
  considered in connection with the constant given below for the same
  relation, when the chloride-ion is substituted for the iodide-ion.

  [552] This is the value of the constant as calculated from the
  data given by Wilsmore (‹Z. phys. Chem.›, «36», 91 (1900))
  for the solution-tension of chlorine under atmospheric
  pressure at 18°. The calculation may be made exactly as in
  the case of the similar constant for iodine (p. 273). ‹There
  must be a concentration of chloride-ion›, which we will
  call [C], ‹with which chlorine, of one atmosphere pressure
  at 18°›, would be directly in equilibrium. The potential of
  chlorine, against any other concentration of chloride-ion,
  would be ε_{Cl_{2}, Cl^{−}} = 0.0575 log([C] / [Cl^{−}]). For
  [Cl^{−}] = 1, ε is +1.694 (see the table at the end of Chapter
  XV), and inserting these values in our equation and solving it
  for [C], we find [C] = 2.88E29. That means, that chlorine, at
  18° and of atmospheric pressure, would be in equilibrium with
  chloride-ion of the concentration given. Since chlorine, at this
  temperature and pressure, has a concentration of 1 / 23.9 moles
  (at 18°, one mole is contained in 23.9 liters, instead of in
  22.4 liters, at O°), we have for the condition of equilibrium:
  [Cl^{−}]^2 : [Cl_{2}] = (2.88E29)^2 : (1 / 23.9) = 2E60. [Cl_{2}]
  represents, thus, in the calculation of this constant, the
  concentration of chlorine gas (see Chapter XV concerning gas
  electrodes) and not the concentration of the dissolved chlorine;
  the latter, however, is proportional to the gas concentration
  (Chapter VII).

[p277]




 CHAPTER XV

 «OXIDATION AND REDUCTION. II. OXIDATION BY OXYGEN, PERMANGANATES,
 ETC.; OXIDATION OF ORGANIC COMPOUNDS»


We will turn now to the consideration of the question, how the
principles of the theory of electric oxidation and reduction may be
applied to the most important oxidizing agent, oxygen, and to such
vigorous and common oxidizing agents as permanganates, dichromates,
nitric acid, and similar substances.

«Oxidation of Hydrogen by Oxygen.»—The oxidation of hydrogen by
oxygen may be first considered, as representing a typical and, in
some respects, the most important case of oxidation by oxygen.
Hydrogen, like copper, zinc, and other elements, has a certain
tendency to form its ion, H^{+}, and the latter, in turn, has a
tendency to be reduced to hydrogen. We may put H_{2} ⇄ 2 H^{+} and
the condition for equilibrium, at a given temperature, will be

 [H^{+}]^2 / [H_{2}] = K_{H^{+}, Hydrogen}.

In this equation [H_{2}] represents the concentration of the hydrogen
in contact with the electrode (see below) and with the solution, and
[H^{+}] represents the concentration of hydrogen-ion in the solution
bathing the electrode. The ionization of hydrogen, at a given
temperature, depends, according to this equation, on ‹two variables›,
the concentration, or pressure, of the gas and the concentration, or
osmotic pressure, of the hydrogen-ion in a given solution.

If platinum gauze, coated with platinum black, is charged with
hydrogen, then, the greater the pressure of the gas, the more
soluble the hydrogen will be in the platinum (p. 121). Such a
charged gauze may be used as a hydrogen electrode (Fig. 13, p. 281),
the concentration of the hydrogen in which is proportional to the
concentration, or pressure, of the hydrogen gas surrounding it; the
platinum will allow of the ready transmission of electric charges
from and to the hydrogen dissolved in it. [p278]

The value of the constant[553] K_{H^{+}, Hydrogen} = [H^{+}]^2 /
[H_{2}], at 18°, is found to be 5.55E−9, and ‹hydrogen, at 18°, under
atmospheric pressure, is directly in equilibrium with hydrogen-ion of
the concentration› [H^{+}] = 1.52E−5.

If such an electrode, in contact with hydrogen of atmospheric
pressure, is dipped into the solution of some neutral salt, say
sodium chloride, in which the concentration of the hydrogen-ion,
formed by the ionization of water, at 18°, is 0.9E−7, which is less
than 1.5E−5, the hydrogen in the electrode must tend to ionize more
rapidly than it is formed from the ion, and the ‹electrode must
receive a negative charge›, exactly as in the case of zinc, placed in
a zinc sulphate solution.

For oxygen similar relations may be developed.[554] We have:
O_{2} ⇄ 2 O^{2−} and

 [O^{2−}]^2 / [O_{2}] = K_{1}.                                     (1)

If we use the relation of the oxide-ion, O^{2−}, to the more stable
hydroxide-ion, HO^{−}, we also have:[555] [p279]

 [HO^{−}]^4 / [O_{2}] = K_{2} = K_{HO^{−}, Oxygen}                 (2)

The value of the constant K_{HO^{−}, Oxygen} is 8.2E49 at 18°,
and ‹oxygen of atmospheric pressure at this temperature should
be in equilibrium with solutions containing hydroxide-ion at a
concentration[556] of› 1.36E12.

An electrode of platinum gauze, charged with oxygen under atmospheric
pressure, when dipped into the solution of a neutral salt,
‹acquires a very strong positive charge›, the minute concentration
of hydroxide-ion, 0.9E−7, being very much smaller than the value
required by the constant, and the oxygen ionizing very much more
rapidly, in consequence, than it is formed by the discharge of
hydroxide ions (see p. 259). [p280]

When we combine the hydrogen and the oxygen electrodes, dipping
into a solution of sodium chloride, we find a current is, in fact,
established (the apparatus discussed on p. 281 is used), and it flows
in the direction anticipated from the above development, the positive
current entering the voltmeter from the oxygen electrode.[557]

The potential of the hydrogen electrode, for a constant pressure
of hydrogen, is dependent on the concentration of hydrogen-ion in
the solution surrounding the electrode, exactly as the potential of
a copper plate, against a solution of cupric-ion, depends on the
concentration, or osmotic pressure, of cupric-ion in the solution in
which the plate is immersed. The concentration of hydrogen-ion, in
the present instance, is very small (0.9E−7, at 18°), the solution
being practically neutral; but the ‹addition of an alkali› must
reduce its concentration far below even this value, since for water
the product of the concentrations of hydrogen-ion and hydroxide-ion
is a constant (p. 176) and the increase in the concentration of
hydroxide-ion, produced by the addition of alkali, must decrease the
concentration of the hydrogen-ion proportionally. We would expect,
then, that the potential of the hydrogen electrode must ‹increase›,
when we add alkali to the solution surrounding it, the hydrogen now
ionizing against a much smaller concentration of its ion. Such is in
fact the case (‹exp.›), and the increase is found to be subject to
a logarithmic function for the relation between potential and the
concentration of the ion, similar to that found to hold for copper
and its ion.[558] In the same way, the potential of the oxygen
electrode must depend on the concentration[559] of the hydroxide-ion
in the solution bathing it. The addition of a strong acid, like
sulphuric acid, to this solution, by suppressing the hydroxide-ion,
small as its concentration is, should increase the potential of the
[p281] electrode and the total potential of the cell. This, in fact,
is the case (‹exp.›); the cell working under these conditions shows
us the largest potential yet observed.[560]

 [Illustration: FIG. 14.]

 The arrangement of the apparatus and the course of the current
 are shown in Fig. 14. The glass tube of the hydrogen electrode
 is connected with a hydrogen generator, the tube of the oxygen
 electrode with a cylinder or gasometer filled with oxygen. The
 hydrogen electrode is connected with the negative post of the
 voltmeter, the oxygen electrode with the positive post. Since the
 hydrogen ionizes, under the conditions used, more rapidly than it is
 formed from the small concentration of the hydrogen ions surrounding
 the hydrogen electrode, ‹hydrogen ions pass from the electrode into
 solution A›, leaving a negative charge on the electrode; there is
 a migration of sodium ions through the salt bridge (see p. 254) to
 solution B, and the hydrogen ions formed combine with hydroxide
 ions and produce water. In a similar way, ‹oxygen passes into
 solution B in the form of hydroxide ions› and these combine with
 hydrogen ions of the sulphuric acid, forming water; SO_{4}^{2−}
 ions migrate from the solution B through the salt bridge toward
 solution A and thus prevent polarization (p. 254). While water is
 an actual product of the action of the cell, working under these
 conditions, ‹the essential feature of the oxidation of hydrogen is
 its ionization›—H_{2} → 2 H^{+}; it would be in the same condition
 of oxidation if the hydrogen ions combined with any negative ions
 other than HO^{−}, or if they remained ions (as they would, if
 sodium chloride surrounded the hydrogen electrode). Similarly, the
 essential feature of the reduction of oxygen is its ionization
 in the form of HO^{−} ions; in the present [p282] instance,
 these actually combine with hydrogen ions and form water, but the
 reduction of oxygen would also be accomplished, if the hydroxide
 ions remained ionized (as they would, if sodium chloride bathed the
 oxygen electrode). The formation of water is the result of a union
 of ions, following the oxidation-reduction reaction, which may be
 expressed in the following condensed form:

 2 H_{2} ⥂ 4 H^{+}

 2 HOH + O_{2} ⥂ 4 HO^{−}

 4 HO^{−} ⥂ 4 H_{2}O

«Summary.»—We thus find that the oxidation of hydrogen by oxygen
may be used to develop an electric current, exactly in the same
way as the other oxidation and reduction reactions, which we have
discussed, are found available for the same purpose. And at a given
temperature, the oxidation is subject to the influence of analogous
factors,—the solution-tension ‹constants, the concentrations of the
corresponding ions› in the solutions surrounding the electrodes, and
the ‹concentrations› of the ‹gases›.

«Interpretation of Oxidation-Reduction Reactions in Terms of the
Oxygen-Hydrogen Gas Cell.»—It is possible to interpret all classes
of reversible oxidations and reductions, carried out in ‹aqueous›
solutions, in terms of this so-called "oxygen-hydrogen gas cell,"
if the assumption is made that ‹each oxidizing agent›, such as
nitric acid, permanganate, dichromate, etc., ‹has a tendency to
liberate›, either from its own molecules or by its action on water,
‹oxygen of a definite concentration or pressure›, and that ‹each
reducing agent›, in turn, ‹has a tendency to liberate hydrogen›,
from water, ‹of a definite pressure or concentration›. The potential
of the oxygen-hydrogen cell is dependent on the concentrations of
the gases with which the electrodes are in contact:[561] therefore,
each oxidation and reducing agent, yielding its own characteristic
concentration of oxygen or hydrogen, respectively, would have ‹a
characteristic constant›, corresponding to the solution-tension
constants of the elements and measuring its oxidizing or reducing
power. This interpretation of oxidation-reduction reactions has
received extended attention and recognition. The study, just made,
of the oxidation of hydrogen by oxygen, sufficiently suggests the
treatment of oxidation and reduction from this viewpoint.

«Interpretation of Oxidation-Reduction Reactions in Terms of Direct
Transfers of Electric Charges.»—In the study of the [p283] oxidation
of zinc by cupric-ion, Zn ↓ + Cu^{2+} ⥂ Cu ↓ + Zn^{2+}, of the
oxidation of iodides and sulphides by ferric salts, 2 Fe^{3+} +
2 I^{−} ⥂ 2 Fe^{2+} + I_{2}, and 2 Fe^{3+} + S^{2−} ⥂ 2 Fe^{2+} + S↓,
and of similar actions, it has been possible to represent the
oxidation-reduction actions as the result of ‹direct transfers of
electric charges› between atoms and their ions.[562] In the following
discussions, the attempt will be made to interpret, in the same
terms, the oxidizing power of the most important remaining oxidizing
agents, which include such compounds as nitric, permanganic,
chromic, arsenic and similar oxygen acids. The interpretation will
avoid the assumption of the liberation of oxygen and hydrogen,
under hypothetical,[563] and, sometimes, enormous pressures, as
‹intermediate products› in the actions.

«Arsenic Acid as an Oxidizing Agent.»—Arsenic acid is occasionally
used as an oxidizing agent (‹e.g.› in the aniline-dye industry), and,
although it is not a very powerful one, its study is of theoretical
interest. If to a solution of potassium arseniate some potassium
iodide is added, practically no iodine is liberated (‹exp.›). If
dilute hydrochloric acid, in excess, is added to this mixture, iodine
is slowly liberated (‹exp.›). But the addition of concentrated
hydrochloric acid causes iodine to be liberated at once in very large
amounts (‹exp.›). We may ask in what way the [p284] addition of the
concentrated acid causes such a decided difference in the ease and
speed with which arsenic acid oxidizes the iodide-ion to free iodine
and is reduced, in turn, to arsenious acid and its derivatives.[564]

We may recall the fact that a solution of potassium arseniate, to
which dilute hydrochloric acid has been added, will remain clear
for some time when the mixture is saturated with hydrogen sulphide
(‹exp.›). If a considerable excess of concentrated hydrochloric
acid is added to this mixture, hydrogen sulphide immediately forms
a dense precipitate (‹exp.›) of arsenic ‹pentasulphide›—presumably
through the union of quinquivalent arsenic-ion with the sulphide-ion:
2 As^{5+} + 5 S^{2−} ⇄ As_{2}S_{5} ↓ (see p. 247). This behavior
suggested that arsenic acid, although a moderately strong acid, might
nevertheless be ‹somewhat amphoteric›, might have ‹slight› basic
properties, as well as its ordinary acid functions. The relation is
expressed in the equations:[565]

 3 H^{+} + AsO_{4}^{3−} ⇄ (HO)_{3}AsO

 (HO)_{3}AsO + HOH ⇄ As(OH)_{5} ⥃ As^{5+} + 5 HO^{−}.

Since oxidations by arsenic acid involve its reduction to arsenious
acid, containing ‹trivalent›,[566] in place of ‹quinquivalent
arsenic›, one might well suspect, that the ‹oxidizing component›
is the ‹quinquivalent arsenic-ion›, As^{5+}, ‹the discharge of
two of whose positive charges would cause oxidation› (‹e.g.› of
iodide-ion), exactly as the discharge of positive charges at the
positive pole of an electric current causes oxidation (p. 252):
As^{5+} + 2 I^{−} ⥂ As^{3+} + I_{2}. [p285]

In a solution of potassium arseniate, we would have only the
faintest trace of the ion As^{5+}, since the addition of an alkali
to the system, expressed in the above equations, would carry the
reversible reactions towards the left. The addition of dilute
hydrochloric acid to the system must carry the reactions towards the
right and ‹increase› the concentration of As^{5+}; the addition of
concentrated acid must increase the concentration of As^{5+} very
much more. Even if the concentration of As^{5+} remained minute, the
oxidizing power would be increased proportionally to the ‹ratio› of
the concentrations in the first and the last solutions. A millionfold
increase in concentration, even when we are dealing with very small
numbers, would imply a millionfold increase in the activity of the
solution. If, then, the ‹oxidizing component of arsenic acid› is the
‹quinquivalent ion›, As^{5+}, which would tend to discharge two of
its positive (oxidizing) charges, arsenic acid should be a much more
powerful oxidizing agent in strong acid solution than in alkaline or
neutral solutions.

We thus arrive at the conclusion that the addition of hydrochloric
acid to a mixture of arseniate and iodide may be effective, in
bringing about the reduction of the arseniate and the oxidation
of the iodide, ‹primarily because of its action on arsenic acid›,
perhaps by facilitating its ionization as a base, and that it is
not effective through any action on the iodide, for instance by
producing free hydroiodic acid, as is often assumed. This conclusion
may easily be tested with the aid of the chemometer (see p. 253):
potassium arseniate against potassium iodide gives only the faintest
possible current, barely perceptible with the aid of a very sensitive
voltmeter.[567] The addition of hydrochloric acid to the beaker
containing the potassium iodide does ‹not increase› the potential
(it rather decreases it somewhat), whereas the addition of the
concentrated acid to the potassium arseniate solution ‹produces a
most decided increase in the potential›[568] (‹exp.›). It is evident,
therefore, that the addition of the acid is primarily and directly
‹intended to increase the oxidizing power of the arsenic acid›,
rather than to increase the reducing power of the iodide. [p286]

 The more common methods of expressing oxidation-reduction reactions
 of this type are illustrated in the following equations:

 Na_{3}AsO_{4} + 2 HI ⇄ Na_{3}AsO_{3} + H_{2}O + I_{2}        (1)[569]

 and AsO_{4}^{3−} + 2 H^{+} + 2 I^{−} ⇄ AsO_{3}^{3−} +
   H_{2}O + I_{2}.                                                 (2)

 Both of these forms of expression give the net results of the
 action correctly. Neither attempts to interpret the interesting and
 important fact that the reduction of arsenic acid is facilitated
 by the presence of acids (of hydrogen-ion). It is, at least,
 also ‹permissible› to consider As^{5+} ions to be present and to
 express the oxidation-reduction reaction with the aid of this
 conception,[570] as has been done in the previous discussion. In
 the final analysis, this method seems to have the advantage of
 showing directly the changes of the valences[571] (electric charges)
 of the atoms involved in the oxidation-reduction, and it also
 expresses, clearly and definitely, the relation of the hydrogen-ion
 to the action.[571] The following case furnishes an illustration
 as to how the new point of view works out from the standpoint of
 a quantitative study of an oxidation-reduction reaction of this
 type[572]: uranyl salts, such as the sulphate UO_{2}SO_{4}, are
 oxidizing reagents, which are readily reduced, particularly in acid
 solutions, to uranous salts (‹e.g.› to the sulphate, U(SO_{4})_{2}).
 The potential of a mixture of uranyl and uranous salts is
 found[573] to depend on the action expressed in the equation
 UO_{2}^{2+} + 4 H^{+} + 2 ⊖ ⇄ U^{4+} + 2 H_{2}O. For the condition
 of equilibrium (zero potential), it follows that

 [UO_{2}^{2+}] × [H^{+}]^4 / [U^{4+}] = K_{equil.}                 (3)

 The value of this constant, at 18°, is found, by calculation,[574]
 to be approximately 1 / 10^{24}. Now, the uranyl-ion UO_{2}^{2+} may
 be assumed to have the power of ionizing, with the aid of water, to
 a very slight degree into ions U^{6+} and HO^{−}, according to

 UO_{2}^{2+} + 2 H_{2}O ⇄ U(OH)_{4}^{2+} ⥃ U^{6+} + 4 HO^{−}.      (4)

 For the ionization of an extremely weak base of this character, we
 have, further, [U^{6+}] × [HO^{-}]^4 / [UO_{2}^{2+}] = k_{base}.
 And, since [HO^{−}] = K_{HOH} / [H^{+}], we also find, by
 substitution and by solving for U^{6+},

 [U^{6+}] = [UO_{2}^{2+}] × [H^{+}]^4 × k_{base} / (K_{HOH})^4.    (5)

 [p287]

 In other words, ‹we may substitute› [U^{6+}] ‹and a constant
 factor› K_{HOH}^4 / k_{base} for [UO_{2}^{2+}] × [H^{+}]^4 in the
 first term (numerator) of the oxidation-reduction equation (3),
 derived from Luther's quantitative work. We thus obtain:

 [U^{6+}] / [U^{4+}] = K_{equil.} × k_{base} / K_{HOH}^4 = K,      (6)

 which must agree just as well with the quantitative data,[575] as
 does the original equilibrium equation (3). It follows, that we
 may write the chemical equation, for the action in acid solutions,
 simply U^{6+} ⇄ U^{4+}, exactly as we have Fe^{3+} ⇄ Fe^{2+} (p.
 269). [U^{6+}] cannot be measured, as yet, but in the analogous case
 of Fe^{3+} ⇄ Fe^{2+}, where both terms of the equilibrium equation
 are accessible to direct measurement, the experimental evidence
 distinctly favors[576] the views expressed.[577]

«Permanganic Acid, Chromic Acids, etc., as Oxidizing Agents.»—We may
extend the same views to the oxidizing power of such important agents
as permanganic, dichromic, and nitric acids. In each case we may
assume that the oxidizing component is a highly charged positive ion,
‹e.g.› in the case of KMnO_{4} a septavalent manganese-ion, Mn^{7+},
whose oxidizing power will depend on its tendency to discharge part
of its heavy positive electrical charge and whose efficiency, in
accordance with the law of equilibrium, will also be proportional
to the concentration, in which the highly charged ion is present.
Permanganate is used as a favorite oxidizing agent in the laboratory,
for instance, in the oxidation of ferrous to ferric salts in
quantitative analysis; the action proceeds quantitatively and rapidly
in acid solution, and the end of the action is recognized by the fact
that the intense pink color of the permanganate is not destroyed
(‹exp.›). [p288]

If we bring permanganate, against potassium iodide, into the beakers
of the chemometer (p. 253), we find that it is a much more vigorous
oxidizing agent than is arsenic acid, and again we find that the
addition of acid (sulphuric) to the permanganate solution enormously
increases the potential (‹exp.›) and therefore its oxidizing power.
The addition of an acid would, obviously, enormously increase the
concentration of a positive septavalent ion, if permanganic acid
is assumed to be, to a slight extent, ‹base forming› and therefore
amphoteric:

 H^{+} + MnO_{4}^{−} ⇄ (HO)MnO_{3}

 (HO)MnO_{3} + 3 HOH ⇄ Mn(OH)_{7} ⥃ Mn^{7+} + 7 OH^{−}.

Similar experiments may be made with ferrous sulphate against
permanganate.

The oxidation of ferro-ion, or of iodide-ion, may be represented,
most simply, by the equations:

 2 Mn^{7+} + 10 Fe^{2+} → 2 Mn^{2+} + 10 Fe^{3+}

and

 2 Mn^{7+} + 10 I^{−} → 2 Mn^{2+} + 5 I_{2}.

 Each heptavalent manganese ion is derived from a salt, such as
 MnX′_{7} or Mn_{2}Y″_{7}, and, consequently, when two manganese
 ions Mn^{7+} are reduced, ten univalent negative ions X′, or five
 bivalent ions Y″, are liberated and become available for salt
 formation with the ferric ions, produced, or with the hydrogen ions
 (from hydroiodic acid) set free by the oxidation of the iodide ions
 to iodine.

 Thus, the oxidation of ferrous sulphate by permanganate, in the
 presence of sulphuric acid, may be represented, in greater detail,
 by the equations:

 2 KMnO_{4} + H_{2}SO_{4} ⇄ K_{2}SO_{4} + 2 HMnO_{4}               (1)

 2 HMnO_{4} + 7 H_{2}SO_{4} ⇄ Mn_{2}(SO_{4})_{7} + 8 H_{2}O        (2)

 Mn_{2}(SO_{4})_{7} ⇄ 2 Mn^{7+} + 7 SO_{4}^{2−}    (3)

 2 Mn^{7+} + 7 SO_{4}^{2−} + 10 Fe^{2+} + 10 SO_{4}^{2−} ⇄
   2 Mn^{2+} + 1 OFe^{3+} + 17 SO_{4}^{2−}                         (4)

 ⇄ 2 MnSO_{4} + 5 Fe_{2}(SO_{4})_{3}                               (5)

Analogous results are obtained with potassium chromate or dichromate
against potassium iodide, ferrous sulphate, hydrogen sulphide, and
other reducing agents.

«Nitric Acid.»—It is characteristic of nitric acid that, ionized
as an acid, it is not a powerful oxidizing agent; that is, the
nitrate-ion, NO_{3}^{−}, is not the oxidizing component. For
instance, a nitrate, such as potassium nitrate, in aqueous
solution, does not appreciably oxidize ferro-ion or iodide-ion
(‹exp.›). Concentrated nitric acid, or a mixture of a large excess
of concentrated [p289] sulphuric acid with a nitrate, are far
more effective in oxidizing the substances mentioned, as shown by
experiments with the chemometer and with the mixtures described. It
is significant that, in concentrated nitric acid, and in the presence
of concentrated sulphuric acid, ‹the basic ionization of nitric acid›

 H^{+} + NO_{3}^{−} ⇄ (HO)NO_{2}

 (HO)NO_{2} + 2 HOH ⇄ N(OH)_{5} ⥃ N^{5+} + 5 HO^{−}

‹would be facilitated› by the high concentration of hydrogen-ion.

«Summary.»—In every instance, then, we find that it is possible to
produce an electric current by using one of these common, powerful
oxidizing agents in aqueous solution, just as it is possible with
oxygen and with the simpler agents discussed earlier. Whatever the
theory of the formation of the current, whether we are dealing, in
the last cases considered, with acids which have the capacity to
ionize minimally as bases, forming highly charged positive ions,
whose discharge involves an oxidation of the substance receiving the
discharged electricity, or whether we accept the view that oxygen
is liberated by them in exceedingly concentrated form and tends to
form in aqueous solutions the hydroxide-ion, HO^{−}, unquestionably
the closest possible relation has been established between
oxidation-reduction reactions and electrical relations, as formulated
on the basis of the theory of ionization. In all cases, at a constant
temperature, as demanded by the law of mass action, the net result of
an action will depend on ‹constant factors›, measuring the tendencies
of atoms to assume or lose electric charges (electrons), and on
‹variable factors›, the concentrations of the reacting components.

«Oxidation of Organic Compounds.»—In conclusion, it may be asked
whether ‹the oxidation of organic compounds› may also be brought
into relation with electrical charges and interpreted on the basis
of the theory which has been presented. For this purpose we may
study the oxidation of one of the simplest of organic compounds,
formaldehyde CH_{2}O, which forms the active component in solutions
of ‹formalin›. Formaldehyde is also intimately related to some
of the most important food products, the carbohydrates, whose
oxidation is utilized in the animal economy. It is formed[578]
in the green leaves of plants by the [p290] reduction of carbon
dioxide, absorbed from the atmosphere, with the aid of the energy of
the sun's light: CO_{2} + H_{2}O → CH_{2}O + O_{2}. It is readily
condensed, forming glucose (6 CH_{2}O → C_{6}H_{12}O_{6}), cane sugar
C_{12}H_{22}O_{11}, and still more complex carbohydrates, such as
starch.

Formaldehyde, like other aldehydes, is readily oxidized. A favorite
reagent, used in oxidizing it, is an ammoniacal solution of silver
nitrate (‹exp.›), the separation of silver from such a solution
being a characteristic reaction of aldehydes. The reagent is
rendered still more sensitive by the addition of sodium or potassium
hydroxide.[579] We may ask how we would interpret, from the point of
view of the electric theory of oxidation and reduction, the oxidation
of formaldehyde and the reduction of silver nitrate to silver, under
these conditions. According to the theory, the oxidizing agent in
silver nitrate is the silver-ion, the discharge of which gives
positive electricity, which the oxidized substance, the formaldehyde,
must absorb. But in a silver nitrate solution there is a far larger
concentration of the silver-ion than in an ammoniacal solution (p.
220), containing the same total concentration of silver. The complex
silver-ammonium-ion Ag(NH_{3})_{2}^{+}, it may be recalled, is a
rather stable one,[580] and, consequently, the addition of ammonia to
silver nitrate should decidedly ‹weaken› its oxidizing power. Still,
the practical use of ammonia, especially in combination with sodium
hydroxide, is found to be most effective. We are led to suspect that,
in spite of the untoward effect of ammonia on the oxidizing power of
the silver compound, an ‹alkaline› solution is desirable for the sake
of the effect of the alkali on formaldehyde, the reducing substance
involved. To follow up this conclusion, we must next consider, in
some detail, the nature of formaldehyde; we shall presently find
that the conclusion, which we have just reached, as to the probably
favorable effect of alkali on the ‹reducing power› of formaldehyde,
will be verified by experiments, which the consideration of
formaldehyde will suggest.

The oxidation of formaldehyde may most clearly be formulated on the
basis of views, developed by Nef, on the formation of methylene[581]
derivatives, containing bivalent carbon atoms. A solution [p291]
of formalin contains formaldehyde in a variety of forms, in a
very complex condition of equilibrium. Of these compounds, the
aldehyde, CH_{2}O, probably exists in two forms, which have the
same composition and molecular weight, but which differ in the
arrangement of the atoms in the molecules (in the ‹structure› of the
molecules); we probably have CH_{2}=O ⥃ CH(OH), the former of which
(CH_{2}=O) is, most likely, by far the more stable and the chief
one of these two substances, present under ordinary conditions. The
second compound CH(OH) may be present in traces only. One difference,
we note, lies in the position of one of the hydrogen atoms in the
respective molecules; the second form contains a hydroxide group
(OH), which gives it the properties of an acid and renders it capable
of forming salts CH(OMe) with bases. But the molecule of this second
form also would ‹contain a carbon atom, only two of whose valences
are satisfied› (by H and OH), two of the ordinary four valences
of a carbon atom being thus left free or ‹unsaturated›. We may
indicate the two free carbon valences in the formula =CH(OH). ‹Such
an unsaturated, bivalent carbon atom› =C ‹would be particularly
sensitive to oxidation›.[582]

Besides these two forms, a formalin solution also contains a
polymerized form, probably (CH_{2}O)_{2}, which in dilute solution,
or under the influence of heat, slowly breaks down into formaldehyde,
(CH_{2}O)_{2} ⇄ 2 CH_{2}O.

The addition of alkali to the mixture probably leads to the formation
of the salt =CH(OMe), thus disturbing all the conditions of
equilibrium and ‹leading to the transformation of a very much larger
part of the aldehyde into a compound containing the characteristic
unsaturated (bivalent) carbon›, than was originally present. The
aldehyde will thus become ‹more susceptible to oxidation› as a result
of the enormous increase in the concentration of the oxidizable
component. We may assume this to be either the salt, =CH(OMe), or
its negative ion, =CH(O^{−}), or both, or some analogous derivative.
Further, the two free valences of a bivalent carbon atom may be
considered to consist of a positive and a negative charge of
electricity, either actual or potential,[583] and ‹the oxidation›
will consist [p292] ‹primarily in the absorption of two positive
charges, from the oxidizing agent, to convert the negative charge on
the carbon atom›, say in ±CH(ONa), ‹into a positive charge›.[584]
If the oxidizing agent is alkaline silver nitrate solution, we may
formulate the successive actions as follows:

 (NaO)HC± + 2 Ag^{+} → (NaO)HC^{2+} + 2 Ag ↓.

The two positive silver ions correspond to two negative ions, ‹e.g.›
hydroxide ions HO^{−}, which are set free by the discharge of the
silver ions, and which, in turn, will combine with the oxidized
carbon atom holding the two positive charges:

 (NaO)HC^{2+} + 2 HO^{−} → (NaO)HC(OH)_{2} → (NaO)HC:O + H_{2}O.

The salt formed, HCO_{2}Na, is ‹sodium formate›, which is the first
isolated product of the oxidation of formaldehyde.

It would appear, from this point of view, that the ‹alkaline nature›
of the silver nitrate mixture is advantageous primarily because a
base is required by the formaldehyde, the reducing agent, to convert
it into some readily oxidizable form. And the proved efficiency
of the alkaline mixture (see above) makes it appear probable that
the advantage gained by this result ‹more than offsets the loss
in oxidizing power›, suffered by the silver nitrate following the
suppression of its real oxidizing component, the silver-ion, when,
in the presence of ammonia, the latter is converted largely into
the ion, Ag(NH_{3})_{2}^{+}. Ammonia, in turn, is employed in
the oxidizing mixture, essentially with the object of preventing
the precipitation of the silver-ion, as silver oxide, by the
hydroxide-ion of an alkaline mixture. These conclusions, as well
as, in particular, the ‹main conception› «that in the oxidation of
formaldehyde there is an actual transfer of electrical charges», may
be fully confirmed with the aid of the chemometer.[585]

 EXP. A small beaker, containing a platinum electrode, which is
 connected with the positive post of the voltmeter, is half filled
 with a solution of silver and sodium nitrates. A similar small
 beaker, containing a platinum electrode leading to the negative post
 of the voltmeter, is charged with a solution of sodium nitrate (to
 render the solution a good conductor) and with some formalin. The
 solutions in the two beakers are connected by means of a salt-bridge
 containing sodium nitrate. [p293]

Only a ‹very slight› current is produced under these conditions; the
potential between silver nitrate and formaldehyde is found to be
‹extremely› small. If, now, sodium hydroxide is added to the formalin
mixture, an ‹enormous increase› in potential is observed, proving,
unmistakably, that the addition of the alkali to the formalin
solution ‹enormously increases the concentration of the reacting,
oxidizable component›.[586]

When some ammonia is added to the silver nitrate mixture, we find,
as anticipated, that the ‹oxidizing power of the silver solution is
greatly reduced›, the silver-ion being converted into the complex
ion, Ag(NH_{3})_{2}^{+}; but the potential is still very much
‹greater› than the potential between silver nitrate and formalin
without any alkali—which shows that the advantage of using alkali
with the formaldehyde greatly outweighs the disadvantage of using
ammonia with the silver nitrate.

An electric current may also be readily obtained by combining
alkaline formaldehyde with other oxidizing agents—for instance with
an ‹oxygen› electrode (p. 279). We find (‹exp.›) that the oxidation
proceeds with remarkable ease under these conditions. Permanganate,
dichromate, etc., may be substituted for oxygen, with the same
general result.

«Summary.»—It is clear, then, that the oxidation of an ‹organic
substance› may readily be interpreted as consisting, ultimately, in
a transfer of electrical charges, of exactly the same nature, as is
found in the other oxidation reactions which we have considered,
[p294] and that the conditions for producing a maximum current,
as investigated with the aid of the chemometer, give us, again,
important guidance in following the course of the reactions. It is
needless to say that the oxidation of other organic compounds, such
as glucose, alcohol, etc., may be profitably studied from the same
point of view.

It also follows, from the conclusions reached, that, under proper
experimental conditions, electricity, in the form of a current,
must be capable of effecting the oxidation, or the reduction,
of organic as well as inorganic compounds (p. 252). Extended
investigations have, indeed, shown that electric currents belong to
the most important and efficient agents for this purpose, because
the oxidation, or the reduction, of the organic compound becomes
susceptible to the most exact control through the regulation of the
potentials used.[587]

 «Tables and Summaries.»—In the first table the equilibrium
 (solution-tension) constants of a number of metals and non-metallic
 elements are given. The table is followed by brief explanations of
 its meaning and a summary of some of its more important applications.

  TABLE[A] OF EQUILIBRIUM (SOLUTION-TENSION) CONSTANTS (IN MOLAR
  TERMS) AND OF POTENTIAL DIFFERENCES BETWEEN ELEMENTS AND THEIR IONS
  IN UNIMOLAR AQUEOUS SOLUTIONS.

  Element, Ion.         E.P._{El.,Ion.}   K_{Ion.}

  K, K^{+}[B]           (−2.92)           6E50
  Na, Na^{+}[C]          −2.44            2.5E42
  Ba, Ba^{2+}           (−2.54)           2.1E88
  Sr, Sr^{2+}           (−2.49)           4.0E86
  Ca, Ca^{2+}           (−2.28)           2.0E79
  Mg, Mg^{2+}           (−2.26)           4.1E78
  Al, Al^{3+}[D]         −0.999 ?         1.3E52
  Mn, Mn^{2+}            −0.798           5.7E27
  Zn, Zn^{2+}            −0.493           1.4E17
  Cd, Cd^{2+}            −0.143           9.5E4
  Fe, Fe^{2+}[E]         −0.122 ?         1.8E4
  Co, Co^{2+}[F]         +0.0138 ?        0.3314
  Ni, Ni^{2+}[G]         +0.108 ?         1.8E−4
  Sn, Sn^{2+}           <+0.085          <1.1E−3
  Pb, Pb^{2+}            +0.129           3.3E−5
  H_{2}, H^{+}[H]        +0.277           1.52E−5
  Cu, Cu^{2+}            +0.606           8.3E−22
  As, As^{+++}          <+0.570          <2.7E−30
  Bi, Bi^{3+}           <+0.668          <1.4E−35
  Sb, Sb^{3+}           <+0.743          <1.7E−39
  Hg, Hg^{+}             +1.027           1.38E−18
  Ag, Ag^{+}             +1.048           6E−19
  Pt, Pt^{4+}           <+1.140           5E−80
  Au, Au^{3+}           <+1.356          <1.8E−71
  F_{3}, F^{−}[H]       (+2.24)           9.0E88
  Cl_{2}, Cl^{−}[H]      +1.694           3.16E29
  Br_{2}, Br^{−}         +1.270           1.23E22
  I_{2}, I^{−}           +0.797 ?         7.26E13
  O_{2}, HO^{−}[I]       +0.698           1.36E12

  TABLE NOTES:

  A. The table is based on Wilsmore's compilation of solution-tension
  potentials, ‹Z. phys. Chem.›, «36», 91 (1901).

  B. Values in parentheses have been estimated by indirect
  measurements.

  C. G. N. Lewis, ‹J. Am. Chem. Soc.›, «32», 1467 (1910).

  D. Values marked with? are uncertain.

  E. Calculated from the data of Richards and Behr (‹Z. phys.
  Chem.›, «58», 301 (1907)), who found the potential of iron against
  0.5 molar FeSO_{4} to be −0.15 volt. The degree of ionization of
  0.5 molar FeSO_{4} is taken as 22%. [Λ = 25.8 (Kohlrausch and
  Holborn, ‹loc. cit.›, p. 152) and Λ_{∞} is taken as 117, as for
  ZnSO_{4} (‹ibid.›, p. 200).] On account of the doubtful value for
  the degree of ionization, the values in the table are marked?, but
  the value found by Richards and Behr appears to be quite accurate.

  F. Calculated from the data of Schildbach (‹Z. für Elektroch.›,
  «16», 967 (1910)). The same uncertainty as to the degree of
  ionization exists as that discussed in the previous footnote.

  G. Calculated from the data of E. P. Schoch (‹Am. Chem. J.›, «41»,
  208 (1909)). The same uncertainty as to the degree of ionization
  exists as that discussed in footnote 5, p. 294.

  H. The values for ‹gaseous› elements refer to the gases under one
  atmosphere pressure.

  I. The potential of oxygen at 18°, 760 mm., against an alkaline
  solution in which [HO^{−}] = 1. K_{Ion} refers to the concentration
  of HO^{−}, with which oxygen under atmospheric pressure would be
  directly in equilibrium, at 18°.

 The potential differences, given in the table, are based on the
 assumption that the ‹absolute zero› of potential is at such a
 point, that the so-called standard normal calomel electrode has
 a value of +0.56 volt relative to this zero (‹cf.› Ostwald, ‹Z.
 phys. Chem.›, «36», 97 (1901)). The exact determination of this
 value is a very difficult matter. Recently Palmaer (‹ibid.›, «59»,
 129 (1907)), located the absolute zero at a point 0.04 volt more
 positive than the above, making the absolute potential of the normal
 calomel electrode, approximately, +0.52 volt. To refer potentials,
 given in this book, to this new zero, one would subtract 0.04
 volt from all positive potentials and add 0.04 to the numbers
 representing negative potentials (‹e.g.› E. P._{Zn,Zn^{2+}} would
 become −0.569 in place of −0.529 volt). Since the ‹equilibrium
 (solution-tension) constants› are calculated from the potential
 differences referred to the absolute zero (p. 259), any change
 in the zero involves corresponding changes in the values of the
 equilibrium constants, as calculated for this book. However, it
 should be noted that all potential differences would be corrected
 by the same constant quantity (0.04 volt for Palmaer's zero): ‹all
 the equilibrium constants for univalent metallic ions would be
 increased proportionally to a constant factor› ‹c› (‹c› is very
 nearly equal to 5, for Palmaer's zero), the equilibrium constants
 for bivalent metallic ions would be increased proportionally to
 ‹c›^2, etc. ‹The equilibrium ratio› for two metals and their
 ions ‹would in no wise be changed› by these alterations: ‹e.g.›
 for the equilibrium between zinc and copper and [p296] their
 ions (p. 267), K_{equil.} = K_{Zn^{2+}} / K_{Cu^{2+}}; the
 factor ‹c›^2 would be introduced into both terms of the ratio
 and would not affect the value of the latter. For the condition
 of equilibrium between silver and copper and their ions (p. 267)
 K_{equil.} = K_{Ag^{+}}^2 / K_{Cu^{2+}}, and since (‹c›)^2 = ‹c›^2,
 this equilibrium ratio would also not be affected. For elements,
 which produce negative ions, the corresponding correction factors
 would be 1 / ‹c›, 1 / ‹c›^2, etc., and the equilibrium relations
 between two such elements and their ions likewise would remain
 unchanged. Since these ‹equilibrium relations› are the ‹significant›
 ones in this work, and since our conclusions have been based on
 them, it is clear that a change in the absolute zero would not
 affect the conclusions reached.

 On account of the uncertainty attaching to the determination of
 the absolute zero of potential, it is preferred, in practice,
 to report the experimentally determined potentials as measured
 against a constant, well-defined electrode (such as the calomel
 electrode or a hydrogen electrode) and thus to eliminate the
 variation, which a change in the determination of the zero potential
 would make necessary. However, for an elementary discussion of
 oxidation-reduction reactions, from the same viewpoint as is used
 in considering all other reversible chemical actions, the idea of
 the absolute potential has certain advantages, making a uniform
 treatment possible.

 1. ‹Meaning of K_{Ion}.› Under K_{Ion} is given, for each element,
 the ‹concentration of its ion›, with which the element would be
 directly in equilibrium at the ordinary temperature (see p. 258).
 The constants for ‹gaseous› elements represent the constants of the
 gases under atmospheric pressure.

 2. ‹The Condition for Equilibrium between Two Elements and Their
 Ions.› The condition of equilibrium in a system of two elements
 and their ions may be found with the aid of the constants K_{Ion},
 as follows: For Zn ↓ + Cu^{2+} ⥂ Zn^{2+} + Cu ↓ we have for the
 condition of equilibrium (see p. 267)

 [Zn^{2+}] / [Cu^{2+}] = K and K = K_{Zn^{2+}} / K_{Cu^{2+}} =
   1.4E17 / 8.3E−22 = 1.7E38.

 Zinc-ion must be present in enormous excess in the condition of
 equilibrium and zinc will precipitate copper from solutions of
 cupric salts until this relation is established. The ‹suppression
 of the cupric-ion›—by precipitation in the form of insoluble salts
 or by conversion into very stable complex ions—makes [Cu^{2+}]
 exceedingly small and makes it increasingly difficult for zinc to
 precipitate copper, and, under certain conditions, the ‹ordinary›
 course of the action may be ‹reversed› (p. 268).

 For Cu ↓ + 2 Ag^{+} ⥂ Cu^{2+} + 2 Ag ↓, we have (p. 267)

 [Cu^{2+}] / [Ag^{+}]^2 = K and

 K = K_{Cu^{2+}} / K_{Ag^{+}}^2 = 8.3E−22 / (6E−19)^2 = 2.3E15.

 3. ‹Potential Differences Calculated with the Aid of K_{Ion}.› For
 ‹metallic elements›, which send out ‹positive ions›, in contact with
 an aqueous solution containing the ion in concentration [C], the
 potential difference is (see p. 261)

 ε_{‹Me, Ion›^{‹v›}} = (0.0575 / ‹v›) ‹log›([C] / K_{Ion}) ‹volts›,

 [p297]

 and for elements which form negative ions (see footnote 1, p.
 261),

 ε_{‹Elem., Ion›^{‹v›}} = (−0.0575 / ‹v›) ‹log›([C] / K_{Ion}) ‹volts›.

 In these equations ‹v› represents the valence of the ion. It is
 clear that for the condition of equilibrium, in which [C] = K_{Ion},
 the potential is 0. Further, for the potential difference between
 copper and a cupric salt solution in which [Cu^{2+}] = 1, we would
 have

 ε_{Cu, Cu^{2+}} = (0.0575 / 2) log(1 / 8.3E−22) =
   21.08 × 0.0575 / 2 = +0.606 volts.

 4. ‹Meaning of E.P._{Element, Ion}.› Under E.P._{Element, Ion}
 the table gives the ‹potential difference in volts›, calculated
 for the ‹element› named and ‹an aqueous solution of its ion in
 unit concentration› (one gram-ion per liter). For instance, for
 zinc and [Zn^{2+}] = 1 (65.4 grams zinc-ion per liter), we have a
 potential E.P._{Zn, Zn^{2+}} = −0.493. The signs used, in accordance
 with the convention adopted (p. 261), indicate the ‹character of
 the charge› on the ‹element electrode› (which is named ‹first› in
 the subscript to E.P.). For instance, zinc in a solution in which
 [Zn^{2+}] = 1 would acquire a ‹negative› charge (p. 266), the
 potential difference E.P._{Zn, Zn^{2+}} being −0.493 according to
 the table; silver, immersed in a solution in which [Ag^{+}] = 1,
 would acquire a ‹positive charge›, the potential difference
 E.P._{Ag, Ag^{+}} = +1.048.

 The potentials given for the ‹gaseous› elements represent the
 potentials of the gases under 760 mm. pressure.

 5. ‹Potential Differences Calculated with the Aid of E.P._{Element,
 Ion}.› The potential corresponding to any concentration [C] of a
 ‹metal ion› may be found from the equation[1]

 ε_{El., Ion^{‹v›}} = E.P._{El., Ion} + (0.0575 / ‹v›) log[C] ‹volts›,

 and the potential for any concentration [C] of the ions of elements
 forming ‹negative ions› is found[588] according to

 ε_{El., Ion^{‹v›}} = E.P._{El., Ion} − (0.0575 / ‹v›) log[C] ‹volts›.

 6. ‹The Condition for Equilibrium between Two Metals and Their Ions,
 Calculated with the Aid of E.P._{Element, Ion}.› The condition
 for equilibrium in a system of two metals and their ions is
 determined by the fact that the potential of the system must be 0
 when equilibrium is established. We have, for instance for the two
 metals zinc and copper and their ions, Zn^{2+} and Cu^{2+}, for
 Zn ↓ + Cu^{2+} ⇄ Cu ↓ + Zn^{2+} the condition for equilibrium that
 ε_{Cu, Cu^{2+}} − ε_{Zn, Zn^{2+}} = 0. According to the equation
 given in § 5, we have, then, for the condition of equilibrium,

 E.P._{Cu, Cu^{2+}} + (0.0575 / 2) log[Cu^{2+}] − E.P._{Zn, Zn^{2+}} +
   (0.0575 / 2) log[Zn^{2+}] = 0.

 [p298]

 Then

 (0.0575 / 2) log([Zn^{2+}] / [Cu^{2+}]) =
   E.P._{Cu,Cu^{2+}} − E.P._{Zn,Zn^{2+}} = +0.606 − (−0.493) = 1.099.

 From the last relation we find log([Zn^{2+}] / [Cu^{2+}]) = 38.2261,
 and therefore, for the condition of equilibrium, [Zn^{2+}] /
 [Cu^{2+}] = 1.7E38.

 7. ‹Equilibrium Constants for Elements with Variable Concentration.›
 The concentration of a pure metal at a given temperature may be
 considered a constant, except in the case of extremely thin films
 of the metal (p. 258). The concentration of hydrogen, and of the
 non-metallic elements given in the table, is variable, and K_{Ion}
 has a definite value only when the concentration of the element
 is defined (see the preceding table, footnotes 3, 4, p. 295). For
 certain estimations the ‹equilibrium constants›, which show the
 relation between the two variables, namely the concentration of
 the element and that of its ion, are very helpful (see pp. 274 and
 275). In the following table some of the more important equilibrium
 constants of this nature are given.

  TABLE OF EQUILIBRIUM CONSTANTS.

  Element.                         K_{equil.}.

  Hydrogen:  [H^{+}]^2 : [H_{2}]     5.6E−9
  Oxygen:    [HO^{−}]^4 : [O_{2}]    8.2E49
  Chlorine:  [Cl^{−}]^2 : [Cl_{2}]   2E60
  Iodine[A]: [I^{−}]^2 : [I_{2}]     5.6E29

  TABLE NOTE:

  A. The value of the constant, as given, is only an approximate
  estimation (p. 273).

 The significance of the constants is indicated by the ratios given
 in the table. The relation of these constants to those given in
 the first table may be seen from the following illustration. For
 hydrogen we have H_{2} ⇄ 2 H^{+}. The first table tells us that
 hydrogen, at 18° under atmospheric pressure, is in equilibrium
 with its ion when the concentration of hydrogen-ion is 1.52E−5
 (under K_{Ion}). Now, a mole of hydrogen at 18° occupies
 22.4 × 291 / 273 = 23.9 liters under atmospheric pressure, and
 its concentration (per liter) is therefore 1 / 23.9 mole. Then
 equilibrium exists, when [H_{2}] = 1 / 23.9 and [H^{+}] = 1.52E−5
 and K_{equil.} = [H^{+}]^2 : [H_{2}] = (1.52E−5)^2 × 23.9 = 5.6E−9.


  FOOTNOTES:

  [553] These constants are calculated from data given in
  Wilsmore's tables (‹loc. cit.›) on the solution tension of
  hydrogen. Hydrogen, at 18° under one atmosphere pressure,
  produces a potential of ε_{H_{2}, H^{+}} = +0.277 (see p.
  261, in regard to the sign) against a solution containing
  hydrogen-ion in a concentration [H^{+}] = 1 (see the table at
  the end of this chapter). Now, there must be some concentration
  of hydrogen-ion, which we will call [C], with which hydrogen
  at 18° and 760 mm. pressure is directly in equilibrium,
  with the potential 0. For any concentration of hydrogen-ion
  [H^{+}], ‹other than› [C], a potential is produced according to
  ε_{H_{2}, H^{+}} = 0.0575 log([H^{+}] / [C]). If we insert into
  this equation the values [H^{+}] = 1 and the potential ε = +0.277,
  and if we solve the equation for [C], we find [C] = 1.52E−5.
  That is the concentration of H^{+}, with which hydrogen of
  one atmosphere pressure at 18° is directly in equilibrium.
  Since under these conditions of temperature and pressure
  [H_{2}] = 1 / 23.9 mole, we have for the condition of ‹equilibrium›
  [H^{+}]^2 / [H_{2}] = K : (1.52E−5)^2 : (1 / 23.9) = 5.55E−9 = K.

  [554] Experimentally the relations for an "oxygen electrode" are
  much more complicated than for a hydrogen electrode, as a result,
  apparently, of the oxidation of the metal (‹e.g.› platinum), with
  the aid of which the electrode is prepared. For a critical review
  and summary of the more recent results on this point, ‹vide›
  Schoch, ‹J. phys. Chem.›, «14», 665 (1910). For the purposes of
  this book it will be sufficient to limit our discussion to the
  behavior of an ideal oxygen electrode.

  [555] The bivalent oxygen ions, O^{2−}, combine with hydrogen ions
  (formed, for instance, by the ionization of water) and form the
  more stable hydroxide ions (p. 246): O^{2−} + H^{+} + HO^{−} ⇄
  2 HO^{−}, or simply, O^{2−} + H^{+} ⇄ HO^{−}. Then, [O^{2−}] ×
  [H^{+}] / [HO^{−}] = k and [O^{2−}] = k × [HO^{−}] / [H^{+}].
  But since we have [H^{+}] × [HO^{−}] = K_{HOH} for the ionization
  of water (p. 176), we also have:

   [H^{+}] = K_{HOH} / [HO^{−}] and
     [O^{2−}] = (k / K_{HOH}) × [HO^{−}]^2.

  By substituting this value for the concentration [O^{2−}] of the
  oxide-ion in equation (1), equation (2) is obtained. The constant
  K_{2} includes then the constants k and K_{HOH}.

  [556] The constants are calculated from the estimated potential
  of the oxygen-hydrogen cell, +1.231 volt, at 18°. (‹Vide›
  G. N. Lewis, ‹Z. phys. Chem.›, «55», 465 (1906); Nernst and
  Wartenberg, ‹ibid.›, «56», 534 (1906); Brönsted, ‹ibid.›,
  «65», 91 (1908); and a summary and discussion by Schoch, ‹loc.
  cit.›) At 18° oxygen, under one atmosphere pressure, gives an
  estimated potential ε_{O_{2}, HO^{−}} = +1.508 against an ‹acid›
  solution, in which the concentration of the ‹hydrogen-ion›
  [H^{+}] = 1 (see the table at the end of this chapter). Since
  at 18° [H^{+}] × [HO^{−}] = 0.81E−14, the value for [HO^{−}] in
  this acid solution is 0.81E−14. Now, for oxygen, at 18° and 760
  mm., there must be some concentration of hydroxide-ion, which we
  will call [C], at which the tendency of the oxygen to ionize is
  exactly balanced by the tendency of the hydroxide-ion to form
  oxygen—at this point the potential is 0. For any concentration
  [HO^{−}] of the hydroxide-ion, ‹other than› [C], a potential
  will exist ε_{O_{2}, HO^{−}} = 0.0575 log([C] / [HO^{−}]). Since
  for [HO^{−}] = 0.81E−14, we have a potential ε_{O_{2}, HO^{−}} =
  +1.508, these values can be introduced into the equation and
  the latter solved for [C]. We find thus [C] = 1.36E12, and
  ‹oxygen, at 18° and› 760 mm. ‹pressure, would be directly in
  equilibrium with a solution in which› [HO^{−}] = 1.36E12. At
  18° and 760 mm. pressure a liter of oxygen contains 1 / 23.9
  mole, and thus we have for the condition of equilibrium
  [HO^{−}]^4 : [O_{2}] = K : (1.36E12)^4 : (1 / 23.9) = 8.2E49 = K.

  [557] The most convenient form of electrode for this purpose
  consists (see Fig. 14) of a cylinder (about one inch long) of
  platinum gauze, which is fused to a glass tube and connected with
  a wire leading through the tube to some mercury, held in a small
  branch tube, fused into the main tube near its upper end. The gas
  is easily conducted to the platinum gauze electrode through such
  a tube. The cylinder of platinum gauze may be made by joining the
  ends of rolled gauze with pieces of molten glass. It is coated with
  platinum black.

  [558] ‹Cf.› footnote 1, p. 278.

  [559] ‹Cf.› footnote 1, p. 279.

  [560] See Ostwald, ‹Z. phys. Chem.›, «11», 521 (1893), Arrhenius,
  ‹ibid.›, «11», 805 (1893), and Nernst, ‹ibid.›, «14», 155 (1893),
  for a detailed discussion of oxygen-hydrogen gas cells. For more
  recent work, ‹vide› G. N. Lewis, ‹J. Am. Chem. Soc.›, «28», 158
  (1905), where references to other recent investigations are given.

  [561] ‹Cf.› footnote 1, p. 261, and pp. 277–279.

  [562] See pp. 42, 252, for the expression of the changes as
  ‹transfers› of ‹electrons›.

  [563] Fredenhagen, ‹Z. anorg. Chem.›, «29», 424 (1902), has
  brought interesting experimental evidence of the charging of
  an electrode with ‹gaseous oxygen›, when ferric-ion is the
  oxidizing agent in aqueous solutions. Whether the oxygen,
  which is liberated by the action of the ferric-ion on water,
  4 Fe^{3+} + 4 HO^{−} ⇄ 4 Fe^{2+} + O_{2} + 2 H_{2}O, is always ‹the
  intermediate product and the direct oxidizing agent› in aqueous
  solution, can hardly be considered decided by the experiment—it
  may well be the product of a ‹parallel action›, which must take
  place to a certain extent, according to the laws of equilibrium,
  in a system containing both Fe^{3+} and HO^{−} ions. The result
  hardly proves that oxygen must be the intermediate product in
  the ‹main action›, when ferric ions act as the oxidizing agent.
  We may consider, for instance, a solution containing an iodide
  and a ferric salt: iodide ions have a far smaller affinity for
  their negative charges (electrons) than hydroxide ions have, and,
  consequently, will transfer their negative charges (electrons)
  more readily to the ferric ions than the hydroxide ions would. The
  action, if oxygen were ‹first› liberated, would lead to the same
  ultimate result, but the observation made by Fredenhagen would not
  prove that the main action would not nevertheless go by the shorter
  direct path rather than through an intermediate formation of oxygen.

  [564] According to the theory, that arsenic acid is an oxidizing
  agent because it gives up oxygen of a definite pressure, ‹this
  pressure would be the more effective, the more completely the
  opposing hydroxide-ion is suppressed› by added acid (p. 280; see
  also p. 272, on the action of ferro-ion on silver-ion in the
  presence and in the absence of fluorides).

  [565] Only the simplest form of basic ionization of arsenic acid
  is considered. Intermediate ionization into As(OH)_{4}^{−},
  As(OH)_{3}^{2−}, etc. (see p. 249), is, of course, to be assumed in
  any complete investigation of the subject.

  [566] Arsenious acid As(OH)_{3}, or HAsO_{2}, as well as its anions
  AsO_{3}^{3−} and AsO_{2}^{−}, may have their own characteristic
  tendencies to assume positive charges and be oxidized to arsenic
  acid and its derivatives (see footnote 1, p. 270). In ‹alkaline›
  solutions these tendencies, and the potentials corresponding to
  them, might well be more important factors in determining the
  course of an action, than the tendency of As^{3+} to form As^{5+}.
  The discussion in the text, which deals primarily with acid
  solutions, does not exclude such relations.

  [567] A millivoltmeter is used for this experiment.

  [568] See footnote 1, p. 284, in regard to the interpretation of
  this experiment on the basis of the theory of liberation of oxygen
  by arsenic acid.

  [569] ‹Cf.› Smith's ‹General Inorganic Chemistry›, p. 712.

  [570] The essential feature of this point of view was first
  published by Abegg, ‹Z. anorg. Chem.›, «39», 330 (1904), and ‹Z.
  phys. Chem.›, «43», 385 (1903); ‹vide› also Stieglitz, ‹Am. Chem.
  J.›, «39», 51 (footnote) (1908), and ‹Qualitative Analysis Notes›,
  University of Chicago (1905). Abegg's view has recently received
  support from J. J. Thomson in his ‹Corpuscular Theory of Matter›,
  p. 118.

  [571] H^{+} does not change its valence (charge) in the action,
  and yet it appears as an essential component in both styles of the
  current equations for the oxidation-reduction reaction.

  [572] A somewhat similar development of these relations, for
  arsenic acid, has been found in Abegg's ‹Anorg. Chem.›, III, 3, p.
  552 (1907).

  [573] Luther and Michie, ‹Z. für Elektroch.›, «14», 826 (1908).

  [574] The calculation is based on the results obtained by Luther
  and Michie.

  [575] The proportion of UO_{2}^{2+} converted into U^{6+} would
  be so minute, that in an experimental determination of the
  concentration [UO_{2}^{2+}], the concentration [U^{6+}] would no
  doubt be a negligible quantity.

  [576] Peters, ‹Z. phys. Chem.›, «26», 193 (1898).

  [577] In other instances, the action of the hydrogen-ion in
  facilitating and accelerating chemical actions (often called its
  "catalytic effect") has been explained, in a similar fashion, as
  being based on ‹salt formation, followed by the ionization of the
  salts formed›, the ‹active› components being the ions (‹vide›,
  for instance, Bredig, ‹Z. für Elektroch.›, «9», 118 and «10»,
  586 (1904) and Stieglitz, ‹Report of the Congress of Arts and
  Sciences›, St. Louis, «4», 276 (1904) and ‹Am. Chem. J.›, «39»,
  29, 415 (1908) and later articles). In many of these cases, the
  ion concentrations of the reacting components have not yet been
  accessible to direct measurements, but the viewpoint has been
  sustained by quantitative studies of analogous reactions, which
  were selected for study, because the factors involved could be
  measured (‹cf.› Stieglitz, ‹loc. cit.›).

  [578] Usher and Priestley, ‹Proc. Roy. Soc.›, B, «77», 369 (1905);
  «78», 318 (1908).

  [579] Tollens, ‹Ber. d. chem. Ges.›, «15», 1635 (1882).

  [580] [Ag^{+}] × [NH_{3}]^2 / [Ag(NH_{3})_{2}^{+}] = 1 / 10^7.

  [581] Methylene CH_{2}, itself, has never been isolated, but
  derivatives of it are known, such as the cyanides, C(NH), C(NK)
  (see pp. 66, 237).

  [582] Potassium cyanide, =C(NK), is a powerful reducing agent (see
  p. 89).

  [583] Pp. 65, 66.

  [584] If a negative charge is an electron, a positive charge the
  absence of an electron in an atom, the bivalent carbon atom ‹loses
  two electrons›, when it is oxidized.

  [585] See Stieglitz, ‹Science›, «27», 774 (1908).

  [586] The oxidation occurs essentially in the same manner as
  described (p, 292) for the action of formaldehyde on ammoniacal
  silver solution, when they are brought together in a single vessel.
  In the present case, where the action is used to produce an
  electric current, there is a ‹migration› of ‹negative ions› into
  the formalin solution through the salt-bridge (p. 254). For every
  two silver ions discharged on the electrode in the silver nitrate
  solution, two hydroxide ions are liberated in the formaldehyde
  solution, as a result of this migration, and they combine with the
  oxidized carbon atom. The oxidation may be expressed, then, simply
  as follows:

   (NaO)HC± + 2 ⊕ + 2 HO^{−} → (NaO)HC^{2+} + 2 HO^{−} →
     (NaO)HC:O + H_{2}O.

  By comparison with the equations given on p. 292, it is evident,
  that the only difference lies in the fact that the ‹positive
  charges›, in the present case, are carried to the formaldehyde salt
  through ‹metal wires› and a ‹metal electrode›, while previously
  they were discharged ‹directly by silver ions on the formaldehyde
  salt›.

  [587] ‹Cf.› Nernst, ‹Theoretical Chemistry› (1904), p. 739, and the
  applications mentioned there.

  [588] Le Blanc, ‹Elektrochemie,› p. 215; ‹v› is the valence of the
  ion.

[p299]




 CHAPTER XVI

 «SYSTEMATIC ANALYSIS FOR ACID IONS»


The systematic analysis for acid ions is made on a plan differing in
an important particular from the systematic analysis for metal ions.
The latter, as has been seen, are divided into groups, which, by
precipitation or solution of characteristic salts, are successively
separated from subsequent groups, before the isolated groups are
analyzed. That is, in general, a group of metal ions is examined
in the absence of the ions of all other groups. Acid ions are also
divided into groups, but, as a rule, the groups are not separated
from each other for analysis. The reason for this difference in
procedure is found, chiefly, in the fact that foreign acid ions
interfere[589] to a smaller degree with the specific tests for the
ions of a group, than is the case in the analysis for metal ions.

«Grouping of Acid Ions.»—While there is general agreement, among
the most important systems of analysis, in the grouping of metal
ions, there is notable variation in the way in which acids are
grouped by different authors. We shall confine ourselves here to the
consideration of two different modes of general procedure and not
discuss differences in minor details.

If acids were present only in the form of the free acids or of their
alkali salts, the division into groups could naturally and profitably
be made to include groups, which are identified by reactions carried
out in ‹neutral› or ‹alkaline› solution, as well as by such as
are made in ‹acid› solutions. Now, cations other than the alkali
ions are liable to interfere with tests designed for alkaline or
neutral solutions. For instance, a group of acid ions, in which
the phosphate-ion is included, is characterized by the fact that
the acids form barium salts, which are soluble in acid but not in
neutral or alkaline solutions. The absence or presence of such a
group may be recognized, if no cations other than the alkali metal
ions are present, by the addition of barium chloride to the solution
and by careful neutralization of any free acid, by ammonium [p300]
hydroxide. Barium phosphate and the barium salts of the other acids
of the group will be precipitated, if their ions are present. It is
clear, however, that a number of metal ions must interfere with the
test. For instance, a solution of aluminium nitrate or of ferric
chloride, treated with barium chloride, and with ammonium hydroxide
to neutralize the acid present in the solution as a result of the
hydrolysis of the salt, would give a precipitate of aluminium
hydroxide or of ferric hydroxide, and ‹not of barium salts›. The
formation of a precipitate under these conditions evidently will not
constitute any basis whatever for reaching a conclusion as to the
presence or absence of acid ions, such as can form precipitates of
barium salts under the same circumstances.

«Systematic Analysis for Acid Ions, Based on the Removal of Metal
Ions other than the Alkali Metal Ions.»—On account of this kind of
interference, by cations other than those of the alkali group, with
a number of group and specific tests for anions, that may be made in
neutral or alkaline solutions, provision is made, in most systems of
analysis, for the removal of such ions by proper treatment of the
substance under examination with sodium carbonate. Interfering metal
ions are thereby converted into carbonates or hydroxides which are
insoluble in water, while the acids form sodium salts which pass into
solution in water. Occasionally, recourse is also taken to hydrogen
sulphide to remove ions of the arsenic and copper groups.

The treatment with sodium carbonate, while advantageous in certain
cases, is ‹not uniformly successful›[590]: it is also frequently
complicated by the presence of amphoteric bases or of organic
substances, and frequently demands treatments and tests beyond those
made with the solution thus prepared. Furthermore, if a group is
found to be present, say a group of acid ions forming barium or
calcium salts insoluble in water, but soluble in acids,[591] all
the acids of the group, which have not been found to be present or
absent in the analysis for metal ions,[592] must be specifically
[p301] tested for, ‹although they may all be absent› and the only
representative of the group present may be an ion previously found in
the analysis for metal ions.[593] Then, too, when the group is found
to be absent by the group test, more sensitive tests for some of the
acid ions of the group must still be made to insure their complete
absence.[594]

While much may be said in favor of the systematic analysis for
acid ions, based on the preparation of a solution containing only
the alkali salts of the anions, and ‹while one should be familiar
with the plan and be able to have recourse to it at will›, yet the
drawbacks mentioned suggest another basis for the analysis.

«Systematic Analysis for Acid Ions in Acid Solution.»—If the
systematic analysis for acid ions is carried out entirely in ‹acid
solutions›, interference of cations with tests for anions is rarely
met with and in those rare cases may be easily provided against.
Such a method of systematic analysis in acid solution is frequently
more direct and more convenient than a method based on the removal
of cations other than the alkali metal ions. Almost all of the most
characteristic tests for anions, as it is, are carried out in acid
solutions, and only a very few good tests, which must be made in
neutral or alkaline solution, are sacrificed by placing the emphasis
on those carried out in acid solutions. The method, on the whole,
has proved a time-saving and convenient one, without loss in the
trustworthiness of the results.

«Desirability of Experience with Both Methods.»—It is desirable to
have experience with both methods, and to learn by such experience,
when to have recourse to the one or the other method. Suggestions as
to the choice of method are given in the Laboratory Manual, p. 119.

«The Groups of Acid Ions.»—The arrangement of the acid ions into
groups, for analysis in acid solution, does not differ in any
essential respect from the arrangement based on the use of solutions
of sodium salts of the acid ions—only one group test, which must
be made in neutral solutions, is omitted when the acid solution is
used, and the individual members of this group are tested [p302]
for, specifically. As that is also very frequently necessary
when solutions of sodium salts are used, no notable sacrifice in
convenience is made.

Since the grouping for both methods of analysis may be made the same,
the following grouping of acid ions has been adopted. Only the group
characteristics are given; the members of the groups are described in
detail in the Laboratory Manual (Part III).

I. ‹Ions of Amphoteric Acids and of Related Acids.› This group
includes those acids whose amphoteric character, or whose ready
reduction by hydrogen or ammonium sulphide, leads to their being
found, or indicated, in the systematic analysis for metal ions.

II. ‹The Carbonate Group.› This group includes those acids whose
physical properties (insolubility), or the physical properties of
decomposition products of which (carbon dioxide is a decomposition
product of carbonic acid), usually lead to their discovery in the
course of the preparation of solutions or of the analysis for cations.

III. ‹The Sulphate Group.› The ‹barium salts› of this group of acid
ions are ‹insoluble in acid solution›. Barium nitrate, added to a
solution acidified with nitric acid, is the group reagent.

IV. ‹The Chloride Group.› The anions of this group form ‹silver
salts›, which are ‹insoluble in nitric acid›. Silver nitrate, added
to a solution acidified with nitric acid, is the group reagent.

V. ‹The Phosphate Group.› A test for this group, as a whole, can be
made only if cations other than the alkali metal ions are absent:
the ‹barium salts› of the acid ions of the group are ‹insoluble
in neutral›, but ‹soluble› in strongly ‹acid, solutions›. Barium
nitrate, used with a neutral solution, is the group reagent in the
absence of metal ions other than the alkali metal ions. In the
presence of other cations, the three members of the group, which
are not found in some other group,[595] namely: phosphate, borate
and fluoride ions, are tested for specifically, and the group test
omitted. Phosphate-ion is tested for in nitric acid solution, in the
same solution as is used for the tests for groups III and IV. [p303]

VI. ‹The Nitrate Group.› The salts of the acids of this group are
readily soluble in water and specific tests for the acid ions are
made; there is no group test.

VII. ‹The Group of Organic Acids.› This group need only be considered
when a test for organic matter reveals its presence.

«Applications of Physico-Chemical Principles and Theories.»—The
physico-chemical principles and theories, which have been developed
in the previous chapters, naturally apply also to the reactions by
which acid ions are identified. In many cases such characteristic
reactions are identical with reactions studied in connection with
the metal ions. For instance, the precipitation of silver chloride,
used to identify the silver-ion (reagent, chloride-ion), may be used,
with certain precautions, to identify chloride-ion as well (reagent,
silver-ion).

In the following, only a few typical and interesting applications
of the principles and theories to acid ions will be given; numerous
other applications will suggest themselves in connection with the
laboratory work on the acids.

 «Fractional Precipitation of Salts with a Common Ion.» For saturated
 solutions of silver chloride, bromide and iodide, we have, according
 to the principle of the solubility-product[596]:

 [Ag^{+}]_{1} × [Cl^{−}]_{1} = K_{AgCl} = 1E−10;

 [Ag^{+}]_{2} × [Br^{−}]_{2} = K_{AgBr} = 4E−13;

 [Ag^{+}]_{3} × [I^{−}]_{3} = K_{AgI} = 3E−16.

 For a solution saturated simultaneously with the three silver
 salts, the value of the concentration of the silver-ion is the
 same in the three solubility-products (see p. 164). Consequently,
 for such a solution, with which the three solid salts are in
 equilibrium, ‹the ratios of the concentrations of the anions› must
 be: [Cl^{−}] : [Br^{−}] : [I^{−}] = K_{AgCl} : K_{AgBr} : K_{AgI} =
 3 × 10^5 : 1300 : 1. That is, if silver nitrate is added to a
 mixture of iodides, bromides and chlorides, ‹silver iodide› must
 be precipitated first, until the concentration of bromide-ion,
 in solution, is 1300 times as great as the concentration of the
 iodide-ion left in solution. Then ‹bromide› and traces of iodide
 of silver will be precipitated, ‹until the concentration of
 chloride-ion› is 300,000 times as great as the concentration of
 iodide-ion and some 250 times as great as the concentration of the
 bromide-ion. In other words, if silver nitrate is added gradually to
 such a mixture, iodide-ion and bromide-ion will be almost completely
 removed from solution ‹before a precipitate of silver chloride can
 be in equilibrium› with the solution. This gives us a convenient and
 rapid method of detecting chlorides, if present, [p304] in more
 than small quantities, with iodides and bromides. Silver nitrate,
 a few drops at a time, is added to the solution and the mixture
 vigorously shaken after each addition. As long as a yellow (AgI)
 or yellowish (AgBr) silver salt is precipitated on the addition of
 silver nitrate to the supernatant liquid (the precipitate settles
 quickly), silver nitrate is added as before; when the color becomes
 quite pale, the solution is filtered and silver nitrate added a
 drop at a time; if a ‹pure white precipitate› results finally,
 chloride-ion is present in the mixture (‹exp.›).

 «Complex Ions.» Instances of the rôle of complex ions in the
 analysis for acid ions are numerous. One of the most interesting
 illustrations is the application of the equilibrium conditions
 for the complex silver-ammonium-ion (p. 224) to the separation of
 silver chloride, bromide and iodide. A rather more convenient and
 more sensitive method[597] for detecting the three halide ions in
 the presence of each other than the method just considered, may be
 discussed from this point of view.

 The condition of equilibrium between silver-ion, ammonia and
 silver-ammonium-ion is expressed in the relation:

 [Ag^{+}] × [NH_{3}]^2 / [Ag(NH_{3})_{2}^{+}] = K = 1 / 10^7.

 The concentration of silver-ion, which may exist in an ammoniacal
 solution, evidently must decrease rapidly with increasing
 concentrations of the free ammonia. Now, let us imagine only
 sufficient free ammonia, in solution, added to a mixture of
 silver chloride, bromide and iodide, to keep the concentration
 of silver-ion, which can exist in the solution, say at
 [Ag^{+}] = 6E−9, which is just 1 / 100th of the concentration of
 silver-ion in a saturated aqueous solution of silver bromide.
 Such a solution of ammonia, in contact with the three silver
 salts mentioned, will dissolve silver chloride, if sufficient
 is present, until [Cl^{−}] = K_{AgCl} / 6E−9 = 0.017 molar.
 At the same time, silver bromide would be dissolved until
 [Br^{−}] = K_{AgBr} / 6E−9 = 0.000,06 molar. In other words, ‹silver
 chloride could be dissolved in some quantity›, while silver bromide
 is dissolved only in traces (the ratio of [Cl^{−}] : [Br^{−}] is
 again about 250 : 1). When such an ammoniacal extract is acidified
 with nitric acid, almost pure (white) silver chloride would be
 precipitated and only traces of bromide would be lost. After the
 extraction of the chloride, an ‹increased concentration of ammonia›
 would lead, similarly, to a solution in which ‹silver bromide would
 dissolve readily› and only traces of the iodide be lost, and thus a
 separation of bromide and iodide may be effected.

 In Hagar's method, the concentration of ammonia, required to
 dissolve silver chloride with but traces of bromide, is attained by
 the use of a solution of ammonium sesqui-carbonate,[598] in which
 free ammonia is present only in small concentration, as a result
 of the hydrolysis of the salt. After the [p305] extraction of
 the chloride by this solution, the bromide is extracted with a 5%
 solution of ammonia.

 «Complex Ions of Acid Ions with Other Acids.»—In the study of
 complex ions we found that positive ions (silver, cupric, etc.) may
 form complex positive ions with ammonia[599] or complex negative
 ions with acid ions (‹e.g.› with cyanide-ion). In the study of the
 acid ions we also meet instances of complexes formed by the ‹union
 of two acids› to form a new complex acid. Ammonium phosphomolybdate,
 an important salt that is extremely useful in detecting the presence
 of phosphate-ion, is the most interesting instance of the salt of
 such an acid, which is met in elementary qualitative analysis.[600]

 Ammonium phosphomolybdate, (NH_{4})_{3}PO_{4}, 12 MoO_{3}, is the
 salt of a complex phosphomolybdic acid, formed from phosphoric
 acid, O:P(OH)_{3}, and molybdic acid, O_{2}Mo(OH)_{2}, by a loss of
 water, much as potassium dichromate is formed from potassium acid
 chromate [KO(CrO_{2})OH + HO(CrO_{2})OK ⇄ KO(CrO_{2})O(CrO_{2})OK].
 The only difference between the two actions lies in the fact that,
 in the case of the dichromate, anhydride formation occurs between
 two molecules of a single acid; in the case of the phosphomolybdate,
 anhydride formation takes place between molecules of different
 acids, and a much larger number of molecules is involved. If
 we suppose the combination between the two acids to proceed
 symmetrically,[601] we may consider the following to be the action:

 O:P(OH)_{3} + 3 [HO(MoO_{2})OH + HO(MoO_{2})OH + HO(MoO_{2})OH +
   HO(MoO_{2})OH] ⇄
   O:P[O(MoO_{2})O(MoO_{2})O(MoO_{2})O(MoO_{2})OH]_{3} + 12 H_{2}O.

 Intermediate complex acids, containing less molybdic acid, are no
 doubt formed first (the action is a relatively slow one), and the
 action proceeds until the formation of an insoluble salt leads
 to the final precipitation of all of the phosphate in this form.
 The precipitate shows the characteristic behavior of an acid
 anhydride—‹alkalies dissolve it readily› and form phosphate and
 molybdate—‹e.g.› ammonium hydroxide forms [NH_{4}]_{2}HPO_{4} and
 (NH_{4})_{2}MoO_{4} (‹exp.›). Dichromates, in a similar way, are
 converted by alkalies into chromates, an action which may readily be
 followed by the change in color (‹exp.›).

 «Oxidation and Reduction.»—While fractional precipitation of silver
 iodide, bromide and chloride, and fractional solution of the silver
 salts in ammonia are convenient methods for detecting the three
 halide ions in the presence of one another, the ‹most accurate› and
 ‹most convenient› methods for this purpose depend on the different
 sensitiveness which iodide, bromide and chloride ions exhibit
 towards ‹oxidizing› agents. Of the three halogens, iodine shows the
 smallest tendency to form its ion (see the table, p. 294), chlorine
 the greatest. ‹Vice versa›, of the three halide ions, iodide-ion
 is most readily, chloride-ion least readily, oxidized. Treatment
 with a mild oxidizing agent, such as ferric-ion [p306] (see Chap.
 XIV and Laboratory Manual under iodide-ion), suffices to oxidize
 iodide-ion to iodine: 2 Fe^{3+} + 2 I^{−} ⥂ 2 Fe^{2+} + I_{2}.
 Bromide-ion and chloride-ion are left practically unaffected
 by this agent (see Chap. XIV). A somewhat stronger oxidizing
 agent, chromic acid (or its ion Cr^{6+}, see Chap. XV), oxidizes
 bromide-ion and leaves chloride-ion practically unaffected:
 2 Cr^{6+} + 6 Br^{−} ⥂ 2 Cr^{3+} + 3 Br_{2}. This method of
 fractional oxidation forms one of the most convenient and sensitive
 methods for detecting the three halide ions in the presence of one
 another.[602]

 We shall discuss here only one other oxidation-reduction reaction,
 taken in connection with the laboratory work—the ‹oxidation of
 hydroiodic acid by exposure to the air› and the resistance to
 oxidation shown by an ‹iodide›, such as potassium iodide, under
 the same conditions. The following method of proximate analysis
 of the chief relations involved may also be used to interpret the
 contrast in the behavior of hydroiodic acid and that of hydrobromic
 or hydrochloric acid (Laboratory Manual, ‹q. v.›). In all of these
 cases the actual relations are rendered more complex in consequence
 of secondary reactions, than is indicated in the text that follows:
 it is intended only to outline the most effective of the factors
 involved and to illuminate the qualitative results observed.

 «Oxidation of Hydroiodic Acid by Air.»—The oxidation of hydroiodic
 acid, or of potassium iodide, by the oxygen of the air may be
 considered (Chapters XIV and XV) to involve primarily the action

 4 I^{−} + O_{2} + 2 HOH ⇄ 2 I_{2} + 4 HO^{−}.                     (1)

 The condition for equilibrium will be

 [I^{−}]^4 × [O_{2}] / ([I_{2}]^2 × [HO^{−}]^4) = K_{equil.}  (2)[603]

 ‹A system in which› I^{−} ‹is directly in equilibrium with› I_{2}
 (for which [I^{−}]_{1}^2 : [I_{2}]_{1} = K_{I^{−}, Iodine} = 5.6E29,
 at room temperature (p. 298)) ‹and in which, at the same time›,
 HO^{−} ‹is directly in equilibrium with› O_{2} (for which at room
 temperature [HO^{−}]_{1}^4 : [O_{2}]_{1} = K_{HO^{−}, Oxygen} =
 8.2E49 (p. 298)) ‹would also represent a condition of equilibrium
 for the› «four» ‹components›. We find thus

 K_{equil.} = K_{I^{−}, Iodine}^2 / K_{HO^{−}, Oxygen} =
   (5.6E29)^2 / (8.2E49) = 4E9.                                    (3)

 With the aid of this constant and of equation (2) we can obtain,
 at least, an approximate interpretation of the results of the
 exposure of hydroiodic acid and of potassium iodide to the
 influence of atmospheric oxygen.[604] We may [p307] calculate,
 first, what concentration of free iodine would be ‹required› to
 ‹prevent› «oxidation» of «hydroiodic acid», in molar solution,
 by the oxygen of the air, ‹i.e.› to establish equilibrium.
 We will call ‹x› that concentration of I_{2}. As hydroiodic
 acid is a very strong acid, ionized to the extent of about 80%
 in molar solution, we may, with sufficient accuracy for our
 purpose, consider it completely ionized and put [I^{−}] = 1 and
 [H^{+}] = 1. Since at 25° [H^{+}] × [HO^{−}] = 1.2E−14 (p. 104),
 we may put [HO^{−}] = 10^{−14}. The concentration of oxygen in the
 air, at room temperature, may be considered to be approximately
 [O_{2}] = (1/5) × (1 / 23.9). Inserting all these given values in
 equation (2), we have

 [I^{−}]^4 × [O_{2}] / ([I_{2}]^2 × [HO^{−}]^4) =
   1 × (1/5) × (1 / 23.9) / (‹x›^2 × (10^{−14})^4) = 4 × 10^9.     (4)

 Solving for ‹x›, we find ‹x› = 10^{22} = [I_{2}]. That is, free
 iodine of this enormous concentration would be required to prevent
 oxidation of hydroiodic acid in molar solution by the oxygen of the
 air at room temperatures. It is obvious that hydroiodic acid must be
 extremely sensitive to oxidation by exposure to air.

 One might estimate, in a similar way, the extent to which hydroiodic
 acid, of a given concentration, would be oxidized by air before
 equilibrium would be reached. The process would involve simultaneous
 changes in three factors—iodide-ion is destroyed, iodine is formed
 and hydroxide-ion increases, as the result of the neutralization
 of hydrogen-ion by the hydroxide-ion formed in the action (see
 above). The solution of the equilibrium equation is too involved for
 the elementary purposes of this discussion: it leads to the same
 qualitative conclusion as was just reached.

 «Oxidation of Potassium Iodide by Air.» We may now ask what the
 relations would be, if we used a molar solution of potassium
 iodide in place of the free acid. [I^{−}] and [O_{2}] would have
 the same value as before. The solution being originally neutral,
 [HO^{−}] would at first have the value √(1.2E−14) = 1.1E−7. But when
 potassium iodide is exposed to the air, if iodine is liberated, the
 solution becomes ‹alkaline›[605] (HO^{−} is formed according to
 equation (1)) and the concentration of HO^{−} consequently ‹grows
 continuously greater›. We will, therefore, formulate the problem as
 follows: ‹how much iodine[606] must be liberated, by oxidation of
 iodide-ion, in molar potassium iodide solution in order to establish
 equilibrium?› For every ‹two› molecules of iodine liberated,
 ‹four› HO^{−} ions are formed (equation (1)). If we call ‹y› the
 concentration of iodine at the point of equilibrium, then 2 ‹y› is
 the concentration of [HO^{−}] at that point, formed by the oxidation
 process. Inserting the given values[607] in equation (2), we have

 [I^{−}]^4 × [O_{2}] / ([I_{2}]^2 × [HO^{−}]^4) =
   1 × (1/5) × (1 / 23.9) / (‹y›^2 × (2 ‹y›)^4) = 4E9.

 [p308]

 Solving for ‹y›, we find ‹y› = 0.007. That is, in molar
 solution, about 1.4% of the iodide[608] would be oxidized (carbonic
 acid and other acids being excluded); in 5 c.c. (see Lab. Manual,
 p. 73) 9  ‹milligrams of iodine[609] would be liberated› to reach a
 condition of equilibrium.[610]

 It is thus clear that the conditions for equilibrium between a
 solution of an iodide and air would be satisfied, in the case of an
 alkali iodide, by the liberation of a mere trace of iodine, whereas,
 as was previously shown, in the case of hydrogen iodide, a very
 large proportion of iodine must be liberated before equilibrium
 could obtain. A careful comparison of the two developments shows
 that the difference in result[610] is plainly due to the higher
 oxidizing power, the higher potential of oxygen (p. 280), in acid
 solutions, containing only a minute concentration of hydroxide-ion,
 as compared with its efficiency in neutral or slightly alkaline
 solution.


  FOOTNOTES:

  [589] In the few cases when there is interference, it is provided
  against.

  [590] ‹Cf.› Fresenius, ‹Qualitative Analysis›, p. 520.

  [591] The group includes phosphate, borate, fluoride, oxalate,
  silicate, arsenite, arseniate, chromate and tartrate ions.

  [592] The ions of the amphoteric acids, arsenic and arsenious
  acids, and chromate-ion, which is reduced by hydrogen sulphide to
  chromium-ion, are found in the systematic analysis for metal ions.

  [593] The ions of the amphoteric acids, arsenic and arsenious
  acids, and chromate-ion, which is reduced by hydrogen sulphide to
  chromium-ion, are found in the systematic analysis for metal ions.

  [594] See Fresenius, ‹loc. cit.›, p. 511, footnote, and p. 520.

  [595] Other acid ions which would show the group test—precipitation
  of a barium salt in a neutral solution—are determined in other
  groups, as follows: arsenite, arseniate and chromate ions in the
  group of amphoteric acids, etc. (I); carbonate and silicate ions
  in the carbonate group (II); and oxalate and tartrate ions in the
  group of organic acids (VII).

  [596] The constants refer to 18°. The subindices are used to
  distinguish the (unequal) concentrations of the silver-ion and of
  the halide ions in the different solutions referred to in the text.

  [597] Hagar's method. See Fresenius, ‹loc. cit.›, pp. 356 and 378.

  [598] See Fresenius, ‹loc. cit.›, pp. 356 and 378, for the
  preparation of the solution and for details of the method, and see
  Smith, ‹General Inorganic Chemistry›, p. 566, as to the nature of
  the sesqui-carbonate.

  [599] They also form complex ions with substances related to
  ammonia, such as the organic amines.

  [600] Ammonium arsenomolybdate is an analogous salt (see Laboratory
  Manual, Part III). A similar complex acid, phosphotungstic acid, is
  used in alkaloidal analysis.

  [601] The exact structure of the complex acid is not known.

  [602] In the Laboratory Manual a second, similar method is also
  given.

  [603] It is considered that water has a constant concentration
  in a dilute solution and that for its active components
  [H^{+}] × [HO^{−}] is a constant (p. 176).

  [604] In the calculation which follows, which is meant merely
  for a rough survey, no account is taken of the formation of
  complex ions I_{3}^{−}, or of the tendency of hydroiodic
  acid to decompose spontaneously into iodine and hydrogen:
  2 H^{+} + 2 I^{−} ⇄ H_{2} + I_{2}, a reaction which could also be
  studied profitably with the aid of the equilibrium constants for
  I_{2} ⇄ 2 I^{−} and for H_{2} ⇄ 2 H^{+}. The value of the iodide
  constant is also uncertain (see p. 273).

  [605] 4 K^{+} + 4 I^{−} + O_{2} + 2 HOH ⇄ 2 I_{2} + 4 K^{+} +
  4 HO^{−}.

  [606] The formation of complex ions I_{3}^{−} and other secondary
  reactions (formation of hypoiodite, iodate, etc.) are ignored.

  [607] ‹y› has so small a value that we may consider [I^{−}]
  ‹practically› unchanged.

  [608] 0.007 I_{2} = 0.014 I^{−}.

  [609] A mole of I_{2} = 2 × 127 = 254 grams;
  (0.007 × 254 × 5) / 1000 = 0.009 gram.

  [610] The tendency of iodine to form hypoiodous acid, iodates,
  etc., is not taken into consideration here and involves another
  relation.




 INDEX

 Numbers marked (†) refer to subjects illustrated by experiments,
 «heavy» numbers refer to tables.


 Acetic acid, 98, 101†, 111–114†

 Acid ions, systematic analysis for, 299 ‹et seq.›
   groups of, 301

 Acids, 81, «82», 100, «104»

 Acid salts, 103

 Alkali group, 158, 159

 Alkaline earth group, 158, 162

 Aluminate-ion, 172

 Aluminium group, 158, 188 ‹et seq.›, 195

 Aluminium hydroxide, 171 ‹et seq.›, 196

 Aluminium-ion, 158, 172, 188 ‹et seq.›

 Ammonia, complex ions of, 216 ‹et seq.›, 224
   ionization of, 87

 Ammonium hydroxide, conductivity of, 77
   dissociation of, 160
   ionization of, 78†, 114
   strength as base, 78†, 79†, 168†

 Ammonium-ion, 161

 Ammonium salts, dissociation of, 34†, 159
   effect on ammonium hydroxide, 168†

 Amphoteric acids, group of, 302

 Amphoteric hydroxides, 171 ‹et seq.›, 187, 188, 196

 Antimony, ions of, 174

 Argenticyanide-ion, 225

 Arrhenius's theory of ionization, ‹see› Ionization

 Arsenic acid, 247, 250, 283

 Arsenic group, 158, 210, 242 ‹et seq.›

 Arsenic, ions of, 158, 174, 242 ‹et seq.›

 Arsenic pentasulphide, 247

 Arsenious sulphide, colloidal, 125†

 Association, 19, 64

 Aurocyanide-ion, 232

 Avogadro's hypothesis, 33, 34

 Avogadro-van 't Hoff Hypothesis, 15, «37»

 Azolitmin, «79»


 Barium carbonate, as reagent, 193

 Barium-ion, 162

 Bases, 79†, «81», 105, «106»

 Basic salts, 106, 194

 Bismuth-ion, 158

 Boiling-point, 17, 36, 38

 Borates, hydrolysis of, 90†

 Bromine, 252†


 Cadmium-ion, 158
   complex ions of, 224, 228†
   sulphide, 209† ‹et seq.›

 Calcium-ion, 162

 Carbonate group, 302

 Carbonic acid, 90, 100

 Chemical activity of ions, 72†, 78†, 87†, 232
   of acids, 81, «82», 105†
   of bases, 79†, «81»
   of molecules, 74, 83, 232
   of salts, 74†, 107, 116†

 Chemical equilibrium, 90 ‹et seq.›, 96†
   and direction of action, 112
   and path of action, 235
   and physical equilibrium, 139 ‹et seq.›
   of electrolytes, 98, 111–115†

 Chemical equilibrium, law of, 91, 94
   and ionization of strong electrolytes, 108
   factors of, 95† ‹et seq.›
   limitations to, 95

 Chemometer, 253

 Chloride group, 302

 Chloride-ion, oxidation of, 275, 276†

 Chlorine, 46, 252†, 275

 Chromium-ion, 158, 188 ‹et seq.›

 Chromic acid, 287

 Cobalt-ion, 158, 192

 Cobalticyanide-ion, 229

 Cobalt sulphide, 192

 Colloidal condition, 125† ‹et seq.›
   definition of, 130
   relations to analysis, 131, 136†
   solution theory of, «128»
   suspension theory of, 129

 Colloids, electric charges on, 131†
   precipitation of, 133†
   protective action of, 136, 137†

 Complex ions, 88, 216 ‹et seq.›
   applications in analysis, 220†, 230†
   of acid ions, 305
   of ammonia, 216† ‹et seq.›
   of cyanide-ion, 225† ‹et seq.›
   of halide ions, 237
   of oxide-ion, 238
   of sulphide-ion, 238, 246
   organic, 238†

 Concentration, definition of, 91

 Conductivity, 44†, 46, 47†, 49, 51, 56
   partial, ‹see› Mobilities

 Copper, equilibrium with cupric-ion, 258, 264†
   oxidation of, 257† ‹et seq.›
   solution-tension of, 259†

 Copper group, 158, 199 ‹et seq.›, 210, 216 ‹et seq.›

 Cupric-ion, complex ions of, 224†
   equilibrium with copper, 258, 264†
   reduction of, 257†
   sulphide, 212

 Cuprous-ion, complex ions of, 228†

 Cyanide-ion, complex ions of, 88†, 225† ‹et seq.›, 232


 Dialysis, 128

 Dielectric constants, 62, «63»

 Diffusion, of gases, 29†
   of ions, 59†
   of solutes, 9†

 Dissociation of complex ions, 219†
   electrolytic, ‹see› Ionization
   gaseous, 34†, 36, 96†

 Dry salts, 74†


 Electrolysis, 46, 58

 Electrolytes, ‹see› Ionogens

 Electron theory, 42

 Equilibrium, ‹see also› Chemical equilibrium and
       Physical equilibrium
   constants, «95», «98», 233, 236, «298»
   oxidation and reduction, 258, 265 ‹et seq.›, 267†, 273 ‹et seq.›


 Faraday's law, 58

 Ferric hydroxide, 127†, 170†

 Ferric-ion, 88†, 251†, 252†, 269†

 Ferricyanide-ion, 88†, 230†

 Ferrocyanide-ion, 88†, 230†

 Ferrous-ion, 88†, 251†, 252†, 269†

 Formaldehyde, 289† ‹et seq.›

 Fractional oxidation, 305, 306

 Fractional precipitation, 163, 165†, 303

 Fractional solution, 304

 Freezing-point, 17, 36, 38

 Fused salts, 75†


 Gold, 158, 242 ‹et seq.›
   colloidal, 126†
   ‹see also› Aurocyanide-ion

 Groups of metal ions, 157

 Groups of acid ions, 301


 Heat, 75, 76†

 Heterogeneous equilibrium, ‹see› Physical equilibrium

 Hydrogen, oxidation of, 277, 278, 280†

 Hydrogen chloride, 34, 37, 42, 72†, 73, 84

 Hydrogen-ion, action on indicators, 79, 105†
   chemical activity, 72–74†, 81, «82», 278 ‹et seq.›
   concentration for precipitation by H_{2}S, 213
   mobility, 54†, 56

 Hydrogen sulphide, ionization of, 199, 245
   oxidation of, 251†, 254†
   precipitation by, 90†, 199† ‹et seq.›, 203†

 Hydrol, 175

 Hydrolysis of salts, 127, 178† ‹et seq.›, 190†

 Hydroxide-ion, action on indicators, 78†, 79
   chemical activity, 79, «81», 168†
   mobility, 54†, «56»


 Indicators, «79», 165, 214

 Instability constants, 219, 224, 226

 Iodide-ion, 88†, 272†, 305

 Iodine, 273, 305

 Ionization and chemical activity, 69, 72†, 79†, 90† ‹et seq.›, 116†,
 232
   and conductivity, 44†, 77†, 115†
   and dielectric constants, 62–«64»
   and electron theory, 42
   and Faraday's law, 58
   and osmotic pressure, 67
   and solvents, 61
   constants, 98, 100, «104», «106», «108»
   degree of, 50
   exceptional, of certain salts, 115†
   in stages, 100, 102†
   of acids, 69, 98, 100, «104», 108
   of bases, 69, 105, «106», 108
   of colloids, 132
   of salts, 69†, 74†, 75†, 107, «108», 115†
   theory of Arrhenius, 40, 41, 51
   theory of Clausius, 51

 Ionogens, 69

 Ion-product, ‹see› Solubility-product

 Ions, 42
   charges on, 41, 58
   combination with solvents, 42, 65
   composition of, 69†, 89†
   migration of, 45†, 53, 54†
   mobilities of, «56»


 Kinetic theory, of gases, 26
   and osmotic pressure, 26


 Lead-ion, 158
   sulphide, 212, 213

 Light, 76

 Litmus, «79»


 Magnesium hydroxide, 168†

 Magnesium-ion, 162

 Manganous-ion, 158

 Mass action, law of, 93, 96†

 Mercuric chloride, 57†, 115†

 Mercuric cyanide, 115†, 116†, 231†

 Mercuric-ion, 158, 257

 Mercurous-ion, 158

 Mercury, 257

 Methyl orange, «79»

 Methyl violet, 213

 Mobilities of ions, 53†, «56»

 Molecular weights, 33, 36, «37»


 Nernst's formula, 261 ‹et seq.›, 296 ‹et seq.›

 Nickel-ion, 158
   cyanide-ion, 229
   sulphide, 192

 Nitrate group, 302

 Nitric acid, 288†


 Organic acids, group of, 302

 Organic substances, complex ions of, 238
   oxidation of, 289† ‹et seq.›

 Osmosis, 10†, 22, 24†

 Osmotic pressure, 8† ‹et seq.›
   and ionization, 40, 67
   definition of, 10
   indirect determination of, 16
   laws of, «12–20»
   measurement of, 10
   theories of, 32

 Oxalates, complex ions of, 241†

 Oxidation, 251† ‹et seq.›, 282† ‹et seq.›
   by electric current, 252†
   definition of, 251
   of organic compounds, 289†
   production of current by, 253†
   relation to theory of ionization, 251† ‹et seq.›

 Oxidation-reduction, reversibility of, 256†, 268† ‹et seq.›
   interpretations of, 251, 282, 286

 Oxygen, oxidation by, 277, 278, 280†, 305

 Oxygen-hydrogen cell, 280†


 Permanganic acid, 287†

 Perpetuum mobile, 12

 Phases, 118

 Phenolphthaleïn, «79»

 Phosphate group, 302

 Phosphomolybdates, 305

 Phosphoric acid, 102†, 134

 Physical equilibrium, 118† ‹et seq.›
   and chemical equilibrium, 139 ‹et seq.›
   applications of law of, 120
   law of, 118

 Platinum, 158, 242 ‹et seq.›

 Potassium hydroxide, 77†−81†, «106»

 Potassium-ion, 158, 161

 Potential differences, 261 ‹et seq.›
   and concentrations, 261, 263†
   and osmotic pressures, 261
   sign of, 261

 Precipitates, ‹see also› Precipitation
   solution of, 151†
   washing of, 148

 Precipitation, 122†, 145† ‹et seq.›
   and ionization, 74†, 90, 152†, 220 ‹et seq.›
   fractional, 163, 165†
   influence of a common ion, 144†, «146», «147»
   influence of electrolytes, 144†, 150†
   of electrolytes, 145†

 Primary ionization, 101, 102†

 Purple of Cassius, 126†, 134†


 Reduction, ‹see also› Oxidation
   by electric current, 252†
   definition of, 252
   interpretations of, 251, 282, 286
   production of current by, 253†


 Salt-effect, 82, 109, 110†

 Secondary ionization, 101, 102†, 246

 Silver, colloidal, 127†

 Silver-ammonium-ion, 217 ‹et seq.›

 Silver bromide, 224, 303

 Silver chloride, colloidal, 138†
   precipitation of, 150
   solubility of, 221

 Silver chromate, 141, 165†

 Silver group, 157, 199 ‹et seq.›, 216 ‹et seq.›

 Silver iodide, 224, 303

 Silver-ion, 158
   as oxidizing agent, 290†
   complex ions of, 216†, 225†

 Sodium hydroxide, «81», «106», 173

 Sodium-ion, 158, 161

 Solubility, 121, 123, «146», «147», 153, «155»

 Solubility-product principle, 141 ‹et seq.›
   applications of, 145†, 147, 149, 151
   derivation of, 139 ‹et seq.›

 Solution, theories of, 8, 32

 Solution of electrolytes, 151

 Solutions, concentrated, 15, 32, 142
   dilute, ‹see› Osmotic pressure
   non-aqueous, 62, 73†, 84
   supersaturated, 121†

 Solution-tension, electrolytic, 258 ‹et seq.›
   constants, 259, 266, «294», «295»

 Solvents and ionization, 61, «64»
   and solubility of electrolytes, 154, «155»

 Strength of acids, «104»

 Strength of bases, 78†, «106»

 Strontium-ion, 158, 162

 Sulphate group, 302

 Sulphide-ion, complex ions of, 238, 246
   concentration of, «202»
   oxidation of, 251†, 254†

 Sulphides, precipitation of, 199†, 203† ‹et seq.›
   solubilities of, 203 ‹et seq.›, 212

 Sulpho-acids, 244 ‹et seq.›

 Sulpho-bases, 244† ‹et seq.›

 Sulpho-salts, 243 ‹et seq.›

 Sulphuric acid, ionization of, 103†

 Supersaturation, 121†

 Systematic analysis, of metal ions, 157 ‹et seq.›
   of acid ions, 299 ‹et seq.›


 Tartaric acid, complex ions of, 238†

 Tin, ions of, 158, 174, 242 ‹et seq.›


 Unsaturated compounds, 64

 Uranyl salts, 286


 Valence, 59
   and precipitating power of ions, 135

 Van 't Hoff's hypothesis, ‹see› Avogadro

 Van 't Hoff's theory of solution, 12 ‹et seq.›
   apparent exceptions to, 18

 Vapor tension, 17, 36, 38

 Velocity of action, 92


 Water, ‹see also› Hydrolysis
   composition of, 175
   dielectric constant of, 63
   formation by electrolytic oxidation, 280, 282†
   ionization by, 37, 41, 47†, 61, 73†, 74†
   ionization of, 53, «104», «106», 176 ‹et seq.›
   oxonium ions of, 238
   secondary ionization of, 246, 278


 Zinc, 257†, 266†

 Zinc group, 158, 188 ‹et seq.›, 210

 Zinc-ion, 266

 Zinc sulphide, 204† ‹et seq.›




TRANSCRIBER'S NOTE.


Original printed spelling and grammar is generally retained.
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mathematical and chemical formulas and equations were modified in
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