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

Copyright, 1911, by THE CENTURY CO.

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

PREFACE

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

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

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

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

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

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

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

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

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

JULIUS STIEGLITZ.

Chicago, September, 1911.

CONTENTS

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 I Footnotes

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

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

CHAPTER II OSMOTIC PRESSURE AND THE THEORY OF SOLUTION I

[p008] [TOC]

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.

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

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.

Definition of Osmotic Pressure.

Measurement of Osmotic Pressure.

Fig. 3.

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

Osmotic Pressure and the Laws of Gases.

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

Boyle's Law.

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

Gay-Lussac's Law.

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

P_t = P₀ (T / 273) or P_t / T = P₀ / 273 = a constant.[16]

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

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

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

The Avogadro-van 't Hoff Hypothesis.

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.

Indirect Determinations of Osmotic Pressure.

Apparent Exceptions.

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

Summary.

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

Chapter II Footnotes

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

[4] This again holds equally for the solvent.

[5] See below.

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

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

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

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

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

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

[12] When appreciable heat of dilution is shown by a solution, some chemical change, resulting from dilution, is indicated (such as, dissociation of the solute, hydration, hydrolysis, etc.). In such a case, the Avogadro-van 't Hoff principle holds for each concentration for its actual composition, and the principle may often be used to determine the extent of the chemical change produced by dilution. But then the osmotic pressure will not obey Boyle's and Gay-Lussac's laws. The same exception applies also to gases which undergo chemical changes, as the result of dilution or change of temperature. In the case, for instance, of nitrogen tetroxide, which dissociates according to N₂O₄ ⇄ 2 NO₂, the extent of the dissociation varies with changes of concentration (pressure) and of temperature, and the gas does not obey the laws of Gay-Lussac and of Boyle. In regard to the rôle of heat of dilution in connection with osmotic pressure, see Bancroft, J. Phys. Chem., 10, 319 (1906).

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

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

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

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

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

[16] The pressure P₀ of a given quantity (weight) of a gas at 0° C., in a given constant volume, is also a given number and consequently P₀/273 is a constant under these conditions.

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

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

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

[20] One gram of cane sugar, C₁₂H₂₂O₁₁ (the mol. wt. is 342) corresponds to 1 / 342 gram molecule or mole and, therefore, to 2.02 / 342 gram of hydrogen. The volume containing this quantity of hydrogen is 100.6 c.c.; a liter would contain 2.02 / 342 × 1000 / 100.6 gram of hydrogen. The pressure of a mole or 2.02 grams of hydrogen, contained in a liter at 0°, is 22.4 atmospheres, and the pressure of the quantity of hydrogen given above, in a liter, would be (2.02 × 1000) / (342 × 100.6) × (22.4 / 2.02) at 0°. At 36° C., for instance, the pressure would be 309 / 273 times as great, or P_calculated = (2.02 × 1000 × 22.4 × 309) / (342 × 100.6 × 2.02 × 273) = 0.735 atmosphere.

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

[22] Vide Raoult, Scientific Memoir Series, 4, 71, 127.

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

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

[25] Cf. Bancroft, J. Phys. Chem., 10, 319 (1906).

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

[27] Footnote 3, p. [12].

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

CHAPTER III OSMOTIC PRESSURE AND THE THEORY OF SOLUTION II

[p021] [TOC]

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

Semipermeability.

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

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

Fig. 4.

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

Fig. 5.

Osmosis.

Fig. 6.

Osmosis and Gas Pressure.

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

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

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

The Kinetic Theory and Osmotic Pressure.

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 mass[40] and velocity, the same as if the alcohol were present as a gas or vapor at the same temperature. If the solution is sufficiently dilute, the dissolved alcohol molecules are sufficiently far apart, for average time, to make the molecular attractions between them negligible, just as is assumed for gases. As far as the alcohol (solute) molecules alone are concerned, they may, evidently, be assumed to be present in the solution, in the same condition, as to number, mean kinetic energy and mean velocity, as they would be in alcohol vapor of the same concentration and temperature. We may ask, now, whether the osmotic pressure of the solution may not result from the pressure on the solvent, growing out of its bombardment by the solute molecules. And we may ask, further, what numerical relation would subsist between such a pressure and the pressure of the solute, if the latter were present as a gas, under the same conditions of temperature and concentration. In order to be prepared to answer these questions, we must consider, in what way the presence of the solvent must modify the motions and the forces of impact of solute molecules.

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

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

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

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

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

We may consider that we have in a cube of unit volume (1 c.c.) n molecules of a gas, each of mass m and average velocity u cm. per second. We may assume that one-third of the total number [p030] of molecules moves in each of the three dimensional directions.[42] A single molecule of mass m, striking the surface with a velocity u and rebounding with the same velocity in the opposite direction, will exert on the surface a force of 2 m u units. But, with a velocity of u cm. per second, it will reach the opposite wall and return to the surface we are considering, u / 2 times in one second. A single molecule will consequently exert a force 2 m u × u / 2 or m 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 III Footnotes

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

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

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

[32] J. Phys. Chem., 10, 141 (1906).

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

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

[35] Z. phys. Chem., 5, 175 (1890).

[36] Ibid., 3, 119 (1889).

[37] Phil. Mag., 38, 206 (1894).

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

[39] The molecules may have different masses in the different conditions, and the principle of the mean kinetic energy would always apply to them as they are, in the condition under observation, and not as they are in some other condition; any change in mass, in solution, for instance, would show itself in the osmotic pressure measurements (see p. [18]), just as it is shown in the measurements of gases, when the gas molecules show a change in composition, as is the case with hydrogen fluoride (H₂F₂ ⇄ 2 HF), nitrogen tetroxide (N₂O₄ ⇄ 2 NO₂), phosphorus pentachloride (PCl₅ ⇄ PCl₃ + Cl₂) and other compounds.

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

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

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

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

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

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

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

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

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

CHAPTER IV THE THEORY OF IONIZATION; IONIZATION AND ELECTRICAL CONDUCTIVITY

[p033] [TOC]

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

When molecular weights are determined in this way, with the aid of Avogadro's hypothesis, results are obtained which agree [p034] perfectly with the chemical behavior of the compounds or elements in question. The molecular weights of hydrogen chloride, water, ammonia, and marsh gas, for instance, are found to be 36.5, 18, 17 and 16, respectively, corresponding to the formulæ[51] HCl, 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.

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

While the application of Avogadro's hypothesis thus gives results agreeing well with the observed chemical behavior of very many important compounds, observations have been made which, at first sight, do not appear to agree with the requirements of the hypothesis and which seem to raise a doubt as to the universal truth of its fundamental assumption. Thus, if equal volumes of hydrogen chloride and ammonia, of the same temperature and pressure, are brought together, ammonium chloride is formed, both gases being totally consumed. Since, according to the hypothesis, equal volumes, under the conditions obtaining, contain the same numbers of molecules, the formation of ammonium chloride takes place according to the equation 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.

Gaseous Dissociation.

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]

Molecular Weight Determinations in Solution.

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.

The Theory of Ionization.

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

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

Main Assumptions of Arrhenius's Theory of Ionization.

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

The dissociation of hydrogen chloride may be expressed, in the terms of the assumptions made, in the following equation: HCl ⇄ H⁺ + Cl⁻; that is, hydrogen chloride is dissociated, to a greater or smaller extent and in reversible fashion, into positively charged hydrogen ions H⁺, and negatively charged chloride ions Cl⁻, and the charge on each chloride ion is equal in quantity to the positive charge on each hydrogen ion. Zinc chloride is dissociated according to the equation 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.

The Theory of Ionization and the Electron Theory of Electricity and of Matter.

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

On the basis of these views, we have in sodium chloride NaCl a substance, whose molecules contain an atom, Na, with a tremendous tendency to lose an electron, and an atom, Cl, which has a tremendous affinity for an electron. It is natural to suppose, then, that both tendencies will be satisfied by the passage of an electron from the sodium to the chlorine atom, NaCl → Na^-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 have[71]: 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.

The Validity of the Theory of Ionization.

Ionization and Electrical Conductivity.

Fig. 8.

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

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

Electrolysis.

Conductivity and Dilution.

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

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

Fig. 9.

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

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

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

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

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

Degree of Ionization of an Electrolyte.

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

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

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

Clausius's Theory of Ionization and the Modern Theory.

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

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

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

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

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

Mobilities or Partial Conductivities of Ions: Principle of Kohlrausch.

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 molecules[89] 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 table[90] gives the limits of the mobilities for gram equivalents of some of the most important ions at 18°.

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]

Faraday's Law.

Diffusion of Ions and Concentration Cells.

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

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

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

The Rôle of the Solvent in Ionization.

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. Thomson[101] and Nernst[102] suggested that the ionizing powers of solvents must be intimately connected with their dielectric behavior, and this view has now been well established. It may be said, in simple terms, that the so-called dielectric constant of a solvent determines the force with which electrical charges will attract and repel each other; the higher the dielectric coefficient of a medium, the smaller will be the attraction between opposite electrical charges, other conditions being the same. In solvents, then, of high dielectric powers, the coëxistence of oppositely charged particles must be more favored than in solvents of low dielectric powers. The dielectric constants of a number of solvents are given in the following table: [p063]

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

Recent extended and exact investigations by Walden[103] have succeeded in bringing the ionizing power of solvents into definite quantitative relations to their dielectric constants, with the result that order has been brought out of a condition of chaos that, for a number of years, existed in this field, as the result of conclusions based on incomplete data. Conductivity being a function both of the proportion of dissociated electrolyte and of the mobility of the ions in a given solution, Walden determined, for a certain salt (an organic derivative of ammonium iodide, namely, tetraethyl ammonium iodide N(C₂H₅)₄I), for all solvents used, not only the conductivities for finite dilutions but also, by extrapolation, the limiting values for infinite dilution. He was thus able to determine the degree of ionization of the salt. Some of his results are particularly interesting; for instance, a poorly conducting solution, such as that of the salt in glycol, a solvent resembling glycerine in general character, may contain the dissolved electrolyte in a highly ionized state, while in a much better conducting solution the degree of ionization may be much smaller—the low conductivity of the first solution being the result of a very high friction and of the slow motion of the ions, while the well-conducting solution might show a very high degree of mobility of the ions. The mobility changes with the nature of the solvent, and the limit, Λ_∞, of the equivalent conductivity of the salt, as found by Walden, ranges from 8 in glycol, which is a thick, viscous oil like glycerine, to 200 in acetonitrile, a thin mobile solvent. In the one solution, an observed conductivity of 4 represents 50% ionization of the salt, in the other only 2%.

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

e₁ : ∛c₁ = e₂ : ∛c₂ = a constant,

where e₁ and e₂ represent the dielectric constants of different solvents, and c₁ and c₂ represent the concentrations of the salt in the solvents when the salt is ionized to the same degree[105] in the two solutions.

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

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

The Ionizing Power of Solvents Related to the Unsaturated Condition of their Simple Molecules and to their Power of Association.

In liquid ammonia we might well have, for instance, the action ⁺NH₃-NH₃⁻ + HCl ⇄ ⁺(NH₃-NH₃)H + Cl⁻, or ⁺NH₃-NH₃⁻ + H⁺Cl⁻ ⇄ ⁺(NH₃-NH₃)H + Cl⁻. Now, in liquid ammonia, the salts NH₄Cl, NH₄NO₃ [or, more probably, (NH₃)_xHCl, (NH₃)_x,HNO₃] have the functions of the aqueous acids[109]; that is, the hydrogen-ion of the acids is found combined with the solvent ammonia. The ion ⁺(NH₃-NH₃)H, and similar ions in liquid ammonia, would correspond then to what is considered the hydrogen-ion in aqueous solutions[110] (formed according to HCl ⇄ H⁺ + Cl⁻, as ordinarily written), and the polarized charges on molecules like ⁺NH₃-NH₃⁻ appear thus as possible active agents in this dissociation of the hydrogen chloride molecules. [p066]

Now, it is a significant fact that all the best ionizing solvents are compounds whose simple molecules are unsaturated exactly like those of ammonia; this is true for water 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 IV Footnotes

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

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

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

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

[53] Liebig's Ann., 123, 199 (1862) (Stud.).

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

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

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

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

[58] See Arrhenius, Z. phys. Chem., 1, 631 (1887).

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

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

[61] A fourth interpretation advanced at one time in opposition to the theory of ionization is that salts like sodium chloride and zinc chloride are hydrolyzed and thereby produce more solute molecules, e.g. NaCl + H₂O → NaOH + HCl. Aside from the fact that such hydrolysis of salts, when it does occur (Chapter X.), is easily detected, and that it can be proved not to occur appreciably in the case of sodium chloride (loc. cit.), this interpretation fails utterly to account for the results obtained with acids, e.g. HCl, HNO₃, H₂SO₄, and with bases, e.g. NaOH, Ba(OH)₂, which in aqueous solutions show an increase in the number of molecules as great as shown by salts. This explanation is therefore untenable.

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

[63] In the case of double salts, such as sodium-ammonium phosphate, and similar compounds, the dissociation leads to the formation of more than two products. The molecules of two or more different products may then be charged positively and, conversely, there may be two or more different products of dissociation carrying negative charges. We have, for instance, Na(NH₄)HPO₄ ⇄ Na⁺ + NH₄⁺ + H⁺ + PO₄³⁻ and Na(NH₄)HPO₄ ⇄ Na⁺ + NH₄⁺ + HPO₄²⁻. In all cases the rule concerning the sum of all the charges, as expressed in (2), must be fulfilled, the charge on the phosphate ion, PO₄³⁻, being three times as great as that on a sodium, ammonium, or hydrogen ion; that on the acid phosphate ion, HPO₄²⁻, being twice as great.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[82] Kohlrausch and Holborn, p. 200.

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

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

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

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

[87] Lectures on Physical Chemistry, 1, p. 131.

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

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

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

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

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