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

NEW YORK THE CENTURY CO. 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

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.

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 Fig. 1. 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

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.

Fig. 2.

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.

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 Frazer8 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 measured9 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.

Space does not permit the presentation of all the details of the evidence confirming this conclusion, but some of the most direct experimental proofs14 will be considered. [p013]

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

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

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.

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:

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.

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.

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

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 Tammann31 has realized such membranes by the use of zeolites—silicates, which hold water of crystallization but are insoluble in water. Kahlenberg32 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.

Fig. 5.

Fig. 6.

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 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 u²). 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 mass40 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.

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 u² on the surface, and the n / 3 molecules moving in the same direction will exert a force n / 3 × m u² 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 u² / (1 − b), where b represents the volume actually occupied by the molecules in 1 c.c. of the gas.43

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

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 weights49 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 formulæ51 HCl, H₂O, NH₃ and CH₄, 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, CH₃Cl, a dichloride, CH₂Cl₂, a trichloride (chloroform), CHCl₃, and a tetrachloride, CCl₄. Water, by proper treatment, may be converted in successive stages into alcohol, (C₂H₅)OH, and then into ether, (C₂H₅)O(C₂H₅), or into sodium hydroxide, NaOH, and sodium oxide, Na₂O.

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 NH₃ + HCl → NH₄Cl, 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.

The gaseous dissociation of other ammonium salts, of phosphorus pentachloride and pentabromide (PX₅ ⇄ PX₃ + X₂), 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

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:

Further, the molecular weight of glucose is found in aqueous solutions to be 180, conforming to the formula C₆H₁₂O₆, 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 ZnCl₂ 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, hcl, 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 h₂, 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.

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 developed62 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.

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 ions64 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 ZnCl₂ ⇄ Zn²⁺ + 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⁺(H₂O)_x and Cl⁻(H₂O)_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.

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 particles69 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^-εCl^+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 have71: NaCl is Na⁺Cl⁻. Similarly we have in hydrogen chloride H^-εCl^+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, Me²⁺ (e.g. Zn²⁺, Fe²⁺, etc.), or trivalent ions, Me³⁺ (e.g. Bi³⁺, Fe³⁺), and so forth. Similarly, atoms of the so-called negative elements may assume two or more electrons, forming bivalent ions, X²⁻ (e.g. S²⁻), and so forth.

Fig. 8.

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

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:

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.

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 mole81 (36.5 grams HCl) at infinite dilution, as deduced from the curve of conductivities at finite dilutions, is 384 reciprocal ohms.82

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.

Clausius84 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 Whetham85 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 of 1 c.c.	Concentration	Conductivity ───────────── 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 Hoff87 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.

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 ∪-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 molecules89 of ionized acid in each half). A measured current is passed through the solution, say, sufficient to liberate 3 molecules of hydrogen H₂, and 3 of chlorine Cl₂, 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.

Fig. 11.

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 table90 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	NO3: 60.8
(NH4): 64.2	OH: 174.0	C2H3O2: 33.7
Ag: 55.7	Cl: 65.9	½ SO4: 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_HgCl2 = 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]

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."

Solvents which cause ionization only to a minimal extent are benzene (C₆H₆), 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. Thomson101 and Nernst102 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]

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.

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 H₂O, 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 H₂O but consists of more complex molecules (H₂O)_n. According to the most recent investigations,111 while steam is H₂O, or monohydrol, ice is trihydrol (H₂O)₃, and liquid water, at ordinary temperatures, a mixture consisting chiefly of dihydrol (H₂O)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.

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 CaCl₂ ⇄ Ca²⁺ + 2 Cl⁻, would give a minimum, not of one-half the formula weight, but of one-third, viz., (Ca²⁺ + 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, Na₆(C₁₂O₁₂), 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, (C₁₂O₁₂)Na₆ ⇄ 6 Na⁺ + (C₁₂O₁₂)⁶⁻.

Loomis119 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 HNO₃, etc., when 0.01 molar aqueous solutions were used. For similar solutions of calcium chloride CaCl₂, magnesium chloride MgCl₂, and sodium sulphate Na₂SO₄, 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″X₂ and Me₂′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 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 ion122). Thus, sodium chloride, nitrate, sulphate, phosphate yield the sodium-ion, Na⁺, and the chloride (Cl⁻), nitrate (NO₃⁻), sulphate (SO₄²⁻), or phosphate (PO₄³⁻) ions; cupric nitrate Cu(NO₃)₂ dissociates into the cupric ion (Cu²⁺) and the nitrate ion, calcium sulphate CaSO₄ into the calcium-ion (Ca²⁺) and the sulphate-ion, aluminium sulphate Al₂(SO₄)₃ into the aluminium-ion (Al³⁺) 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, NO₃⁻, the nitrogen atom carrying all of the oxygen atoms with it in the negative ion?

Fig. 13.

The composition of the ions of a salt can be determined experimentally123 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 NO₃⁻, but let us say into positive ions NaO⁺ and negative ions NO₂⁻, 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 NO₂⁻, 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 NO₂⁻), as there are hydrogen ions, the solution showing no excess of free electricity at any point. Now, if NO₂⁻ 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 NO₂⁻ combining to form nitrous acid, HNO₂. 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, HNO₃, resulting obviously from the presence in space P of both hydrogen ions and nitrate ions, NO₃⁻, 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 NO₃⁻ and not, say, NO₂⁻. 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.

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 ammonia125 or act upon dry calcium carbonate126 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] electricity127 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

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 dioxide129 (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.

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.

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.

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 solutions136:

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 water138 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 [p080] 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,

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:

For ammonium hydroxide we have similarly,

Now, Arrhenius140 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.

Chemical Activity of Acids and Their Ionization.A

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]

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.

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, K₄Fe(CN)₆, precipitates ferric ferrocyanide, Fe₄[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 K₃Fe(CN)₆ precipitates ferro-ferricyanide Fe₃[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 solution163; 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, Fe³⁺ and Fe²⁺, respectively,—but potassium ferrocyanide ionizes into potassium ions and the negative ferrocyanide ions Fe(CN)₆⁴⁻, and shows the actions of ferrous ions as little as chlorate ions ClO₃⁻ exhibit the reactions of chloride ions Cl⁻. Potassium ferricyanide, in turn, gives rise to trivalent, negative ferricyanide ions Fe(CN)₆³⁻ 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:

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⁺ + CO₃²⁻ + Ba²⁺ + 2 Cl⁻ → BaCO₃ ↓ + 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, CO₃²⁻. 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.), Zn²⁺ + SO₄²⁻ + 2 H⁺ + S²⁻ → ZnS ↓ + 2 H⁺ + SO₄²⁻; 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.

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.

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] and [D] are used to represent the concentrations166 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 number168 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

where k₁ 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 k₁ × [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, v₁ of the action for any concentrations, [A] and [B], of A and B at any moment at a given temperature, we have

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 moment169 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 concentrations171 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

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, k₂, and, at any given moment, proportional also to their respective concentrations at that moment:

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, v₁ must be equal to v₂ and therefore

or

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 ⇄ H₂ + I₂. A condition of equilibrium is reached, at a given temperature when

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, I₂ or H₂. [p095]

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).

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):

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

For the condition of equilibrium in the two cases we have

The intensity of the color of the bromine vapor shows that the concentration of bromine, [Br₂]″, in the PCl₃Br₂ tube, is greater than the corresponding concentration, [Br₂]′, in the PBr₅ tube. As a molecule of pentahalide PX₅ dissociates into one molecule of PX₃ and one molecule of X₂, [PCl₃] equals [Br₂]″ and is greater than [PBr₃], which is equal to [Br₂]′. Further, more of the pentabromide than of the trichlordibromide must be left undecomposed, i.e. [PCl₃Br₂] is smaller than PBr₅. 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, k₂ must be greater than k₁. 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:

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

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.

The concentration of the free bromine, ([Br₂]′ − x), under the new conditions of equilibrium, is smaller than the original concentration [Br₂]′—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.

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, [CH₃CO₂⁻], is the same. The concentration of the non-ionized acetic acid, [CH₃CO₂H], is 0.1 × 0.9866. If these values are inserted in the equation for the condition of equilibrium, we have

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⁺] × [CH₃CO₂⁻] / [CH₃CO₂H] 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 [CH₃CO₂⁻] = 0.01 × 0.0417 and [CH₃CO₂H] = 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 table180 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.

It is evident, that a constant value is found for the ratio [H⁺] × [CH₃CO₂⁻] / [CH₃CO₂H] 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.

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.

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 HCO₃⁻, according to H₂CO₃ ⇄ H⁺ + HCO₃⁻.

For this reversible reaction we have184

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

The acid carbonate-ion HCO₃⁻, in turn, is ionized to a certain extent, producing another hydrogen ion and the carbonate-ion, CO₃²⁻. We have HCO₃⁻ ⇄ H⁺ + CO₃²⁻, and

The value of this constant186, 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

or

This is equation (1), derived originally by the application of the law of mass action to the relation between the carbonate-ion, CO₃²⁻, the hydrogen-ion, and carbonic acid, H₂CO₃.

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⁺ + CO₃²⁻ ⇄ H₂CO₃), 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, HCO₃⁻, will be proportional to the (total) concentration of the hydrogen ions; the product, HCO₃⁻, to form H₂CO₃, 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 CO₃²⁻ into H₂CO₃ 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).

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-ion191 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 ConstantsA of Bases

While the constants of a large number of organic bases194 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

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 ionization215 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

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:

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

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

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

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) when217 [CH₃CO₂⁻] = 0.53, [H⁺] = 0.000,034 and [CH₃CO₂H] = 0.999,966. If we use two characteristic places in the decimals, we have

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 follows218:

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 bases220—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:

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 weaker222—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.

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 soluble225 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.

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

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 S₁ ⇄ S₂, 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:

The bracketed symbols denote concentrations.

It should be noted that the condition of equilibrium is independent of the total quantity227 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 v₁ = k₁. 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 k₁.

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, v₂, of the bromine into the water is also proportional to a characteristic constant, k₂, and to the concentration of the bromine in the chloroform [Br]_ch.. We have, therefore v₂ = [Br]_ch. × k₂.

Equilibrium between the two solutions will be reached when

from which follows that230 for the condition of equilibrium

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, [CHCl₃]_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, [O₂]_gas : [O₂]_solut. = k.

If the oxygen is under a given pressure at a definite temperature, its concentration [O₂]_gas is fixed, and consequently the second term, [O₂]_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

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, [C₁₂H₂₂O₁₁]_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.)

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

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 As₂O₃ + 3 H₂S ⇄ As₂S₃ + 3 H₂O. 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.

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

The following measurements of osmotic pressures may be given:246

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 types254 of such mixtures. [p131]

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 (As₂S₃, As₂S₅, 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.

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 removes289 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 precipitate290 of silver chloride, the reaction which is used to determine the presence of the silver-ion in systematic analysis.

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.

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:

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

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

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

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

for a saturated solution of silver acetate in water at the given temperature. Now, since the concentration of the nonionized silver acetate, [CH₃COOAg], 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,

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.

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 [CH₃COOAg], 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, [CH₃COO⁻] × [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 classes297 of salts (e.g. Me₂X, MeY₂, etc.), for which the first equation has a different form; for instance, for Me₂X,

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.

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:

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:

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. [CH₃COO⁻] × y [Ag⁺] > K_S.P., and precipitation results. Silver acetate therefore crystallizes out, until

In passing, we may ask what the approximate loss of dissolved nonionized barium sulphate would amount to. The value of the ratio ([Ba²⁺] × [SO₄²⁻]) : [BaSO₄], 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.

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, K₃Co(NO₂)₆, which is used in the separation of cobalt from nickel, is washed313 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.

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.).

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 questions318 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.

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.

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.

Pb²⁺ (the chloride is somewhat soluble), Ag⁺, Hg⁺.

The Copper Group.—Hg²⁺, (Pb²⁺), Bi³⁺, Cu²⁺, Cd²⁺.

The Arsenic Group.—As³⁺, As⁵⁺, Sb³⁺, Sb⁵⁺, Sn²⁺, Sn⁴⁺, Pt²⁺, Pt⁴⁺, Au⁺, Au³⁺.

The Aluminium Group.—Fe³⁺, Al³⁺, Cr³⁺.

The Zinc Group.—Fe²⁺, Ni²⁺, Co²⁺, Mn²⁺, Zn²⁺.

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 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, NH₄X, decompose more or less readily into ammonia and the free acids,328 according to the reversible reaction,

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, NH₄OH ⇄ NH₃ + HOH.

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 K₂PtCl₆, precipitated by the addition of chloroplatinic acid H₂PtCl₆ to concentrated solutions of potassium salts, gives very satisfactory results, both in qualitative and in quantitative work. The acid tartrate, KHC₄H₄O₆, the picrate, KC₆H₂N₃O₇, and the cobaltinitrite, K₃Co(NO₂)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, Na₂H₂Sb₂O₇, 6 aq., is sufficiently difficultly soluble and characteristic to be used as a means of identifying sodium-ion.

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.

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,

and for a saturated solution of strontium sulphate, we have similarly336

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

New symbols, [Ba²⁺]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, [SO₄²⁻]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,

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 Ag₂CrO₄ is an intensely red precipitate, that is rather difficultly soluble in water (exp.); a liter of water dissolves338 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 Ag₂CrO₄), 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.

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

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

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 MgCl₂,NH₄Cl. 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 MgCl₃, then the corresponding double salts of magnesium chloride with potassium and sodium chloride (e.g. MgCl₂,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.

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.

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.

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 aluminate354 and hydrogen ions, characteristic ions of an acid:

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, O₂S(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)ClO₃, and sulphuric acid, (HO)₂SO₂, 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⁺, O²⁻, and Na⁺. [p174]

The position of aluminium in the periodic system adequately accounts, then, for the amphoteric character of its hydroxide.357

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 (H₂O)₂. H₂O, 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.

Hydrolysis of Salts

As the concentration of pure water, or of the water in dilute solutions, may be considered nearly a constant, we may put

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_H2O 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_H2O, 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

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

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.

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:

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 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]

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:

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⁺] reduced373 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.