4+ * ** * M . 1 A 625981 74 T . ، | -- * ا 2 : : ا ء ا LITIQ8 يالالالالالا للللللللللا MIU SCIENTIA للملننمنللننلنلنلندا ARTES وحدت نمونه ElIIIIIIIIIIIIIIIIIIIIIII LIBRARY VERITAS OF THE WVERSITY OF MICHI UNIVERSIT اف جون av3 ت ---- . - . - !. ! ..... ننننننننننننننننننن ح - - , م- - . - .. Tt:EI() مسلملنننننلسملسمنضنلننللنننليا . . .. - . ... د - . . -- - subtilitirliululululutlulunilicultitouillartmlllllllllllllluricultunitiethin | . " | N : . : - --- ن ننن 1. QUXR13 URIS. PENINSUL! . ULAMAMOENAM AWAM NAME : . -- درصد و و ساعت ..امروc مهنتون : . .. به :مدل . . . . . . . . . ذ/...... J رل , , ممممممممممممممنممنم IIIIIIII... نننننننننيببينددننندند I IIIIIIIIIIIIIII l . . . . IIIIIIIIIIIIIIIIIIIIIIII I IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII I Al Simu waimunnhguinminbiurbtilihinnanmu uttuinitud . .. .. .. ج منه من CAMBRIDGE PHYSICAL SERIES. GENERAL EDITORS :-F. H. NEVILLE, M.A., F.R.S. AND W. C. D. WHETHAM, M.A., F.R.S. A TREATISE ON THE London: C. J. CLAY AND SONS, CAMBRIDGE UNIVERSITY PRESS WAREHOUSE, AVE MARIA LANE, AND H. K. LEWIS, 136, GOWER STREET, W.C. K Leipzig: F. A. BROCKHAUS. New York: THE MACMILLAN COMPANY. Bombay and Calcutta : MACMILLAN AND CO., LTD. [All Rights reserved.] A TREATISE ON THE THEORY OF SOLUTION INCLUDING THE PHENOMENA OF ELECTROLYSIS BY WILLIAM CECIL DAMPIER- WHETHAM, M.A., F.R.S. FELLOW OF TRINITY COLLEGE, CAMBRIDGE CAMBRIDGE: AT THE UNIVERSITY PRESS. 1902 Cambridge: PRINTED BY J. AND C. F. CLAY, AT THE UNIVERSITY PRESS. PREFACE. U T HIS book was at first intended as the second edition of a 1 small volume on Solution and Electrolysis published in the year 1895. It was, however, soon found necessary to rewrite such large portions of the text, and to incorporate so much fresh matter, that the result is in effect a new work. Our knowledge of the phenomena of solution is growing rapidly, and as yet there is considerable difficulty in producing a systematic treatise. Moreover, the use of modern thermo- dynamic methods, founded on the investigations of Willard Gibbs, is extending to almost all branches of the subject, while such methods are still unfamiliar to many students of physics and chemistry. An introductory chapter has therefore been prefixed, explaining the thermodynamic principles which are applied in the body of the work. Besides the papers of Willard Gibbs, the following books should be especially mentioned among those to which the writer is indebted: Buckingham's Theory of Thermodynamics, Roozeboom's Heterogenen Gleichgewicht, Bancroft's Phase Rule, Larmor's Æther and Matter, Duhem's Mécanique Chimique, Ostwald's Lehrbuch der Allgemeinen Chemie, Nernst's Theo- retische Chemie, the works on Physical Chemistry of van 't Hoff, Lehfeldt, and J. Walker, van 't Hoff's Chemical Dynamics, Le Blanc's Electrochemistry, and Das Leitvermögen der Elek- trolyte by Kohlrausch and Holborn. In these books the reader will find further details on particular points, while most of the new work on the subject can be studied, either in full or in abstract, in the pages of the Zeitschrift für Physikalische IT PREFACE Chemie, the Journal of Physical Chemistry or the Zeitschrift für Elektrochemie. Much that is of value in this book must be attributed to the kindly help of many friends. Notes and corrections of the older work referred to were sent by Professors J. H. Poynting, L. R. Wilberforce, and W. McF. Orr, while the wise and suggestive criticism of the late Professor G. F. FitzGerald added another to the many kindnesses for which the writer will always gratefully cherish his memory. Mr F. H. Neville read the earlier part of the manuscript of the new book, and gave useful information and advice; help on particular points was sought from the Earl of Berkeley, Professor J. J. Thomson, Dr J. N. Langley, Principal E. H. Griffiths, Mr S. Skinner and Mr G. F. C. Searle, while Professor Poynting read and criticized the chapters on osmotic pressure and allied phenomena. To all the writer offers his cordial thanks. Especially would he express his sincere gratitude and deep sense of obligation to Mr J. Larmor, whose kindness in reading some of the manuscript and all the proof sheets it is impossible adequately to acknow- ledge. Mr Larmor's wide knowledge and deep insight have enabled the writer to gain clear ideas on many points which before were doubtful, and the ungrudging way in which he has given time and trouble to this work has removed many blemishes which would otherwise have appeared therein. Finally the writer's thanks are due to his wife for preparing the index and for constant correction both of the manuscript and of the proof sheets which have developed into the following pages. TRINITY COLLEGE, CAMBRIDGE. December, 1902. CONTENTS. CHAP. I. 1 THERMODYNAMICS . . . . . Experimental basis of Thermodynamics. The first law. The second law. Work and cnergy. Complete cycles. Reversible processes. Reversible engines. The absolute scale of temperature. Generalized co-ordinates. Internal energy. Entropy. Thermodynamic potential. Conditions of equilibrium. Application of thermodynamic potential. Free energy. Application of the free energy principle. 32 II. THE PHASE RULE . . . . . . Equilibrium. Equilibrium of phases. The phase rule. Non-variant systems. Monovariant systems. Divariant systems. Other systems. The principle of latent heat. Application of the phase rule. One component. Labile equilibrium. Allotropic solids. III. THE PHASE RULE. Two COMPONENTS. SOLUTIONS : 48 Compounds, mixtures and solutions. Anhydrous solutes. Hydrated solids. Concentration curves. Two liquid com- ponents. Alloys. Solid solutions. Two volatile components. Three components. The problems of solution. IV. 78 SOLUBILITY . . . . . . . . General problem of solubility. Supersaturation. Solu- bility of gases in solids. Solubility of gases in liquids. Henry's law. Solubility of gases in salt solutions. Solubility of liquids in liquids. Solubility of solids in liquids. Influence of pressure on the solubility of solids. Solubility of mixtures. Solubility in mixed liquids. Tables of solubility. viii CONTENTS СНАР. PAGE V. OSMOTIC PRESSURE . . . . . . . 95 Semi-permeable membranes. Osmotic pressure and vapour pressure. Perfect semi-permeable rembranes. Theoretical laws of osmotic pressure. Osmotic pressure and heat of solution. Experimental measurements of osmotic pressure. VI. VAPOUR PRESSURES AND FREEZING POINTS : 122 Connection with osmotic pressure. The latent heat equation. The depression of the freezing point. Vapour pressures of concentrated solutions. Solubility of gases in liquids. Experimental measurements of vapour pressures. Boiling points. Determination of molecular weights. Freezing points. Osmotic pressure and freezing points of concentrated solutions. Experiments on the freezing points of solutions. Determination of molecular weights. Freezing points of alloys. Experiments on concentrated solutions. VII. THEORIES OF SOLUTION . . . . . . 165 Thermodynamics as a basis for physical science. Appli- cation to the case of solution. Theory of direct molecular bombardment. Theory of chemical combination. Con- clusion. VIII. ELECTROLYSIS . . . . . . . . 176 Introduction. Volta's pile. Early experiments. Faraday's work, Polarization. Faraday's laws. Electrochemical equi- valents. The electrolysis of gases. Nature of the ions. IX. CONDUCTIVITY OF ELECTROLYTES .. 197, Ohm's law. Experimental methods. Experimental re- sults. Consequences of Ohm's law. Migration of the ions and transport numbers. Mobility of the ions. Experimental measurements of ionic velocity. Influence of concentration. Complex ions. Connexion between the mobility of an ion and its chemical constitution. Conductivity of liquid films. GALVANIC CELLS : . . . . . . 232 Introduction. Reversible cells. Electromotive force." Effect of pressure. Concentration cells. Different con- centrations of the electrodes. Different concentrations of the solutions. Concentration double cells. Effect of low concentrations. Chemical cells. Oxidation and reduction cells. Transition cells. Irreversible cells. Secondary cells or accumulators. S X. GALVAN CONTENTS ix CHAP. PAGE 267 XI. CONTACT ELECTRICITY AND POLARIZATION ... Volta's contact effect. Thermo-electricity. The theory of electrons. Single potential differences at the junctions of metals with electrolytes. Dropping electrodes. Electro- capillary phenomena. The theory of von Helmholtz. Electric endosmose. Single potential differences (continued). Electro- lytic solution-pressure. Electrochemical series. Polarization. Decomposition voltage. Polarization at each electrode. Evo- lution of gases. Electrolytic separations.. XII. THE THEORY OF ELECTROLYTIC DISSOCIATION . . 312 Introduction. Osmotic pressure of electrolytes. Additive properties of electrolytic solutions. Dissociation and chemical activity. The mass law. Equilibrium between electrolytes. Thermal properties of electrolytes. Heat of ionization. Dissociation of water. The function of the solvent. Hydrolysis. Conclusion. XIII. DIFFUSION IN SOLUTIONS . . . . . . 369. • Theory of diffusion. Experiments on diffusion. Diffusion and osmotic pressure. Diffusion of electrolytes. Potential differences between electrolytes. Liquid cells. Complete theory of ionic migration. Electrolytic solution pressure. Diffusion through membranes. XIV. SOLUTIONS OF COLLOIDS . . . 391 The colloidal state. Process of gelation and structure of gels. Coagulative power of electrolytes. The nature of colloidal solutions. ADDITIONS . . . . . . . . . . . 403 TABLE OF ELECTROCHEMICAL SOLUTIONS . . . INDEX'. . . . . PROPERTIES OF AQUEOUS . . . . . . . 407 . . . . . . 476 CORRECTIONS. Page 12, line 8, read: But consequences of the second law of thermodynamics which only hold for reversible systems have sometimes been applied, etc. Page 26, footnote, read : Zeits. phys. Chem. XI. 289 (1893). Page 117, footnote 3, read: Zeits. phys. Cheni. I. 481 (1887). Page 122, add to heading of chapter: Freezing points of alloys. Experiments on concentrated solutions. Page 162, the equation should be numbered (35). Page 193, line 19, read: 0.404 x 10–11. Page 197, add to heading of chapter: Conductivity of liquid films. Page 206, the equation should be numbered (36). Page 231, add to footnote : Patterson, Phil. Mag. Dec. 1902. Page 241, line 18, read: to all kinds of reversible cells, etc. Page 248, line 18, in the denominator of the expression for E, 96440 should be 9644, the ionic charge being here measured in C.G.S. units and not in coulombs. Page 272, line 15, read: Let us imagine a circuit composed of two wires of different metals surrounded by a dielectric, the two metallic junctions being maintained at different temperatures. In applying, etc. Page 328, the Figure should be numbered 64. ᏟᎻᎪᏢᎢᎬᎡ Ꮮ. THERMODYNAMICS. Work and energy. Complete cycles. Reversible processes. Reversible engines. The absolute scale of temperature. Generalized co-ordinates. Internal energy. Entropy. Thermodynamic potential. Conditions of equilibrium. Application of thermodynamic potential. Free energy. Application of the free euergy principle. basis of thermo- dynamics. The first law. THE subject of thermodynamics, which deals with the relations Experimental between heat and the other forms of energy - possessed by material systems, rests ultimately, like all physical sciences, on a basis of observa- tion and experiment. Careful measurements by Joule, Rowland, Griffiths and others have shown that, when various forms of mechanical and electrical energy are completely converted into heat by friction and similar processes, the quantity of heat produced by a given amount of work is always the same in whatever form and by whatever means the work is applied. Heat is thus a form of energy, and one thermal unit must have its definite mechanical equivalent in other forms of energy. This experimental gene- ralization is one case of the principle of the conservation of energy, and constitutes the first law of thermodynamics. The best modern determinations show that the amount of heat necessary to raise one gram of water from 17° to 18° centigrade, which is taken as the practical thermal unit and called the calorie, is always developed when 4:184 x 107 ergs of work are expended in heat. W. S. SOLUTION TAN [CH. I AND ELECTROLYSIS The second law. If we try to bring about the reverse change and convert heat energy into mechanical work, experience shows that no heat engine will act if the whole of the available system is at a uniform temperature. Thus all steam engines have a boiler and a condenser, the atmo- sphere acting as condenser in the case of high-pressure engines. Oil engines work by the explosion of oil spray in the cylinder; a high temperature is thus produced, the atmosphere again acting as condenser. It will always be found that there is some heat given up to the condenser besides that which is transformed into work, and, in all cases, the heat is absorbed by the engine from the botter parts of the system. Such observed facts can be generalized in the statement that it is impossible by inanimate mechanical means to obtain a con- tinual supply of useful work by cooling a body below the temperature of the coldest of the surrounding bodies. It is possible to get a certain amount of work in this way, for in- stance, by allowing gas or vapour to expand, thus cooling itself and doing work; but a continual supply cannot be so produced. When the gas or vapour is used in a heat engine, and put through complete cycles of changes, an external supply of heat at a high temperature must be constantly maintained, and the engine will continually give up some of this heat to: the cooler parts of the system. It will now be seen that if a range of temperature is . available, and a heat-engine' be constructed to use it, the process will tend to diminish the difference of temperature between the parts of the system, heat passing from the hotter to the colder parts. Again, when heat flows by conduction, the transference always occurs in this same direction, and never in the reverse one. It is thus a general result of observation that heat cannot of itself, or by means of a self-acting mechanism, pass from a body of lower to a body of higher temperature. This statement will be found to be equivalent to that enunciated above in the form that a continual supply of mechanical work cannot be obtained from the heat energy of the coldest part of the system. Both statements embody the CH. 1] THERMODYNAMICS experimental generalization known as the second law of thermodynamics. On the results of experience, as formulated in these two laws, the whole subject of thermodynamics is founded. When a force X moves its point of application through a distance da, the work done by the force is X.doc, Work and energy. 188 and, if the force acts on a system, this amount of energy is added to the system. Take as an example the case of a quantity of fluid confined in the cylinder of an engine (Fig. 1). If the piston be forced inwards, work is done on the system, and if the piston be allowed to move outwards, work is done by the system on the environment. If the area of the piston be A, and the pressure be p, the force is Ap, and if the piston rise through a small height dh, the work done by the contents of the cylinder is Ap.dh. But the change of volume of the working substance is A.dh, so that, representing the change of volume by dv, the work done is p.dv. In order to find the work done when a large volume change occurs, we must find the sum of all the separate values of p.dv. This process is termed integration, and is represented by the symbol Spdv. When Fig. 1. certain simple relations hold between the pres- sures and the volumes, we can find the value of this integral. For instance, if p remains constant throughout the operation, the sum of all the p.du's is the same as p multiplied by the sum of all the du's, or p (V2 — vy) where ~ and V, represent the initial and final volumes. This constancy of pressure is practically attained when the working substance is a liquid in contact with its own saturated vapour: for instance, the water and steam in the boiler of an engine. If heat be supplied, evaporation goes on at constant temperature, and the pressure remains unchanged. Another important case arises when a gas, such as air, fills the cylinder. While the temperature keeps constant, the pressure is inversely pro- portional to the volume, and, as is well known, the whole 1--2 SOLUTION AND ELECTROLYSIS [CH. I lo pressure, volume and temperature relations have been found ex- perimentally to be represented very accurately by the equation pv = RT, where T is the temperature measured on the gas thermometer, of which the zero corresponds to – 273° centigrade, and R is a constant, the numerical value of which can be calculated for any given mass of gas. If we take as our unit mass the number of grams equal to the chemical constant known as the molecular weight of the gas (a number which is commonly called the gram-molecule), the volumes of different gases under the same conditions of temperature and pressure will be equal, and the value of R the same for all. The volume of the gram-molecule is found experimentally to be 22320 cubic centimetres when the pressure is that of the standard atmosphere (760 millimetres of mercury or 1:013 dynes per square centimetre) and the tem- perature is 0° centigrade, or 273° on the absolute scale of the gas thermometer. These numbers give for the value of R corresponding to the chemical unit of mass or the gram- molecule, 8.284 x 107 ergs or 1.980 calories per degree centi- grade. In approximate calculations R may therefore be taken as 2 calories per degree for each gram-molecule of gas. As we have seen, the work done, while the volume changes from v, to va, is dv. ruz 02 RT ? | pdv = . Ju, vi V rug 1 For isothermal changes, both R and T are constant, and can be put outside the sign of integration. Now RT("dv = RT logo (2) ............(1), and thus we know the value of the work done by the gas when its volume increases at constant temperature. Similarly, when the volume is diminished, the same integral gives the work done on the gas. These results can be well shown on a diagram (Fig. 2), in which the abscissae represent volumes and the ordinates pres- sures. On such a diagram the isothermal lines, defined by the relation that T and therefore pv is constant, will be rectangular CH. 1] THERMODYNAMICS hyperbolas. Consider the work done while the gas passes from a state represented by the point A to a state represented by B. pal Lako pa TP - - - - - - - -- - - - - V, VVD Fig. 2. LV2 For a small change in volume v to va, the pressure can be taken as constant, and the work, which is pdv, is represented by the area of the narrow strip papava Vz. The work from vo to v is measured by the area of the corresponding strip pova Vy, and it is now obvious that the total work from vi to v, is represented by the area of the figure ABV,V, under the curve AB, which there- fore is equivalent to the value of the integral pdv. Passing from A to B, the volume increases, and therefore work is done by the gas. If the process had been performed in the reverse order, from B to A, the work represented by the area would have been done on the gas, and the work done by the gas could be written - pdv. Now pv = constant; hence differentiating, pdv + vdp= 0, or -pdv=vdp. Thus as regards the integrals – Spdv = fvdp. pui JVO SOLUTION AND ELECTROLYSIS [CH. I The latter integral is represented by the area ABpap, on the diagram, which is therefore equal to the area ABv2v, as long as the curve is a rectangular hyperbola, that is, as long as Boyle's law holds good for the working substance. Como Now let us imagine that the working substance, whatever it may be, is carried round a complete cycle of e cycles.. changes, so that in the end it is brought back to its original state, represented by A on the diagram. If the changes are not isothermal, the curve on the diagram can be made of any form we please. Thus on Fig. 3, let the cycle be Fig. 3. performed in the order ACBDA. The work done by the system along ACB is, as we have seen, measured by the area ACBHG, and that done on the system along BDA by the area BDAGH. The balance of work done by the system through- out the cycle is therefore the area ACBHG, less the area BDAGH, that is the area ACBDA enclosed by the curve representing the successive states of the substance as regards pressure and volume. This area is measured by the integral Spdv taken all round the cycle. The area ACBDA is also the difference between the areas ACBFE and BDA EF, it can therefore be also represented by – ſvdp, which thus measures the work done in a complete cycle of any kind; while, when the cycle is not complete, this converse integral only measures CH. I] 7 THERMODYNAMICS the work in the case of the isothermal changes in an ideal gas, the properties of which are exactly described by Boyle's law, pv is constant. Adiabatic rela- tions of an The relation pv = constant, as we have seen, describes the behaviour of an ideal gas under isothermal conditions. The corresponding rela- tion for adiabatic changes may be deduced by ideal gas. the help of the general equation which holds under all conditions for gaseous substances, pv = RT. We must also remember that experiment has proved that there is only a very small change in the internal energy of a gas when its volume is changed isothermally, or, in other words, that no appreciable work is absorbed or liberated in merely separating the parts of the gas from each other. This work becomes less as the gas approaches the ideal condition, and may, for an ideal gas, be considered to be zero. When a gas is heated at constant volume, no external work is done, and the whole of the heat energy is used in raising the temperature of the gas. On the other hand, if the pressure be constant, an amount of external work equal to pdu is done. Let us express everything in mechanical units, and denote the specific heats at constant pressure and constant volume by Cp and Co respectively. Then, considering unit mass and unit rise of temperature, we have, since the internal work is negligible, Cp - Co = pdv. But the gas constant R is equal to pv/T, that is, to pdv/dt, or the pressure multiplied by the change in volume per degree. Hence R= Cp;— Co. Now for the general case, when a quantity of heat is allowed to enter an ideal gas, it is used in raising the temperature through a range which we will call dT, and in performing an amount of external work, which, for an infinitesimal change, SOLUTION AND ELECTROLYSIS [CH. I (2). may be denoted by pdv. Thus, for an adiabatic process, when there is no gain for loss of heat, CodT + pdv = 0... Again from the equation pu= RT, we have, by differentiating, pdv + vdp= RIT. Substituting for dT in (2), and replacing R by Cp – Co, we get : Cppdv + Covdp=0. Then, denoting the ratio Cp/C, by Y, du dp = 0. UP This ratio of the specific heats y is found by experiment to be nearly independent of the pressure, volume and temperature. The equation can therefore be integrated. Thus y log v + log p = constant, or puy = constant......... the adiabatic relation required. Let us imagine a quantity of water in contact with its Reversible pro- vapour in an engine cylinder. It is known cesses. that, for a given temperature, there is one and only one pressure at which the system will be in equi- librium. If the pressure be slightly increased, vapour will condense till it again falls to its original value, or, if the excess of pressure be kept up, the whole of the vapour becomes liquid. Conversely, if the pressure be kept slightly below the equilibrium value, the whole of the liquid will evaporate. Either of these changes can be produced, theoretically at any rate, by a change of pressure infinitesimally small, if time enough is allowed. Similar changes can be produced if, instead of varying the pressure, the temperature be slightly altered, the least variation from the equilibrium value being enough to cause the system to move in one direction or the other. In such a case it is obvious that, when we have taken the system along a path ACB (Fig. 3) by CH. 1] 9 THERMODYNAMICS A such infinitesimal changes, we can by similar infinitesimal changes in the other direction of the external variables, pres- sure or temperature, cause the same path to be described in the reverse direction. Such processes are called reversible, and it is clear that in practice, though we can never use infinitely slow variations and thus get strictly reversible processes, we can make the processes which actually go on more or less nearly reversible by keeping the changes in the external variables more or less slow. It is evident that, to get reversible processes, we must keep the pressure and temperature indefinitely near their equi- librium values at all parts of the operations. If the temperature be kept constant, heat can be passed into the system while this condition is realized, provided that the temperature of the external source of heat, which must be higher than that of the working substance in order to produce a flow of heat at all, is made to differ from it by an amount infinitesimal only. The process is then very nearly reversible. Another case in which reversibility may be nearly attained arises when there is no passage of heat at all. The changes which then go on are called adiabatic. If the external pressure be kept indefinitely near that of the working substance throughout, such changes will be very nearly reversible. A good example of changes practically adiabatic is found in the alterations of pressure and volume which accompany the passage of a wave of sound through air, the vibrations being so quick that there is no time for heat to enter or leave the parts of the air affected. This case may also be used to illustrate what occurs when the changes are neither isothermal nor adiabatic. If, for instance, the air remained compressed long enough for a flow of heat to occur from parts of the air which have been heated by the compression to parts which have been cooled by expansion, the conduction of heat could not be reversed by an infinitesimal change of tem- perature, and the process becomes irreversible. It will be noticed that, for a process to be reversible in the thermodynamic sense of the word, it is not enough that it can be made to proceed in the reverse direction. It is also necessary 10 [CH. I SOLUTION AND ELECTROLYSIS that this change in the direction of the process should be effected by a change of an infinitesimal amount in the external conditions. No real process can be an exactly reversible one, though physical and chemical actions which are not accompanied by anything of the nature of friction, can be made almost reversible by keeping the conditions very near those of equilibrium, and the action consequently slow. Viscous forces, such as those which a liquid offers to the passage of a body through it, do not interfere with this result, for they may be made indefinitely small by reducing indefinitely the velocity of change. The existence of viscosity, then, does not prevent a system under- going reversible operations. Ordinary friction, on the other hand, such as that between solid surfaces, restrains a system from change till the driving forces reach a finite value, and entirely prevents even an approximation to a condition of re- versibility. Thus, although reversibility can never be attained in practice, systems can be divided into those which can be made very nearly reversible, and those which cannot. The directive forces of the former could be diminished without limit as the changes in them become indefinitely slow; they are therefore called rever- sible systems. A similar distinction can be drawn between the equilibria of these two classes of systems. The weight of a body spring, and the body will move in one direction or the other as the weight is increased or diminished by a very small amount. So a liquid in contact with its own vapour is in equilibrium when the rates of evaporation and condensation are equal. dissolved per second is equal to the amount precipitated. Such cases of true equilibrium are at once known by the fact that a small change in one of the external conditions, temperature or pressure, will at once cause a corresponding change in the factors of equilibrium; more liquid will evaporate or condense, or more solid go into or out of solution. But equilibrium often exists which is not the effect of the balance of such oppositely directed active tendencies. A body CH. I] 11 THERMODYNAMICS can be kept on an inclined plane by the roughness of the surfaces in contact; and so some physical and chemical trans- formations may possibly be prevented by forces analogous to friction. Such forces might be overcome by changing the condi- tions: for example, by heating some explosive substances which are unchangeable at ordinary temperatures; but, as long as the frictional forces keep the system in equilibrium, it will not be disturbed by any small change in the external conditions. Thus it is thought a false equilibrium may be distinguished from a true one. On the other hand, viscous resistances, like those exerted on a moving body by fluids, delay but do not prevent motion, and will not affect the final conditions of true equi- librium. The equilibrium reached, then, will, if we wait long enough, be independent of all such viscous forces. Now the importance of this distinction between true and false equilibrium lies in the fact that, while the first law of thermodynamics, the principle of the conservation of energy, holds good for all processes whatever, the second law can only be applied to obtain quantitative results in a system which exists in true equilibrium. Such a system will respond to a slight change in external conditions. It is therefore strictly reversible and capable of being taken reversibly through a complete cycle of operations, and can finally be brought back to exactly that state from which it started, each part of the change being reversible. As we have seen, a very slow physical or chemical change is reversible when an indefinitely small alteration in one of the external conditions, such as temperature or pressure, is enough to reverse the direction in which the change proceeds. Thus the system must at each instant be indefinitely near its equilibrium condition. A good example of such an arrangement, described above, is seen when a liquid is in contact with its own saturated vapour at a given temperature. By bringing it into contact with a body at a temperature higher than its own by an infini- tesimal amount, heat slowly enters the system, liquid evaporates and external work can be done. On replacing the source of heat by a body the temperature of which is infinitesimally lower, the direction of flow of heat will change, and energy will 12 [CH. I SOLUTION AND ELECTROLYSIS be absorbed by the system, showing that the process is rever- sible. Similar considerations apply to all processes where a true chemical or physical equilibrium exists. The systems are rever- sible, and can be carried through complete cycles of changes. Examples, such as the evolution of carbon dioxide from calcium carbonate or the solution of a solid in water, are numerous. But the second law of thermodynamics has sometimes been by frictional forces, and to chemical actions, explosions and the like, which are not reversible, and cannot be carried through a conclusions reached, though they may be correct expressions of tendencies, are not exact results. To study the laws which describe the transference of Reversible heat into work, it is best to examine the sim- engines. plest possible form of engine, consisting of a cylinder wherein is confined some substance, the volume of which depends on the temperature. The walls of the cylinder are perfect non-conductors of heat, and its bottom a perfect conductor. By putting the cylinder on a non-conducting stand, the contents are thermally isolated, and by transferring it to a conducting body of large size they are placed in isothermal conditions and an indefinite supply of heat can be a high temperature, one at a low temperature. We now have an engine reduced to its simplest form. In order to draw valid conclusions about the heat absorbed and the mechan- ical energy developed, we must put the engine through a complete cycle, and bring the working substance back to its original state: its internal energy will then be the same as it was at first, and any work done must be due to the heat energy absorbed from the surroundings. This simplest theoretical form of engine was first described by Carnot, who revolutionized this branch of physics by calling attention to the importance of considering complete cycles of operations. We have already deduced the conditions of reversibility, CH. 1] THERMODYNAMICS , and have seen that the co-ordinates which determine the state of the substance must, at any instant, differ only infinitesimally from their equilibrium values. Now the simplest reversible cycle we can arrange consists of four processes, illustrated graphically by the diagram of Fig. 4. Fig. 4. --- (1) Allow the substance to expand isothermally in contact with the hot body from the state A to the state B. (2) Thermally isolate the substance, and continue the expansion adiabatically from B to C. (3) Transfer the cylinder to the cold enclosure, and com- press it isothermally from C to D. (4) Again isolate the cylinder, and compress it adiabatic- ally till the working substance again reaches the state defined by A. It will be observed that, since the temperature is, on the average, higher during the processes (1) and (2) than it is during (3) and (4), the pressure must be higher also, and therefore more work is done by the substance in expanding than is done on it while contracting. On the whole, then, a balance of useful work is performed by the engine, and this work has been obtained at the expense of some of the heat absorbed from the surroundings during process (1); for the quantity of heat given up to the environment during process (3) 14 [CH. I SOLUTION AND ELECTROLYSIS is less than that absorbed during (1) by an amount dynamically equivalent to the balance of work done. Now, in order that this cycle should be performed at all, the external conditions of temperature and pressure must differ appreciably from their equilibrium values, but to insure the reversibility of the cycle, they must only differ by infinitesimal amounts. Nevertheless, although the required conditions cannot be obtained, theoretically the cycle is a reversible one, and we can imagine each process performed in the reverse order, heat being taken in at the low temperature, a balance of work being done on the substance, and the thermal equivalent of this work added to the heat absorbed, and given out with it as a larger quantity of heat at the higher temperature. The whole cycle, and all the individual parts of it are theoreti- cally reversible. In no actual engine can a reversible cycle be obtained, and, if an indicator diagram, as it is called, be drawn to represent the relation at each instant between the pressure and the volume of the steam in the cylinder, and its form compared with the isothermal and adiabatic lines for saturated steam, it will be seen in what ways the engine fails. Since the working sub- stance must be colder than the source of heat and warmer than the condenser, and partly also in consequence of the unavoidable thermal losses which will occur, the top and the bottom of the indicator diagram will be nearer together than in the theoretical diagram of Fig. 4, the corners will be rounded off and the available area, that is the work done, will be less. In fact, it can be shown that a reversible engine is the theoretically perfect engine, and bas the highest efficiency which an engine can possess : it will transform the greatest possible fraction of the heat absorbed into useful mechanical work. For, if possible, let an engine have a greater efficiency than a reversible engine, and let us use it in conjunction with a reversible engine in such a way that it works the reversible engine backwards over the cycle of Fig. 4, putting work into it, and forcing it to give up heat to the hot reservoir, which is common to the two engines. The more efficient engine is at CH. 1] . 15 . THERMODYNAMICS the same time constantly taking a supply of heat from this reservoir, and, in virtue of its assumed efficiency, it can perform the work required, that is to keep the reversible engine in operation, by using a smaller quantity of heat than the rever- sible engine returns to the hot reservoir. This excess must be obtained from the cold reservoir, and therefore the combined machine enables heat to pass regularly and automatically from a cold to a hot body. Such a result is contrary to experience; it proves that our hypothesis is false, and that no imaginable engine can possess a greater efficiency than a reversible engine. We have already seen that no actual engine can do the amount of work corresponding to a strictly reversible cycle. It therefore follows that no other engine can have as great an efficiency as a reversible engine. A reversible engine, then, has the maximum efficiency The absolute scale possible and we need not limit ourselves in of temperature. choosing the working substance. Any system, the volume of which depends on temperature, might be used. The efficiency of a reversible engine is thus independent of the nature of the working substance and of the kind of process employed. It depends only on the temperatures of the hot and cold bodies which are used as the source of heat and as the condenser of the engine. Now the efficiency of an engine, the fraction of the heat taken in which is transformed into work, can be expressed in terms of the heat changes only, för by the principle of the Conservation of Energy, if H, is the quantity of heat absorbed from the hot reservoir, and H, the quantity of heat given out to the cold reservoir, the work done must be equivalent to their difference, and the efficiency must be . : H.-H, H; Thus H /H], which is obtained by subtracting this expression from unity, must also depend only on the temperatures. But any property which depends only on the temperature can be used as a means of measuring temperature, just as the change in volume of mercury is used as a means of measuring 16 [CH. I SOLUTION AND ELECTROLYSIS temperature in the common mercury thermometer. We may thus agree to compare two temperatures by finding the ratio of the quantities of heat absorbed and ejected by a perfect reversible engine working between those temperatures. Then denoting by 0, and 0, the temperatures as thus defined, 0, H ........................(4), O, H,.. and this therinodynamic temperature scale, unlike those which depend on any one property of a particular substance, such as the volume relations of mercury or the like, is a true absolute scale. Moreover this scale of temperature is a consistent one: for if a second reversible engine be coupled with the first, taking in as its supply of heat at 0, the heat given out to its condenser by the first engine, the ratio of the heat taken in at 0, to that finally given out at 0, by the compound engine will be H, H, 0, 0, H, H, O, Öz' giving the same formula as before, H 0 HO: It remains to connect this absolute scale of temperature with some scale which can be practically constructed. Now, since all reversible engines have the same efficiency, to calculate the efficiency of any one such engine is to know that of all. It is easy to find the ratio of the heats taken in and given out by an engine using as its working substance a gas which is described by the laws of Boyle and Charles and suffers no changes of internal energy when its volume varies isothermally. Experiments can afterwards be made to determine how far any known gas departs from those ideal relations. We have seen that a simple reversible cycle may be performed by means of. isothermal and adiabatic processes; the experimental gaseous laws show that isothermal changes can be represented by the expression pu = constant, CH. 1] THERMODYNAMICS . 17 VR while we have already deduced the adiabatic relation, pvp = constant. Let us then take unit mass of an ideal gas through a simple cycle like that described above. As we see by equation (1) on p. 4, during an isothermal expansion at a temperature Tı, an amount of work is done by the gas equal to RT Similarly the work done on the gas during the isothermal contraction at T, is - RT, log= RT, log If the gas absorbs no internal work, that is, if no energy is needed to separate or concentrate the molecules, these expressions for the external work done by the gas can also be taken as giving the heat absorbed and ejected during each process. Thus H - RT, log v/v. H, RT, log vg/v4 Now the change from v to v, is isothermal and PzV = P2V2. Similarly P4V4 = PzV3. Dividing the first of these equations by the second PiVi _ P2V2 ...........(5) P4V4 P3 V3 Again the changes from v, to vz and from vi to v are adiabatic, and therefore PV Y = Pavly and pavy= PzV37. Hence Pivi? 1_P2V, Down=1 = pouvy ................(6). Dividing (6) by (5) and clearing the indices We therefore have H_RT, log va/V _T, H, RT, log vg/V4, T, ............. W. S. 18 [CH. I SOLUTION AND ELECTROLYSIS and thus find that the thermodynamic temperatures are the same as those measured on an ideal gas thermometer. Ex-, periments have shown that an air or hydrogen thermometer agrees very nearly indeed with the ideal gas thermometer. We may therefore take the air thermometer as giving a very near approximation to the absolute thermodynamic scale, and write indiscriminately 01, 0, or T1, T2. The cycle of Fig. 4, consisting of two isothermal and two Complex adiabatic processes, is the simplest form of re- . versible cycle, but any curve on the pressure- volume diagram can represent a reversible cycle if the external conditions are kept throughout in- cyc es. values. A closed curve, such as that in Fig. 5, can be described by taking the substance through small isothermal and adiabatic changes alternately, as indicated in the figure. If these changes are small enough, the lines representing them practically become the closed curve, and the cycle remains re- versible. Fig. 5. We have hitherto expressed the work done on or by the Generalized system as the product of a force and a length co-ordinates or of a pressure and a volume; but the same 1 other pairs of quantities, such as surface tension and area, electromotive force and quantity of electricity, etc. Each of these products consists of a coordinate defining some quantity in the system (volume, quantity of electricity, etc.) and a term often called an intensity factor (pressure, electromotive force, etc.), analogous to the force in the first case. Now, in the general case, the work done by a system may contain all such possible products, and its expression will then involve a series of terms X 8x1 + x28x2 + x38x3 + ...... CH. 1] THERMODYNAMICS 19 The factors X1, X2, etc. are the intensity factors or the “generalized forces,” though, as we have seen, they are not all necessarily of the physical dimensions of real forces, and X1, X2, etc. may similarly be called the quantity factors or the “ generalized coordinates." All the forms of energy thus considered are mutually convertible and, if perfect machines could be obtained, com- pletely convertible. Thus, the whole of a quantity of mechanical energy might, by the aid of a theoretically perfect dynamo, be transformed into electrical energy, while the electrical energy might drive a motor and be reconverted, theoretically without loss. All such forms of energy are therefore said to have the same value, and may be grouped in a single term, which may for convenience be written as E (X8x). I The fact that heat cannot in general be completely con- verted into other forms of energy, shows that it Internal energy. is not of the same value as they are, and should be represented by a separate term in the expression for the energy. The equation giving the increase in total energy e of a system which takes in a quantity of heat SH, and also absorbs various kinds of external work, represented by E(X8x), may therefore, in accordance with the first principle be written de=SH +E (X8x). Now the internal energy of a body is, by the principle of conservation, the same when the body is in a given state, what- ever its previous history has been; thus a change in energy can be expressed as the difference between the absolute values of the energy content of the system, and for finite changes we may write ERE €3-64=L{8H+ (880)}; JA U where the integral refers to any path of change between the states A and B. 2-2 SOLUTION AND ELECTROLYSIS [CH. I Entropy. For a simple reversible cycle, between two temperatures 04 and 0,, we have seen that H, 0 H, , Treating heat taken into the system as positive and that given out as negative, this is equivalent to the statement that H, H, =+ =0. O 02 Similarly for any complex reversible cycle such as that illus- trated by Fig. 5, the same principle holds and fdH TĀ=0. If the operations are not reversible, the efficiency of the cycle must, as we have seen, be less, thus H.-H, 0, -0,. HO or, subtracting unity from each side, we deduce and for a complex non-reversible cycle the corresponding relation is samt 0. Thus the minimum possible value of 080 is 0, while for all actual changes it has a greater value, and it follows that every possible change in the system is attended by an increase in the entropy. Therefore in an isolated system, stable equilibrium is attained when the entropy is at a maximum, for no further spontaneous change can occur. In order to obtain a clearer idea about the nature of entropy, we may write the equation.. oot 80 = ē in the form d¢ 1 dᎻ dᎾ , Ꮎ dᎾ which shows that the change of entropy per degree is equal to the specific heat of the substance under the given conditions, divided by the absolute temperature. In considering finite changes, it is necessary to notice that we no more want to know the absolute value of the entropy of a body than the absolute value of the energy. In each case it is with the changes in the value that we are alone concerned. The equation can be integrated in certain cases where the relations between the properties of the substance are simple, as, for instance, in an ideal gas. Here the internal work is zero, and any heat applied is used in raising the temperature and in doing external work. Now the specific heat, Co, of a gas CH. 1] THERMODYNAMICS at constant volume is the heat required to raise unit mass one degree without doing external work, thus &H = 0,80+pov, Bé - Hồ Pºp de der = C, C+RCO $. - $ = C, log +R logo so that, integrating, From this equation it is easy to calculate the change in entropy corresponding to any given alteration in the state of the gas. potential. When the system is not isolated, further considerations are dynamic involved. The first law gives as the change in energy in a system de = 8H+(X8x), which, by the second law, gives for a reversible transformation de=088+ E(X8x). Subtract from each side 8(04)= 080 +080, then 8(e-00)=-*80 + £ (X8w). Again, taking the equation de = 086 +(X8æ), subtract 8 {09 + X(Xx)} = 080 +886 + (X8x) + (x8X), then ${€ - 00 - E (Xx)} = -080 - $(w8X). If we write y for (e-00) and & for {e – 00-E (X)} the two equations become St=-480+ £ (X8x)...................(8), 88=-080 – £ (x8X)....................(9), 24 [CH. I: SOLUTION AND ELECTROLYSIS these expressions again characterizing reversible changes. For non-reversible transformations the relation yields 84 <-080 + E (X 8x), 8€ <-080 - E(&&X). Let us apply these results to two special cases : (1) When the temperature and the generalized external coordinates 21, &g ... are constant, and consequently so and da vanish and Sf) (7. - 1) 30 (1) + mai may Thus *:- (1.-G- A) +0.("") }(0-modele (9 35.)........(34) an equation which gives the relation between the osmotic pressure and the depression of freezing point, T. – Tı. CH. VI] 153 VAPOUR PRESSURES AND FREEZING POINTS Experiments on of solutions. U It has long been known that the freezing point of a salt solution, such as sea water, is lower than that the freezing points of the water when pure, and in 1788 Blagden? published some observations on the subject, which showed that the depression of the freezing point produced by dissolving a substance in water, was approximately pro- portional to the quantity of substance in solution, except when the concentration became considerable.. More recent observations were made by Rüdorff and de Coppets. The latter noticed that if the lowering of the freezing point produced by chemically equivalent quantities of different salts was examined, it was found that the molecular lowering was nearly equal for salts of similar chemical con- stitution. The whole subject was first fully examined by Raoult“, who extended his observations to non-electrolytes, such as solutions in pure benzene, and solutions of organic compounds in water. He found that the depressions produced by equi-molecular quantities of different substances were nearly of the same value. . Further measurements have been made by Arrhenius, H. C. Jones, Loomis?, Wildermann, Archibald', Barnes 10, Pickeringli, and many others. The theory of such determina- tions has been treated by Nernst and Abegg12, and since the publication of their results the precautions necessary to ascer- tain the true freezing point have been more fully understood. 1 Phil. Trans., LXXVIII. p. 277. ? Pogg. Ann., 1861, 114 et seq. . 3 Ann. Chim. Phys., 1871, 11. 23, 25, 26. 4 Comp. Rend. (1882), xciv. p. 1517, xov. pp. 188, 1030. Ann. Chim. Phys. (6), II. p. 66, (5), XXVIII. p. 137, (6), IV. p. 401. Zeits. phys. Chem. XXVIII. 617 (1898) and Cryoscopie, Paris 1901. 5 Zeits. phys. Chemie, 11. 491 (1888). .6 Zeits. phys. Chemie, XI. 110 and 529 (1893); XII. 623 (1893). ? Phys. Review, 1. 199 and 274 (1893-4); III. 270 (1896); IV. 273 (1897); XI. 220 (1901). 8 Zeits. Phys. Chemie, XIX. 233 (1896). 9 Trans. Nova Scotia Inst. Sci. x. 33 (1898). 10 Trans. Nova Scotia Inst. Sci. x. 139 (1899) and Trans. R. S. Canada (II. ] yI. 37 (1900). 11 Chem. Soc. Jour. 1893. 12 Zeits. für physikal. Chemie (1894), xv. 7, 681. 154 SOLUTION AND ELECTROLYSIS ..[CH. VI The freezing point may, as we have said, be defined as the temperature at which an isolated mass of liquid can exist in permanent equilibrium with its own solid under the normal, atmospheric pressure. It had been assumed that the stationary temperature assumed by a small quantity of a partly frozen liquid, contained in a vessel surrounded by a freezing mixture, gave at once the true freezing point, but Nernst and Abegg pointed out that this limited volume of liquid, radiating to an outer enclosure, would, irrespective of freezing, tend to reach a convergence or equilibrium temperature, which depends on the amount of heat evolved by stirring and on the temperature of the environment; and, unless this equilibrium temperature coincides with the freezing point, or unless the rate of approach to the freezing point is very great compared with the rate of approach to this temperature, the thermometer will not show the true freezing point. The corrections necessary on this account can be experi- agreement between the results of experiments performed under conditions so different, that the uncorrected numbers for the molecular depression of the freezing point of a one per cent. solution of sugar varied from 1.6 to 2:1. Their mean corrected 1 L calculated from the melting point and heat of fusion of ice (p. 147). In order to make the convergence temperature coincide with the freezing point, Ponsoti forined crystals of ice in his solution by surrounding it with a freezing mixture, and then removed the vessel containing the solution, placing it in an air jacket which was surrounded by a vessel filled with a mixture of ice and brine of such a concentration that its temperature was as nearly as possible that of the solution to be examined. of its own freezing point, and the only variation in the con- vergence point is due to the heat evolved by stirring. When 1 Ann. de Chim. et de Phys., and Congélation des Solutions Aqueuses, Paris 1896. CH. VI 155 VAPOUR PRESSURES AND FREEZING POINTS antir no the temperature becomes constant, therefore, it is very nearly indeed the true freezing point. The apparatus generally used for freezing point determi- nations when great accuracy is not required was introduced by Beck- malin, and is represented in Fig. 45. The solution to be examined is placed in a wide test-tube A, which is surrounded by a second larger tube B to serve as an air jacket. This is placed in a vessel C, into which a freezing mixture can be introduced. There is one stirrer in C, and another, made of a platinum wire, in A. A delicate thermo- meter graduated to hundredths of a degree, is also placed in A. It has a little reservoir at the top, into which some of the mercury can be driven, to make the instrument available for different solvents, which freeze at different temperatures. The method of using Beckmann's apparatus is as follows. A weighed Fig. 45. quantity of the pure solvent is intro- duced into A, and its freezing point determined by placing in C some mixture whose temperature is just below the point to be reached. The tube A is then removed, and the solvent melted. A weighed quantity of the substance to be dissolved is intro- duced through the side tube D, and the tube replaced. It is better to cool it slightly below the temperature at which it will finally stand. This can be done if it be kept quite at rest. The undercooled liquid is then stirred by means of the platinum wire, when small crystals of ice form. The temperature rises to a certain point, and then keeps stationary, but will again begin to sink if we go on freezing the solution; for as the solvent is frozen out, the remaining solution gets stronger, and so has a lower freezing point. The highest of these temperatures is IU Nam Only reto : . 1 !! .313nrotter italii .. .... . . . 156 [CH. VI SOLUTION AND ELECTROLYSIS . 38.8 Amyl therefore the one giving the freezing point of the solution, the concentration being corrected for the volume of ice formed. An immense number of observations have been made with one of the many forms of this apparatus. Some of Raoult's results are given below. They represent what he calls the molecular depression, that is the lowering which would be pro- duced by one gram-molecule of the substance in 100 grams of the solvent. The numbers are calculated from observations on solutions of much less concentration than this, on the assump- tion that the law of proportionality is still applicable. Solutions in Acetic Acid. Van 't Hoff's formula gives 38.8. Methyl iodide Butyric acid 37.3 Chloroform 38.6 Benzoic , 43.0 Carbon disulphide 38.4 Water 33.0 Ethylene chloride 40.0 Methyl alcohol 35.7 Nitrobenzene 41:0 Ethyl 36.4 Ether 39.4 39.4 Chloral 39.2 Glycerine 36.2 Formic acid 36-5 Phenol 36.2 Sulphur dioxide 38.5 Stannic chloride 41.3 Sulphuric acid 18.6 Magnesium acetate 18-2 Hydrochloric acid 17:2 Solutions in Formic Acid. Van 't Hoff's formula gives 28.4. Chloroform 26.5 Potassium formate 28.9 Benzene 29.4 Arsenious chloride 26.6 Ether 28.2 Aldehyde 26.1 Magnesium formate 13.9 Acetic acid 26.5 Solutions in Benzene. Van 't Hoff's formula gives 53.0. Methyl iodide 50•4 Chloroform 51:1 ; Methyl alcohol 25.3 Carbon disulphide 49.7 Ethyl 28.2 Ethylene chloride 48.6 Amyl Nitrobenzene 48.0 Phenol 32:4 Ether 49.7 Formic acid 23.2 Chloral 50.3 Acetic 1 25.3 Nitroglycerine 49.9 Benzoic, 25.4 Aniline 46:3 39.7 CH. VI] 157 VAPOUR PRESSURES AND FREEZING POINTS 15.3 Solutions in Nitrobenzene. Van 't Hoff's formula gives 69.5. Chloroform 69.9 · Methyl alcohol 35.4 Benzene 70.6 Ethyl 35.6 Ether 67.4 Acetic acid 36.1 Stannous chloride 71.4 Benzoic , 37:7 Solutions in Water. Van 't Hoff's formula gives 18.9. Methyl alcohol 17.3 Hydrochloric acid 39.1 Ethyl 17.3 Nitric acid 35.8 Glycerine 17.1 Sulphuric acid 38.2 Cane sugar 18.5 Potash 35.3 Phenol 15.5 Soda 36.2 Formic acid 19.3 Potassium chloride 33.6 Acetic , 19.0 Sodium 35:1 Butyric 18.7 Calcium ; . 49.9 Oxalice. 22.9 Bariuir 48.6 Ether 16.6 Potassium nitrate 30.8 Ammonia 19.9 Magnesium sulphate 19.2 Aniline Copper » 18.0 An examination of these tables at once shows that the molecular depressions produced by different substances in the same solvent are approximately constant. Leaving out of consideration, for the present, solutions in water, we find that in other solvents, besides a series of normal compounds, having molecular depressions which agree with the number deduced from Van 't Hoff's theory, there is in general a series of abnormal substances which give depressions of about half this value. Since on Van 't Hoff's theory the effect is proportional to the number of dissolved molecules, and independent of their nature, it is at once suggested, that, in these cases, the number of molecules is halved owing to the formation of aggregates of two ordinary molecules, so that the molecular weight is doubled. There is further confirmation in that some of the compounds which show this effect (such for instance as the acids of the formic acid series, which give half values when dissolved in benzene or nitrobenzene) are known to form compound molecules in the gaseous state, and there is evidence from other sources (e.g. from the surface tensions) that these acids and also certain alcohols form polymeric molecules when liquid. 158 (CH. VI SOLUTION AND ELECTROLYSIS The most accurate experiments yet attempted on the freez- ing points of very dilute solutions are those of E. H. Griffiths, who has adapted the most refined methods of platinum thermo- metry to this problem. The details of the apparatus have not yet been published, but its general features together with described to the British Association in 1901. In order to avoid any action of the solutions on glass, the vessels containing them are of platinum and the water used is finally distilled from a platinum still. The duplicate principle of compensation is adopted, simultaneous observations being made on water and a solution, contained in similar platinum vessels. These vessels are completely surrounded, except for tubes of entrance for the thermometers, etc., by air jackets; the water apparatus is then immersed in a large bath of ice and water, and that holding the solution in a similar bath filled with ice and brine arranged to give, as nearly as possible, the anticipated temperature of the freezing point. The two sides are then frozen by evaporating ether in the air spaces; the local cooling produced by this operation soon disappears. Both the solution and the outer bath are kept constantly stirred by means of water motors, the heating effect due to the work thus done being the same on each side. Platinum thermometry is particularly sensitive when used in this differential manner, and about the hundred thousandth of a centigrade degree can be measured. A solution of cane sugar gave constant molecular depressions of the freezing point while the concentration was varied from 0:0005 to 0:02 normal, the numerical value of the molecular de- pression being 1°:858. A series of experiments on solutions of potassium chloride gave a limiting value of the molecular depression equal to 30.720, which, on the assumption that KCI produces twice the effect of a single molecule, gives for the characteristic number, 1°:860, a result identical with that obtained for cane sugar within the limits of experimental error. Determination of molecular weight. op terreination It is evident then, that the determination of the freezing point of a solution affords à means of controlling the measurement of the molecular weight of point of CH. VI] 159 VAPOUR PRESSURES AND FREEZING POINTS the dissolved substance. If we do not know whether the molecular weight of a body is M or nM, we can see which of these values we must use in calculating the molecular depression in order to get a number nearly equal to the theo- retical value for the constant. It must be noticed that we only determine the molecular weight of a body in a certain solvent; for the same substance may have different molecular weights in different solvents (as witness the alcohols in benzene and acetic acid) and of course these values may be all different from its molecular weight in the gaseous state, though in general this weight corresponds to one of the others. The nature of the solvent may affect the state of molecular aggregation, even as it is affected by conditions of temperature and pressure when the substance is a gas. The. solvents of the benzene series appear to favour polymerisation, while formic acid and its analogues seem generally to produce simple molecules. In the case of aqueous solutions also we have two series, and, taken alone, we might be inclined to consider the higher numbers as normal, and to assign doubled molecular weights to those substances which give the lower values. But when we work out Van 't Hoff's formula for the case of water, it gives, as we have seen, a value 18.6 for the molecular depression. This at once shows that the lower numbers are the normal values, and that they can be explained on Van 't Hoff's theory. It is the higher series which requires some further explanation. Are we to suppose that, as in the case of certain gases at high temperatures, dissociation occurs, and increases the number of effective pressure-producing molecules, or are we to assume that some new cause is brought into operation ? In favour of the dissociation hypothesis it may be urged that the numbers for such salts as KCl, NaCl, etc., which can only be dissociated into two parts, never show values which are much greater than double the normal, while salts such as CaCl2, which can be split into three, sometimes give a molecular depression which is about three times the normal value. We must defer the fuller discussion of these phenomena till we are considering the electrical properties of solutions, but attention is here drawn to the important fact that all those substances which give 160 (CH. VI SOLUTION AND ELECTROLYSIS abnormally great values for the molecular depression of the freezing point in aqueous solution, form, when dissolved in water, solutions which are electrolytes. Moreover their elec- trical conductivities bear at all events an approximate relation to the amount of dissociation which it is necessary to assume point. Whatever is the cause of this abnormally great molecular depression, seems to be also the cause of electrolytic conductivity. Freezing When metals are dissolved in mercury, they produce de- e points pression of the point of solidification, just as of alloys. bodies dissolved in water produce depression of the freezing point. Tammann examined solutions of potassium, sodium, thallium and zinc, and found Raoult's laws approxi- mately true. These metals seem to form monatomic molecules. Heycock and Neville have used many metals as solvents, the following: Solutions in Tin. Theoretical depression, 3º.0. 2.93 2.93 Silver Gold Copper Sodium Magnesium Lead 2.91 Cadmium Mercury Calcium Indium Aluminium 2.43 2:39 2:40 1.86 2.84 2.76 1.25 2.76 Indium and Aluminium thus show a tendency to form more complex molecules when dissolved in tin. The importance of experimentally examining Van 't Hoff's theory has directed special attention to dilute Experiments on solutions, but the effect of increasing concen- solutions. tration on the freezing points of non-electro- lytes has been studied by many observers, among others by concentrated i Chem. Soc. Journ. 1889, 1890. CH. VI] 161 VAPOUR PRESSURES AND FREEZING POINTS Beckmann', Eykman”, Raoults and Ponsot4 They find that in almost all cases the curves drawn with the concentrations in a given mass of solvent as abscissae and the molecular depressions as ordinates are nearly straight lines, inclined at a small angle with the axis of the abscissae. In some few cases the molecular depression decreases fast as the concentration increases, and, at high concentrations, may even be reduced to half its former value. If we extend our method of calculating molecular weights to such solutions, the result indicates that the molecular weight has doubled at the high concentration, so that polymerisation must have occurred. These cases are few; they include such solutions as those of acetoxim and alcohol in benzene, and must be considered analogous to the polymerisation of gaseous nitrogen peroxide at moderate temperatures. less than in these solutions, and is probably analogous to the variation from the usual laws shown by gases at high pressures, rather than to a case of gaseous polymerisation. The best value for the molecular weight at infinite dilution the depression of the freezing point till it cut the axis of no concentration. It is probable that the small deviations of Raoult's numbers for non-electrolytes from the calculated values would become still smaller if this correction for con- centration were applied to his observations. The variation from their ideal laws of gases at high pressures can be approximately expressed by Van der Waals' formula LI b) = RT, where the pressure p is changed by a term proportional to the molecular attraction (a) and inversely proportional to the i Zeits. f. physikal. Chemie, II. p. 715 (1888). 2 Zeits. f. physikal. Chemie, Iv. p. 497 (1889). 3 Comp. Rend., April and November, 1897; Cryoscopie, Paris, 1901. 4 Ann. de Chem. et Phys. [7] x. 79 (1897). W. s. 162 [CH. VI · SOLUTION AND ELECTROLYSIS . square of the volume, and the effective volume v is diminished by a constant b which, according to the theory, is equal to four times the actual volume occupied by the molecules themselves. An equation of the same nature has been developed by Ostwald, Bredig and Noyes, taking account of the molecular volumes of the solvent and of the substance dissolved, and of the inter- actions between them. In general these latter are very small, and the formula reduces to p(v – d)= K ... . . . . . . . ............(16), where the constant d expresses a correction for volume, which depends on the nature both of the solvent and of the substance in solution. On the assumption that the depression of the freezing point is proportional to the osmotịc pressure, the results deduced from this equation give the linear relation for the freezing point curves found in the experiments described above. · Experiments on the effect. of concentration on the freezing points of electrolytes will be considered in a future chapter; but from the most recent results of Ponsot and Raoult on the aqueous solutions of non-electrolytes the following examples may here be quoted. Cane Sugar. C12H,20.1 = 342:18. (Ponsot. Mean values.) Gram-equivalents of sugar Depression of per thousand grams per thousand grams freezing point of water (12) of solution (n) (OT) 87/n 8T/n' 1.89 1.93 ·0287 •0742 •2219 -7358 1.3823 ·0284 •0723 2063 •5878 •9384 054 •140 .419 1:430 2.941 1.88 1.89 1.89 1.94 2:13 2:03 2:44 3:13 CH. VI) 163 VAPOUR PRESSURES AND FREEZING POINTS (Raoult.) OT ST/n 0284 0652 •1250 •2499 •5054 1.0102 0532 •1230 -2372 •4806 .9892 2:0897 1.87 1.89 1.90 1.92 1.96 2:07 Alcohol. C,H,0 = 46.05. ST 8T/n 0328 •0660 •1292 2595 •5251 1.0890 0600 •1207 ·2367 •4760 -9645 1.9900 1.830 1.829 1.832 1.834 1.837 1.828 The behaviour of very strong aqueous solutions has been examined by Pickeringi who finds the following molecular depressions produced by n molecules dissolved in 100 mole- cules of solvent. Substance 10 50 100 300 | 1000 2000 Alethyl alcohol Ethyſ Acetic acid Solvent = Water 1.05 | 1:05 | 1.05 11:03 10:825 | 1.10 | 1:06 1.15 10.815 0·548 1:04 | 0.944 0.865 0:52 Solvent=Benzene Methyl alcohol 10.6 10:31 10:22 10.077 | 0.055 0·042 0·040 | 0.031 Ethyl 2 10 0.6 0-33 0·22 0·10 0·076 0.067 0.044 0.038 i Chem. Soc. Journ. Trans. LXIII. p. 998 (1893). 11-2 164 (CH. VI SOLUTION AND ELECTROLYSIS The difference between the results obtained by measuring the concentration by the number of gram-molecules of solute per 1000 grams of solution and measuring it by the number of gram-molecules per 1000 grams of solvent, is well shown by the tables and diagrams given by Ponsot, who has determined the freezing points of many concentrated solutions. A higher value for the molecular depression is always obtained by using the former method, and as the concentration increases the difference becomes very great indeed. CHAPTER VII. THEORIES OF SOLUTION. Thermodynamics as a basis for physical science. Application to the case of solution. Theory of direct molecular bombardment. Theory of chemical combination. Conclusion. The results obtained in the last two chapters show that the : osmotic phenomena can, by the aid of the prin- Thermodynamics as a basis for ciples of energetics, be deduced for volatile physical science. ence. solutes, and hence extended to other cases. The investigation may start either from the experimental solubility law of gases, or from general molecular theory, which supposes the solute to exist as a number of discrete particles each immersed in and surrounded by the mass of the solvent. By the first of these methods it is possible to develop the theoretical relations of the subject without involving the molecular hypothesis. Such treatment, using as its sole principle of coordination the law of available energy, ulti- mately rests on the experimental impossibility of perpetual motion. This way of treating physical science has recently been adopted by a certain number of chemists, as a means of presenting their subject without applying to it the language or conceptions of the atomic theory, in terms of which even its simplest experimental facts have come to be expressed. It may be granted that students have become too apt to ascribe purely hypothetical properties to atoms and molecules, 166 [CH. VII SOLUTION AND ELECTROLYSIS and that it is often instructive to carry Dalton's atomic theory' as far as possible merely as a principle of chemically equivalent weights. But a body of doctrine, based on the statical theory of energy alone, will be limited in its scope, and cases in which it ceases to be sufficient are soon reached. For instance, the phenomena of highly rarefied gases have only been successfully interpreted by the aid of strictly molecular conceptions. While the gases are dense enough to be treated as matter in bulk, their characteristic equations can be constructed from their be- haviour with regard to pressure, temperature, etc., and then their other relations can be deduced from the principles of thermodynamics. But this method offers no explanation of the identity of the physical constants for different gases, and also for substances in dilute solution. In such matters we are driven back to molecular theory, which offers an alternative method, equally definite, if in some ways more speculative, of correlating the phenomena. tion. In considering the subject of osmotics, the same alternatives appear. The theory can be developed from ex- Application to the case of solu- perimental facts by the principles of energetics alone, or it can be obtained by tắe application of the fundamental ideas of the molecular theory combined with the laws of energetics. Now, whichever method we adopt, the resulting relations do not depend in any way on the physical mode of action of the osmotic pressure; conversely, therefore, the agreement of the results with observation throws no light on the physical cause of osmotic pressure or the fundamental nature of the state of a dissolved substance. It has often been supposed that the analogy between the laws of the gaseous and osmotic pressures in dilute systems, and still more the identity in the absolute values of those pressures, implies a corresponding identity in their physical nature. But it is now evident that no such conclusion can legitimately be drawn. Whatever the cause of the pressure or the nature of solution may be, they must, by the principles of thermo- dynamics, have the properties which have been theoretically deduced from known facts and experimentally confirmed. If CH. VII] 167 THEORIES OF SOLUTION we do not accept this result as a sufficient explanation, but wish to analyse the phenomena further, we must regard the exact physical method by which osmotic pressure is produced as still a subject of enquiry. Two possibilities have been suggested. First, that, like gaseous pressure, osmotic pressure is due to the impacts of the dissolved molecules on the walls of the membrane, which is impervious to them and permeable to the molecules of the solvent; second, that the cause of the pressure is the force of chemical affinity between the solute and the solvent, which tends to make more solvent enter a solution. It may be, however, that these two views will shade into each other in course of development. bombardment. On the theory of direct molecular bombardment, the phenomena of the osmotic cell are exactly Theory of direct molecular analogous to those of the diffusion of gases. When a mass of gas is placed in an empty vessel, it finally, if the small effects due to gravity are negligible, distributes itself equally throughout the volume. This result at once follows from the molecular theory, for the particles of which the gas is composed are imagined as always in rapid motion, though with very short free paths. If then we suppose that an imaginary partition is placed anywhere in the gas, the number of molecules crossing it in one second from left to right will be proportional to the number present, in unit volume (i.e. the concentration) on the left-hand side, and the number crossing from right to left proportional to the number per unit volume on the right. If the concentration is greater on one side than the other, more molecules will leave that side per second than enter it, and thus the concentration will be reduced till it is equal on both sides. A similar process goes on in the case of a substance dissolved in a liquid: uniformity of distri- bution is finally reached, though here the difficulties put in the paths of the dissolved molecules by the presence of the denser solvent prevent their travelling fast, and make the process of diffusion very slow. In the case of mixed gases it is found that the final state 168 SOLUTION AND ELECTROLYSIS [CH. VII UT of distribution of one gas is not affected by the presence of another. Thus the amount of aqueous vapour which diffuses from water into a vacuum, is sensibly the same as if the empty space previously contained air, though in this case the process of diffusion is slower. This too is obviously à necessary consequence of the molecular theory, for, provided the molecules are on the whole too far apart to exert mutual influence, the dynamical equilibrium of water and its vapour will not be affected by the presence of molecules of air. Encounters between the molecules of a gas are continually taking place, and the average energy of translation of each molecule becomes on the whole the same, though sometimes the molecule may be travelling faster and sometimes slower than the average. This can be proved to hold good even if the molecules are of different kinds, as in a mass of mixed gas—the average energy of each is still the same; thus light molecules will travel faster than heavy ones and will therefore diffuse more quickly. This result can be illustrated by the familiar experiment of filling a closed porous pot with air and surrounding it by an atmosphere of hydrogen or coal gas. The molecules of hydrogen enter more rapidly than the heavier ones of air go out, and a pressure gauge will show that the pressure inside the pot becomes greater than outside. If we could in any way entirely prevent the air from ultimately becoming equalized inside and out, we could get a permanent increase of pressure, for the hydrogen would enter till its concentration was the same within as without. The corresponding phenomenon actually occurs in the case of liquids and is shown by osmotic pressure, which can, as we have described, be demonstrated by the use of membranes which are practically semi-permeable in the manner required. Let us place a solution of some substance, cane sugar for example, inside a semi-permeable cell, and immerse it in pure water. The molecules of liquid will strike the walls of the membrane on both sides, but since there are both sugar and water molecules inside, fewer water molecules will, in a given time, hit the wall inside than outside. More water molecules pass in therefore than go out, and since none of the sugar can CH. VII] 169 THEORIES OF SOLUTION escape, an internal pressure is produced which can be measured by any convenient gauge. The process will go on until the pressure due to the water is the same on both sides: the excess of pressure may then be regarded as due to the sugar alone. Sugar is here chosen because little or no contraction in volume occurs when it is dissolved, or when the solution is diluted, which makes the theory of the subject much less complicated than in other cases. The simple physical explana- · tion of colliding molecules gives, at any rate, some idea of a possible mode of action of the phenomena. In most cases, even on this theory, the osmotic pressure, as experimentally measured, must involve other properties which cause a diminution in the available energy of the system on dilution. There may be, for example, a change of volume, or a certain amount of chemical action between the solvent and the dissolved substance, as well as the pressure due to the bombardment of the molecules in solution. When equilibrium is attained, the available energy of the whole system must have reached a minimum value. For very dilute solutions, however, the cause of osmotic pressure is, on this hypothesis, referred simply to bombardment; and Boltzmann, on special assumptions required for the extension to liquids of the methods of the kinetic theory of gases, has offered a demonstration of the law of osmotic pressure on the basis that the mean energy of translation of a molecule shall be the same in the liquid as in the gaseous state at the same temperature? Such an extension of the bombardment theory to liquids seems however vague and speculative, and, as has been often pointed out by Lord Kelvin and others, the similarity in the mathematical laws of gases and dilute solutions does not necessarily connote identity of physical nature. Theory of The alternative theory of the nature of solution already mentioned, refers osmotic pressure to something chemical com- resembling chemical affinity, which tends to bination. make solvent enter the osmotic cell and combine with the solution. There are two varieties of this theory to be i Zeit. phys. Chem. VI. 478 (1890). 170 [CH. VII SOLUTION AND ELECTROLYSIS. considered. There is what is often called the hydrate theory; and there is the view that each particle of soluté unites with or influences in some way a large and uncertain number of solvent molecules, thus forming a mobile and somewhat loosely con- structed molecular complex, which constantly interchanges its parts with those of other similar complexes. The hydrate theory imagines that definite hydrates exist in solution, the hydrates being chemical compounds of the solute with water, which, like other chemical compounds, agree with the laws of definite and multiple proportions. As more solvent is added, new compounds containing a larger number of water molecules are formed, and the mixture of these different hydrates allows the continuous variation of composition which is found in solutions. Theories based on these ideas have been recently framed by H. E. Armstrong!, S. U. Pickering? and others. Pickering supposes that, when solvent is frozen out, some of the existing hydrate is decomposed, and the next lower one formed. From the heats of dilution of solutions of sulphuric acid of different strengths, he calculates the work required to do this, and, adding it to that required to compress the molecules dissolved, deduces the lowering of freezing points. The agreement of his numbers with observation shows that the excess of freezing point depression can be calculated from the heat of dilution, but does not decide whether that heat of dilution is due to the combination with additional molecules of water or (partly at any rate) to the resolution of some sulphuric acid molecules into their ions. Pickering's main argument for the existence of hydrates in solution is however based on the sudden changes in curvature, first noticed by Mendeléeff, which appear in the lines drawn to represent the variation of some physical property with the concentration. He has made, for instance, a long and careful determination of the densities of sulphuric acid solutions of different strengths, and drawn a curve to show his results.. LU 1 Proc. R. S. No. 243 (1886). 2 For general account see Watts' Dict., Art. Solutions, II. 3 B. A. Report, 1890, p. 320. CH. VII] THEORIES OF SOLUTION 171 a Changes of curvature appear at points corresponding to defi- nite molecular proportions (e.g. H2SO4. H20 and H2SO4.4H,O). These changes can be more readily seen if a new curve is drawn connecting the concentration with the rate of change of density with concentration (i.e. with the slope at different points of the first curve). By this process of “differentiation” a series of straight lines is obtained with breaks at the positions where, in the first curve, changes of curvature appeared. Similar figures were drawn for electric conductivity, expansion by heat, contraction on formation, heat of dissolution, heat capacity, refractive index, magnetic rotation, and freezing point, and changes of curvature were found at the same points for all. Ostwald however saysł that the position of the breaks alters with change of temperature. With weak solutions it is impos- sible to say whether such points correspond to definite molecular proportions, owing to the smallness of the change in percentage composition which would be caused by the addition of another water molecule to H,SO.; but the breaks are found of precisely the same character as in the case of stronger solutions, and are, apparently, due to the same cause. The thermal change, result- ing from dilution of a strong solution, is usually of the same sign as that obtained by dissolving the solid in the first instance, and this also indicates that, if hydrates are present in concentrated, they are also present in dilute, solutions. If we allow this, it follows that one acid molecule is able to combine with, or at all events to influence in some way, an enormous number of water molecules. Several hydrates, before unknown, were indicated by the presence of these breaks, and subsequently obtained in the solid form. Thus Pickering isolated H2SO4.4H,O, HBr.3H,O, HBr. 4H,0, HC1.3H,0, HNO3. H,0 and HNO3.31,0. He considers that the crystallization of a definite hydrate is strong evidence that it exists in solution, for bodies suddenly formed at the instant of precipitation come down as amorphous substances—a common observation in the processes of chemical analysis. Dilute sulphuric acid, dissolved in acetic acid, pro- duces a smaller depression of the freezing point than the sum i i Watts' Dict., Art. Solutions, I. 172 [CH. VII SOLUTION AND ELECTROLYSIS 1 of those due to the acid and water separately, hence Pickering argues that no dissociation, but rather chemical union, result- ing in a reduction in the number of molecules, has occurred. The combination of large numbers of solvent molecules with one molecule of a body in solution may produce forces equal in all directions and thus secure the mobility of the dissolved molecules. Certain definite numbers of solvent molecules will be capable of more symmetrical arrangement than others, and will form hydrates, but their parts are freely interchangeable with each other. A dissolved molecule will be able to pass through a crevasse only when the number of solvent molecules requisite to keep it in solution can pass simultaneously, and this may explain the action of semi-per- meable membranes. Pickering, as described on p. 97, found that, when a mixture of propyl alcohol and water was placed in a porous pot, and the whole immersed either in pure water or pure alcohol, the volume of liquid inside the porous pot increased, showing that the phenomenon is due, not to the impermeability of the pot to either constituent alone, but to its impermeability to the solution as a whole. On the other hand, it may be argued that the evidence in favour of the existence of definite hydrates in the liquid phase is inconclusive, for the study of saturated solutions as special cases of systems in equilibrium, which has been made in the early chapters of this book, shows that it does not follow because a definite solid crystallizes from a solution, that it must necessarily exist in the same state of molecular aggre- gation in the liquid phase. The general analogy between the process of solution and cases of definite chemical action is, nevertheless, very close; and it was accepted as a real identityl till the development of osmotic theory by Van't Hoff showed the similarity between solutions and gases, and thus caused more stress to be laid on that aspect of the subject. There is evidence to show that chemical action does not always result in the formation of compounds in which the usual valencies of the elements present are exactly satisfied. The fact that salts often combine 1 Tilden, B. A. Report, 1886, p. 444. CH. VII] 173 THEORIES OF SOLUTION ' with one or more molecules of water to form definite crystalline hydrates is an instance of this property, and the phenomena have been extensively studied by chemists, sometimes under the name of residual affinity, the resultant substances being usually known as molecular compounds. From such bodies as these to the mobile aggregations required by the molecular complex view of solution is no impossible step. It is easy to imagine a loose kind of chemical union in which the continuously variable compositions and the general mobility characteristic of solutions might be realized, but the chief difficulty in the way of such a chemical theory has been its inability to suggest a probable mechanism by which the equality in absolute values of the osmotic and gaseous pressures would necessarily follow. The same difficulty has confronted the theory of definite chemical compounds, but in the year 1896 Poynting showed that, if certain assumptions were made, the observed result would follow? Let us consider the effect of combination on the vapour pressure. “If the molecules of salt were simply mixed with those of the solvent, or if they combined to form stable non- evaporating compounds with the solvent, which compounds were simply mixed, then the mixture should have the same vapour pressure as the pure solvent. For we might regard the salt or compound molecules at the surface as equally reducing the effective evaporating and the effective condensing area, somewhat as a perforated plate or gauze laid on the surface would do. But the salt probably combines with the solvent to form unstable molecules which continually interchange consti- tuents, so that when near the surface they may serve equally with those of the pure solvent to entangle the molecules of vapour coming downwards, these descending vapour molecules taking the place of molecules attached to the salt. Probably, however, they are less energetic than the pure solvent molecules and do not contribute so much to evaporation. We shall make the supposition that they do not contribute at all.” It may be observed that the same result will be reached if each salt molecule diminishes the facility for evaporation of x solvent molecules by the 1/ath part. i Phil. Mag. XLII. 298 (1896). 174 [CH. VII SOLUTION AND ELECTROLYSIS If N is the number of gram molecules of solvent per litre and n the number of gram-molecules of solute, the number of solvent molecules left unaffected is N - n. There are then N molecules active for condensation, and only N-n active for evaporation. Hence the vapour pressure is reduced in the ratio (N-n)/ N. Thus p N-n pN p-p' n and PN which is the relation already deduced on p. 130, from the known value of the osmotic pressure. Conversely, this last result yields the true osmotic law by an inversion of the process there used. Reasons have already been stated for believing that the osmotic pressure is proportional to the number of spheres of influence of solute particles immersed in the solvent, and there- fore that, in solutions of electrolytes, which have abnormally great osmotic pressures, partial dissociation must occur, resulting in an increase in the number of such effective particles. Later, we shall find that a similar dissociation is indicated by the facts of electrolysis, which lead to the conclusion that some of the molecules of salts, etc. are resolved into two or more parts by the act of solution, and that these parts, or ions as they are called, travel through the liquid in opposite directions under the action of an electromotive force and are therefore charged electrically. The two independent lines of enquiry thus lead to the same hypothesis of electrolytic dissociation, and the evidence for and against this theory will have to be fully considered in future chapters. On Poynting's view of osmotic pressure then, as the writer has previously indicated', the supposition of combination be- tween the solute and the solvent has to be extended to include the case where the solute is resolved into its ions. We must imagine that each ion itself destroys the facility for evaporation of one solvent molecule, or diminishes that facility in like pro- portion in a group of solvent molecules, just as each molecule 1 Nature, Liv. 571 ; Lv. 33 (1896). 'THEORIES OF SOLUTION 175 : of a non-electrolytic solute does? With this extension, the theory of chemical combination seems to agree with the facts. There are thus different views as to the nature of solution, i each offering a reasonable explanation of the Conclusion. e phenomena. At first sight, the idea of mo- lecular bombardment on the walls of the membrane by solute particles which are dynamically independent of the solvent chemical combination between them; but we know too little about the nature of chemical affinity to be quite sure that it is not due to some relation in the dynamical properties of the reagents, and the two views of solution may after all be different statements of the same truth. However tbis may be, the two theories at present stand opposed, and each seems capable of explaining the ordinary facts of osmotic pressure. These phenomena, therefore, are unable to provide a crucial experiment to decide between the hypotheses. It will, however, be noticed that Pickering's ex- periment, in which either propyl alcohol or water enters as solvent an osmotic cell containing a mixture of these two liquids, seems to show that it is to a combination that the membrane is impervious, and is thus in favour of the view that solution is due to something analogous to chemical action. It must be clearly understood that an enquiry about the nature of solution and the physical mode of action of osmotic pressure is a problem entirely distinct from that of the essential difference between an electrolyte and a non-electrolyte. The hypothesis of ionic dissociation is quite independent of the direct bombardment theory of osmotic pressure, with which it has often been confused, and is perfectly consistent with the view that solution is a process of the same ultimate nature as ordinary chemical action. Stress is laid on this point, because criticisms of the direct bombardment theory of osmotic pressure have sometimes been adduced as reasons for refusing to accept the idea of the ionic dissociation of electrolytes?. 1 For a controversial discussion of these questions see Nature, LIV., LV., indexed under “Osmotic Pressure," "Ions, theory of,” etc. CHAPTER VIII. ELECTROLYSIS. Introduction. Volta's pile. Early experiments. Faraday's work. Polarization. Faraday's laws. Electrochemical equivalents. The electrolysis of gases. Nature of the ious. Introduction. The origin of the study of electrolysis is to be found in the work of Galvani at Bologna. About the year * 1786 he noticed that the leg of a frog con- tracted under the influence of a discharge from an electric machine. Following up this discovery, he observed the same contraction when a nerve and a muscle were connected with two dissimilar metals, placed in contact with each other. Galvani attributed these effects to a so-called animal electricity, and it was left for another Italian, Volta of Pavia, to show that the essential phenomena did not depend on the presence of an animal substance. In 1800 Volta invented the pile still known by his name, which, by reason of the greater intensity of its action, provided a means of investigation that was at once put into use by himself and his contemporary workers in other countries. Volta's pile consisted of a series of little discs of zinc, copper and blotting-paper moistened with water or Volta's pile. brine, placed one on top of the other in the order zinc, copper, paper, zinc, etc., finishing with copper! 1 Volta thought that the origin of the effects was at the junction of the two metals, hence the order of discs in the pile, and the terminal metal plates in air in the crown of cups. These plates are now known to be useless. CH. VIII] 177 ELECTROLYSIS Such an arrangement is really a primitive primary battery, each little pair of discs separated by moistened paper acting as a cell, and giving a certain difference of electric potential, the differences due to each little cell being added together and producing a considerable difference of potential or electro- motive force between the zinc and copper terminals of the pile. Another arrangement was the crown of cups, consisting of a series of vessels filled with brine or dilute acid, each of which contained a plate of zinc and a plate of copper. The zinc of one cell was fastened to the copper of the next and so on, the isolated copper and zinc plates' in the first and last cups forming the terminals of the battery. Volta arranged the metals in an electromotive series so that, when placed in a solution, a metal is always positive to any of those below it in the series and negative to those above it. J. W. Ritter pointed out that the order of this list is also the order in which the metals precipitate each other from solution, an important connexion between electrical and chemical phenomena only appreciated long afterwards. Volta also discovered that the same difference of potential is given by two metals, whether they are directly connected, or joined by means of a third metal. Thus, in any complete circuit made up of a number of different metals, the total electromotive force must vanish. Early Experi- Using a copy of Volta's original pile, Nicholson and Carlisle ? xperi found that when two brass wires leading from ments. its terminals were immersed near each other in water, there was an evolution of hydrogen gas from one, while the other became oxidised. If platinum or gold wires were used, no oxidation occurred, but oxygen was evolved as gas. They noticed that the volume of hydrogen was about double that of oxygen, and, since this is the proportion in which these elements are contained in water, they explained the phenomenon as a decomposition of water. They also noticed ? See note, p. 176. ? Nicholson's Journal, iv. p. 179 (1800). . W. s. 12 178 [CH. VIII SOLUTION AND. ELECTROLYSIS that a similar kind of chemical action went on in the pile itself, or in the cups when that arrangement was used. Cruickshank? soon afterwards decomposed the chlorides of magnesia, soda and ammonia, and precipitated silver and copper from their solutions--an observation which afterwards led to the process of electroplating. He also found that the liquid round the pole connected with the positive terminal of the pile became alkaline and the liquid round the other pole acid. In 1806 Sir Humphry Davyề proved that the formation of the acid and alkali was due to impurities in of water could be effected although the two poles were placed in separate vessels connected together by vegetable or animal substances, and established an intimate connexion between the galvanic effects and the chemical changes going on in the pile. The identity of“ galvanism” and electricity, which had been maintained by Volta, and had formed the subject of many investigations, was finally established in 1801 by Wollaston, who showed that the same effects were produced by both, while in 1802 Erman measured with an electroscope the potential differences furnished by .a voltaic pile. In 1804 Hisinger and Berzelius3 stated that neutral salt solutions could be decomposed by electricity, the acid appearing at one pole and the metal at the other, and drew the con- clusion that nascent hydrogen was not, as had been supposed, the cause of the separation of metals from their solutions. Many of the metals then known were thus prepared, and in 1807 Davy decomposed potash and soda, which had previously been considered to be elements, by passing the current from a powerful battery through them when in a moistened con- dition, and so isolated the metals potassium and sodium. The remarkable fact that the products of decomposition menters on the subject, who suggested various explanations. i Nicholson's Journal, iv. p. 187. 2 Bakerian Lecture for 1806, Phil. Trans. 3 Ann. de Chimie, LI. p. 167 (1804). CH. VIII) 179 ELECTROLYSIS Grotthusin 1806 supposed that it was due to successive decompositions and recombinations in the substance of the liquid. Thus if we have a compound AB in solution, the molecule next the positive pole is decomposed, the B atom being set free. The A atom attacks the next molecule, seizing AB AB AB AB AB Fig. 46. the B atom and separating it from its partner which attacks the next molecule and so on. The last molecule in the chain gives up its B atom to the A atom separated from the last molecule but one, and liberates its A atom at the negative pole. Grotthus, and other pioneers in the subject, thought that Faraday's the decomposition was due to a direct attrac- tion exerted by the poles on the opposite constituents of the decomposing compound, which varied as the square or some other power of the distance. This explana- tion of electrolytic action, as framed by the early experimenters, was finally disproved by Faraday?, who placed two platinum strips, kept at a constant difference apart and connected through a galvanometer, at different positions in a trough of dilute acid through which a current was flowing. The deflection of the galvanometer was the same for all positions of the strips, thus showing that the electric forces were the same everywhere between the poles. He also showed that chemical decom- position could be produced without the presence of any metallic pole. An electric discharge from a sharp point connected with a frictional machine, was directed on to a strip of turmeric work. i Ann. de Chimie, LVIII, p. 54 (1806). 2 Experimental Researches, 1833. '12--2 180 [CH. VIII SOLUTION AND ELECTROLYSIS paper moistened with sulphate of soda solution, the other end of the paper being joined to the other terminal of the machine. Alkali appeared on the paper opposite to the discharging point. Another experiment showed that insoluble hydrate of magnesia was produced at the junction between a strong solution of sulphate of magnesia and pure water when a current was passed across it. Faraday accepted the idea of Grotthus' chain, but held that there were chemical forces between atoms of opposite kinds in neighbouring molecules as well as in the same molecule, and that when the electric force was added to these they became strong enough to overcome the attractions between the atoms in the same molecule, so that a transfer of partners occurred. We shall see later that transfers of part- ners are probably always going on in solutions, whether a current is passing or not, and that the function of the electric forces is merely directive, but Faraday's account of the conse- quences of this interchange still holds good. He pointed out how it explained all the facts, including the passage of acids through alkalies under the influence of the current, a pheno- menon which had created great surprise when discovered by Davy. Faraday remarked that the presence of the alkali not only facilitated the passage of the acid, but was even necessary, for, without something with which to combine on its way, the acid would be unable to travel. Thus Faraday's view amounts to supposing a constant stream of acid in one direction and of alkali in the other. Faraday introduced a new terminology which is still used. Instead of the word pole which implied the old idea of attraction and repulsion, he used the word electrode, and called the plate of higher electric potential, by which the current is usually said to enter the liquid, the anode, and that by which it leaves the liquid, the cathode. The parts of the compound which travel in opposite directions through the solution he called ionscations if they went towards the cathode and anions if they went towards the anode. He also introduced the words electrolyte, electrolyse, etc., which we have already used. Faraday pointed out that the difference between the effects CH. VIII 181 ELECTROLYSIS of a frictional electric machine and of a voltaic battery lay in the fact that the machine produced a very great difference of potential, but could only supply a small quantity of electricity, while the battery gave a constant supply, much larger in quantity, but only produced a very small difference of potential. Polarization. 1 The diminution with time of the intensity of the voltaic pile or cell was noticed by the early observers, and was investigated by Davy and Faraday. The researches of the latter physicist brought out its con- nexion with the accumulation at the electrodes of the products of the decomposition of an electrolyte through which a current is passed. Faraday showed that a definite minimum "intensity," depending on the nature of the electrolyte, was necessary for the ions or their products to be liberated at the electrodes. He arranged certain substances in the order of what we should now term their decomposition voltages, and pointed out the relation between this order and that in which the same bodies could be placed with reference to the intensity of secondary current they would furnish when disconnected from the primary battery and then joined with a galvanometer. This phenomenon, originally observed by Ritter, lies at the base of the action of the accumulator. When the intensity of the primary current is not enough to visibly decompose an electrolyte, Faraday showed that a small current still passed. Whether this leakage current really flows without chemical separation at the electrodes, or is kept up by the removal of the products of the action as fast as they are formed, is a question to be considered later. When the nature of the electromotive force of a battery was more generally understood, it was evident that Faraday's work showed that the reverse electromotive force of “polariza- tion," as the phenomenon under consideration was named, must be subtracted from the primary electromotive force of the battery, before the effective electromotive force of the system could be calculated. 1 182 SOLUTION AND ELECTROLYSIS The injurious effects of polarization in primary batteries led to many attempts to overcome it. The methods in ise in the common form of cell are well known. They can be classed in three groups, according as their action is: (1) mechanical, as in Smee's cell, where the silver plate is covered with crystals of platinum, the sharp edges of which .(2) chemical, as in the bichromate cell, where the hydrogen is converted into water by an oxidising agent; or (3) electrochemical, as in Daniell's cell, where the hydrogen ions enter a solution of copper sulphate, and are therefore replaced on the electrode by copper, which has a lower de- composition voltage... : Davy had previously shown that there was no accumulation of electricity in any part of a voltaic circuit, Faraday's Laws. : and that a uniform flow or current existed throughout. Faraday set himself to examine the relation between the strength of this current and the amount of chemical decomposition. He first proved by observations on the decomposition of acidulated water, that the amount of chemical action in each of several cells was the same when the cells were joined together and a current passed through them all in series, even if the sizes of the platinum plates were different in each. The volume of hydrogen was unchanged even if electrodes of different materials such as zinc or copper--were used. He then divided the current after it had passed through one cell into two parts, each of which passed through another cell before being reunited. The sum of the volumes of the gases evolved in these two cells was equal to the volume evolved in the first cell. The strength of the acid solution was then varied, so that it was different in the different cells in one series, but the chemical action still remained the same in all. . Thus the induction known as Faraday's first law. was made :- : The amount of decomposition is proportional to the quantity of electricity which passes. CH. VIII] 183 ELECTROLYSIS An apparatus for the decomposition of water can therefore be used to measure the total quantity of electricity which has passed round a circuit. Such instruments are termed voltameters. The same law was then shown to be true for solutions of various metallic salts, and also for salts in a state of fusion—the weight of metal deposited being always the same for the same quantity of electricity. A second law also was formulated : The mass of an ion liberated by a definite quantity of electricity is proportional to its chemical equivalent weight. In the case of elementary ions this equivalent weight is the atomic weight divided by the valency, and in the case of compound ions it is the molecular weight divided by the valency. It was then proved that the amount of zinc consumed in each cell of the battery was identical with that deposited by the same current in an electrolytic cell placed in the external circuit. Faraday's work laid the foundations of the modern quan- titative science of electrolysis. His results can be gathered into one statement, as follows:- The quantity of a substance which separates at an elec- trode is proportional to the whole amount of electricity which passes and to the chemical equivalent weight of the substance. This statement implies that no current flows without a corresponding amount of chemical separation at the electrodes. Faraday himself thought that, in certain cases, a small current could leak through electrolytes without causing separation, a point which cannot yet be regarded as settled. In the case of the electrolysis of solutions in water of metallic salts, such as those of silver, copper, etc., experiments seem to show that there is no leakage current, and that the deposition of metal or the evolution of gas is strictly proportional to the electric transfer as long as the electromotive force is high enough to overcome the reverse force of polarization, which is generally present in cases of electrolysis. When a smaller electromotive 184 [CH. VIII ' SOLUTION AND ELECTROLYSIS force than this is applied, the current flows at first, but its strength gradually diminishes, until finally it almost vanishes. The cause of the slight leakage current that then remains will be considered later. In connexion with this, it is interesting to note that Nernst has recently investigated mixtures of the oxides of certain metals, such as magnesium, zirconium, etc., which conduct well when hot, and give very little chemical decom- position. These substances however show signs of polarization, and are also transparent to light, a property considered in- compatible with true metallic conductivitył Again, metallic sodium dissolves in liquid ammonia, giving a conducting solution which shows no polarization and seems to undergo no chemical changes?. It is as yet uncertain whether metallic and electro- lytic conductivity are ever associated in the same substance, and further experiments are necessary to decide the point. equivalents. The confirmation of Faraday's law for solutions of silver Electrochemical salts has been incidentally effected in the lents. course of many experimental determinations of the electrochemical equivalent of silver. If the value obtained for the silver deposited by unit quantity of electricity is the same when the strength of current and the other conditions of the experiment are varied, the quantity of elec- tricity and the mass of silver deposited must be proportional to each other. An exact knowledge of the electrochemical equivalent of silver is of great importance, since, given this constant, a silver voltameter can be used as a means of measuring accurately the total quantity of electricity, or the average current, which has passed through a circuit. This method has been adopted in the determination of the electro- motive force of the standard Clark cell, and in several measurements that have been made by electrical means of the thermal equivalent of the unit of mechanical energy. In order to determine the electrochemical equivalent, a i Zeits. Elektrochem. VI. 41 (1899). 3 Cady, Jour. Phys. Chem. 1. 710 (1897). CH. VIII] 185 ELECTROLYSIS constant current of known strength is passed for a measured time through a solution of some silver salt. The most constant results are obtained when a neutral solution of the nitrate is used containing about fifteen parts of salt to one hundred of water, and the current has an intensity of about one hundredth of an ampère to the square centimetre. The silver may be deposited on a platinum bowl used as cathode, the anode being a silver plate wrapped in filter paper to catch any particles disintegrated. The electrochemical equivalent is expressed as the number of grams of silver deposited by a current of one ampère in one second. The following are perhaps the best determinations of this constant: Lord Rayleigh and Mrs Sidgwick F. and W. Kohlrausch? Pellat and Potiers ... Patterson and Guthe Richards, Collins and Heimrod 5 ... ... 0:00111795. 0.0011183. 0.0011192. 0.0011192. ... 0:0011172. Thus the mean result is about 0.001118 or 0:001119 grams per ampère-second. The electrical measurements of the thermal equivalent agree better with the mechanical ones if the higher value is taken, and we shall therefore consider that the most probable value in the present state of our knowledge is 0.001119 grams of silver per ampère-second. The correspond- ing constant for other elements or compounds can be calculated from this number by dividing it by the chemical equivalent of silver, viz. 107.9, and multiplying by the chemical equivalent of the substance required. The value for hydrogen thus comes out 1.045 x 10-5, its atomic weight being taken as 1.008, when oxygen is 16. It will be noticed that the chemical constant involved is the equivalent, and not the atomic weight. Therefore, in the i Phil, Trans. CLXXV. 411 (1884). 3 Wied. Ann. XXVII. 1 (1886). 3 Journal de Physique [2] ix. 381 (1890). 4 Phys. Rev. vii. 257 (1898). 3 Zeit. Phys. Chem. XXXII. 301 (1900). 186 (CH. VIII TTI SOLUTION AND ELECTROLYSIS case of substances like iron, which form two series of salts, the amounts deposited will be different when solutions of the different salts are used. The two amounts will be in the proportion of the two chemical equivalents; if a current is sent through solutions of a ferric and a ferrous salt in series, the resultant weights will be as 56/3:56/2. With no substance other than silver have such accurate experimental results been obtained, though many observations have been made on copper and other metals in aqueous solutions of their salts. In all cases, Faraday's law has been found to be true within the limits of experimental error, the apparent variations which sometimes appear, especially with copper, having been traced to known causes, such as the solubility of the metal in the solution. The experimental errors are much greater when gases are evolved, as in the electrolysis of acidulated water. The gases are to some extent soluble in the liquid, and may be absorbed in the substance of the electrodes; oxygen is often liberated partly in the condition of ozone, while gases like chlorine attack the liquid or the electrodes, forming chemical com- pounds with them. Although several direct measurements of the electrochemical equivalent of water have been made, on account of these sources of uncertainty, none of them can be considered as very accurate. Since the general evidence for Faraday's law is very strong, it is better to calculate electro- chemical equivalents from the measured value for silver and the known chemical equivalents of the different ions. Kohl- rausch and Holborn" give a list of equivalent and electrochemical equivalent weights, the experimental value for silver being taken as 1.118 mg./amp.-sec. It is now probable that this number should be raised by one part in a thousand, and the electrochemical equivalents in the following table have all been increased in the same proportion. 1 W. N. Shaw, B. d. Report, 1886, p. 411. ? Leitvermogen der Elektrolyte, Leipzig, 1898. CH. VIII] 187 ELECTROLYSIS Equivalent weights A (10= 8.00), and electrochemical equivalents E in. mg./(amp.-sec.) of mono- and di-valent ions. Cations Anions E FI CN NO3 Clo Bro 1.008 39.14 23:05 7.03 107.92 18:07 68.70 43.81 20.02 12:17 32:7 56.05 318 28.01 27.5 29:35 103:46 26.07 0.01037 0.01045 0.4059 0-2390 ()•0729 1.119 0.1874 0.7124 0:4544 0.2076 0:1262 0:3391 0.5812 0:3297 0-2905 0.2852 0:3044 1.0728 0.2704 35.45 79.96 126.86 19.05 17.01 26.04 62.04 83.45 127.96 174.86 45.01 59:02 8.00 16.03 48:03 58.07 30.00 44:00 38.20 0:3677 0.8291 1:3152 0.1975 0·1764 0.2701 0.6433 0.8653 1:3269 1.8132 0.4668 0.6120 0.08296 0.1663 0.4981 0.6022 0.3111 0.4563 0:3961 CHO. C,H,82 O 22 Mn SO, Cro COR Ni Pb Cr Solvents other than water, for example acetone and pyri- dine, have often been used. Faraday's laws also hold good in such cases, and the electrochemical equivalents seem to be identical with those obtained when the solvent is water?. Faraday's laws have also been demonstrated for fused salts, many of which are good electrolytes, with conductivities of the same order as those of aqueous solutions?. Again, in recent years it has been shown that the discharge of electricity through gases is an electrolytic process accom- panied by chemical decomposition. Here also the same laws describe the phenomena, the electric charge associated with a gaseous ion being the same in amount as the charge on an ion in solution. J. J. Thomson has found that the sign of the i Kahlenberg, Journ. Phys. Chem. IV. 349 (1900); and Skinner, B. A. Report, 1901. 2 Faraday, Experimental Researches, and Helfenstein, Zeits. Anorg. Chem. XXIII. 255 (1900). 3 Proc. R. S. LIII. 90 (1893); LVIII. 244 (1895): 188 [CH. VIII SOLUTION AND ELECTROLYSIS charge depends on the nature of any other ion present. More- over, it may even be changed by varying the conditions of the experiment: the electrodes at which hydrogen and oxygen are liberated in the electrolysis of steam are reversed when an arc instead of a spark discharge is used. In every case of electrolysis Faraday's laws seem to apply, and the amount of a given substance liberated by a given transfer of electricity appears to be the same under all conditions. This result leads to an exact view as to the nature of the process. Since the amount of substance de- posited is proportional to the quantity of electricity which passes, it follows that a definite charge of electricity is associated with a definite mass of the substance. We are thus led to look. on electrolysis as a kind of convection, each ion carrying with it a fixed charge of electricity, positive or negative, which is given up to the electrode under the influence of an electromotive force above a certain limit. It is clear that, on this convective view of electrolysis, the conductivity of a solution must be proportional to the charge on each ion, to the number of ions, and to the velocity with which they move through the solution. Whenever one gram-atom or gram-molecule of any mono- valent ion is separated at an electrode, the same quantity of electricity passes round the circuit; if the ion is divalent, the quantity is twice as great, and so on. All monovalent ions must therefore be associated with the same charge, all divalent ions with twice that charge, etc. The quantity of electricity involved is easily calculated by considering an example. If a current of one ampère flows for one second, experiment shows that 0:001119 grams of silver are liberated from the solution of one of its salts. Thus, when the equivalent weight in grams is deposited, the quantity of electricity passing is 107.92/0·001119 or 96440 ampère-seconds or coulombs. The same result is of course true for the gram- equivalent of any other substance, the gram-equivalent being the gram-molecule or gram-atom divided by the valency. Whenever a gram-equivalent of a substance is decomposed, therefore, 96440 coulombs of electricity pass round the circuit, 7m CH. VIII] 189 ELECTROLYSIS actually transported through the electrolyte by one gram- equivalent of any ion. It is possible to calculate approximately the absolute electric charge carried by a single monovalent ion, since the number of molecules in a given volume of gas can be estimated by the kinetic theory from the viscosity and diffusion constant. At 2:5 x 1019 molecules in one cubic centimetre of any gas. As we have seen, one electromagnetic unit of electricity evolves 1.045 x 10-4 gram of hydrogen, which at normal tem- perature and pressure fills a volume of 1.16 c.c., and therefore contains about 3 x 1019 molecules or 6 x 1019 atoms, and yields the latter number of ions when dissolved as a hydrogen salt. Each ion is then associated with 1.7 x 10–20 electromagnetic units. The ratio between the units of electric quantity being 3 x 1010, the ionic charge is about 5 x 10-10 electrostatic units. Another value for the number of molecules of gas can be deduced from the measured variations of the gases from Boyle's law. The kinetic theory here leads to the result 1.2 x 1019, and the corresponding ionic charge is about 10-9 electrostatic units. The charge on the ions produced by the passage of Röntgen The electrolysis rays through gases has been investigated by of gases. J. J. Thomson? If N is the number of ions in unit volume of the gas, e the charge on each of them, and v the mean velocity of the positive and negative ions under a given electromotive force, the product Neu can be determined by exposing a gas to the action of Röntgen rays and measuring the current produced through it by a known electromotive force. Rutherfordhas determined v for a considerable number of gases, and the number N can be estimated by a method due to C. T. R. Wilson, who, as described on p. 43, has shown that gaseous ions act as condensation nuclei in air saturated with aqueous vapour. From the velocity of fall of the cloud so formed, it is possible to calculate the approximate size of the 1 Phil. Mag. XLVI. 528 (1898). 2 Phil. Mag. XLIV. 422 (1897). 190 [CH. VIII SOLUTION AND ELECTROLYSIS resulting drops of water, and from the weight of the drops precipitated their number is known. Assuming that each ion acts as a centre of condensation, this result gives the number of ions present. The measure of the current through the ionized gas then furnishes, a' value for e the ionic charge equal to about 6'5 x 10-10 electrostatic units. This result, it will be seen, lies between those reached by the aid of the kinetic theory of gases, and indicates that the ionic charge is the same in this case as it is in liquid electrolytes. This identity was established in another way by J. S. Townsend? At 15° and normal pressure one electromagnetic unit evolves 1.23 c.c. of hydrogen: if the number of molecules in one. cubic centimetre is N, the number of atoms or ions associated with the unit of electricity is 2:46N, so that, if E is the charge on an ion in the liquid electrolyte, : 2:46 NE=1 electromagnetic unit = 3 x 1010 electrostatic units. Hence NE=1:22 x 1020 electrostatic units. Now, by investigating the rates of diffusion of the gaseous ions produced by the action of Röntgen rays, and using Rutherford's values for the corresponding ionic velocities, Townsend deduced the following results for the product NE in gases: Air 1:35 x 1.010, Oxygen 1:25 x 1010, Carbonic acid 1.30 x 1010, Hydrogen 1:00 1010, numbers agreeing with that calculated for liquid electrolytes. Since N is a constant for all gases, it follows that the charges on the ions in these gases are all the same, and equal to the charge on a monovalent ion in a liquid electrolyte. In all cases in which gaseous ions are produced by the action of Röntgen rays and similar agencies, their charges seem to consist of the same quantity of electricity as that associated with a monovalent ion in a liquid electrolyte. When steam is 1 Phil. Trans. cxcii. A, 129 (1899). CH. VIII) 191 ELECTROLYSIS : electrolyzed by an electric spark, the ions of divalent substances like oxygen possess a double charge as they do in liquids, but these larger charges are always simple multiples of the mono- valent charge. The quantity of electricity on a monovalent ion seems to be a natural unit, and the results summarized above lead to an atomic theory of electricity. This natural unit of electricity is called an electron. The effect of magnetic and electrostatic forces on their patbs gives evidence to show that the negative ions produced by Röntgen rays, etc., are of much smaller mass than hydrogen atoms, while the positive ions are comparable in mass to ordinary molecules. Thomson? holds that these negative ions or corpuscles constitute the funda- mental basis of all chemical atoms, and are likewise identical with electrons or free charges of negative electricity, a positive ion being produced when one of these corpuscles is removed from any neutral atom or molecule. According to this view, the ions in liquid electrolytes, or in gases through which an electric spark or discharge passes, consist of separated parts of molecules possessing an excess or defect of one electron, and in this way being negatively or positively charged. On the other hand, the ionizing action of Röntgen rays, etc., causes one particle to be detached from the undissociated molecule of the gas, leaving that molecule positively electrified and furnishing a free corpuscle, which constitutes an isolated negative charge or electron. early years of the electrolyhemical act Speculation as to the nature of the ions began at an early The nature of period in the history of electrolysis. In the the ions. early years of the nineteenth century, Berzelius, from a prolonged study of the electrolytic decomposition of neutral salts, enunciated a theory that all chemical action was the result of electric forces between oppositely charged atoms. When two atoms united, he supposed that the charges were not exactly neutralised, and the group of atoms was left with a balance of positive or negative electricity, and so could still combine with other atoms or groups of atoms. He regarded 1 Phil. Mag. XLIV. 293 (1897) ; XLVIII. 547 (1899). 192 [CH. VIII SOLUTION AND ELECTROLYSIS each chemical compound as formed by the union of an electro- positive group with an electro-negative group, and held that the action of the electric current in producing acid round the anode, and alkali round the cathode, of a neutral salt solution, was to be explained simply as a direct separation of the salt into acid and base. When the attention of experimenters was directed to organic chemistry, the dualistic conception of Berzelius was perforce abandoned, and even from the physical side his theories were soon found to need alteration. Thus Daniell showed that in the electrolysis of a solution of sodium sulphate an equivalent of hydrogen was produced as well as an equivalent of acid and base. This is at once reconciled with Faraday's law if we suppose that the parts of the salt, from an electrolytic point of view, are Na and SOs, and that the hydrogen results from a secondary action of the sodium on the water of the solution. With simple salts, acids and alkalies, there is seldom any doubt about the character of the ions; the cation is the metal or hydrogen, the anion is the halogen (chlorine, bromine or iodine), a compound acid group (such as SOs), or hydroxyl HO when the electrolyte is an alkali. A study of the products of decomposition does not neces- sarily lead directly to a knowledge of the ions actually involved in the passage of the current through the electrolyte. Since the electric force is active throughout the whole solution, all the ions must come under its influence and therefore move, but their separation from the electrodes is determined by the electro- motive force needed to liberate them. Therefore as long as every ion of the solution is present in the layer of liquid next the electrode, the one which responds to the least electro- motive force will alone be set free until the amount of this ion becomes too small to carry all the current across the junction layer, when the other ions begin to appear. In aqueous solu- tions, a few hydrogen and hydroxyl ions derived from the water are always present, as we shall see later, and will be liberated if the other ions require a higher electromotive force and the current be kept small. The issue is also obscured in another way. When the ions CH. VIII) 193 ELECTROLYSIS are set free at the electrodes, they may unite with the sub- stance of the electrode or some constituent of the solution and form secondary products. The hydroxyl mentioned above decomposes into water and oxygen, and the chlorine produced by the electrolysis of a chloride may attack the metal of the anode. This leads us to examine more closely the part played by water in electrolysis. It was at first thought to be the only active body, and to be necessary in every case of electrolytic decomposition. The dilute acid or alkali which was always added when water was to be decomposed, was supposed merely to allow the passage of the current by reason of its conductivity, and it was imagined that the current then directly decomposed the water. Now pure water is known to be a very bad conductor, though when great care is taken to remove all dis- solved bodies, there is evidence to show that some part of the small trace of conductivity remaining is really due to the water itself. Thus F. Kohlrausch has prepared water the conduc- tivity of which as compared with that of mercury was 1.8 x 10-11 at 18° C. Even here some little impurity was present, and Kohlrausch estimates that the conductivity of chemically pure water would be 0:36 x 10-11 at 18°C. As we shall see later, the conductivity of very dilute salt solutions is proportional to the concentration, so that it is probable that in most cases practically all the current is carried by the salt. At the elec- trodes, however, the small quantity of hydrogen and hydroxyl ions from the water are first liberated in cases where the ions of the salt have a higher deposition voltage. The water being present in excess, the hydrogen and hydroxyl are at once re-formed, and therefore constantly liberated. If the current is so strong that new hydrogen and hydroxyl ions cannot be formed in time, other substances are liberated; in a solution of sulphuric acid, a strong current will evolve sulphur dioxide, the more readily as the concentration of the solution is in- creased. Similar phenomena are seen in the case of a solution of hydrochloric acid in water. When the solution is weak, hydrogen and oxygen are evolved; but, as the concentration is 1 Wied. Ann. LIII. 209 (1894). 13 W. S. 194 [CH. VIII SOLUTION TY AND ELECTROLYSIS increased, and the current raised, more and more chlorine is liberated. We shall return to this point in a later chapter in connexion with the study of decomposition voltages. An interesting example of secondary action is furnished by the common technical process of electroplating with silver from a bath of potassium silver cyanide. The operation has been studied by Hittorf among others, who holds that the cation is potassium, and the anion the group AgCyz. Each K ion, as it reaches the cathode, precipitates silver by reacting with the solution in accordance with the equation K + KAgCy2 = 2KCy + Ag, while the anion AgCy, dissolves an atom of silver from the with the 2KCy produced in the reaction described by the above equation. If the anode consists of platinum, cyanogen gas is evolved thereat from the anion AgCy2, and the platinum becomés covered with the insoluble silver cyanide AgCy, which VI) I process described above is coherent and homogeneous, while that deposited from a solution of silver nitrate, as the result of the primary action of the current, is crystalline and easily detached. The corresponding cyanide process in the case of gold is now extensively used for the extraction of gold from its ores. The rock, containing small quantities of gold in a state of very fine division, is treated with potassium cyanide, and the solution of the double cyanide obtained in this way is electrolysed between steel anodes and lead cathodes. Prussian blue, which is again worked up into potassium cyanide, is formed on the anodes, and the gold is removed from the lead cathodes by cupellation. In the electrolysis of a concentrated solution of sodium acetate, hydrogen is evolved at the cathode and a mixture of ethane and carbon dioxide at the anode. According to Jahn?, 1 Pogg. An. GVI. 517 (1859). 2 Grundriss der Elektrochemie, p. 292 (1895). CH. VIII) 195 ELECTROLYSIS the processes at the anode can be represented by the equa- tions 2CH. COO + H,0 = 2CH. COOH +0, 2CH. COOH + 0 = C,He + 2C0, + H20. The hydrogen at the cathode is developed by the secondary action 2Na + 2H,0 = 2NaOH + Hg. Many organic compounds can be synthetically prepared by taking advantage of secondary actions at the electrodes, such as reduction by the cathodic hydrogen, or oxidation at the anode? Our knowledge of the nature of the ions has been profitably extended by another method. The changes in the concen- tration of a solution which occur near the electrodes are in some cases very marked, and it seems necessary to assume that unaltered salt is attached to one of the ions, forming a complex ion. In alcoholic and concentrated aqueous solutions of cad- mium iodide, some of the anions appear to be CdI, or I, (Cdly), and are perhaps derived from double or Cd.Id molecules?. It has even been suggested that molecules of solvent may be attached to ions and be carried along with them under the influence of the electric forces*. It is sometimes possible to study the question by examining the conductivity of a solution and its variation with the concentration. The rate of variation with concentration of the equivalent conductivity of an electrolyte (that is, the conduc- tivity divided by the concentration) is much less for salts of monovalent acids than when the valency of the acid is higher. The conductivity curve of potassium permanganate, for example", indicates that the acid is monovalent, and the formula of the salt consequently KMnO4. Again, it is possible to distinguish between double salts and salts of compound acids. Thus Hittorf showed that when a current was passed through a solution of sodium platinichloride, 1 Lüpke's Elektrochemie, Eng. Trans. p. 29. ? Hittorf, see below. 3 W. N. Shaw, B. A. Report, 1890, 201; see below, Electric Endosmose. 4 W. C. D. Whetham, Phil. Trans. A, CXCIV. 321 (1900). 13–2 196 CH. VIII SOLUTION AND ELECTROLYSIS the platinum appeared at the anode. The salt must therefore be derived from a compound acid, and have the formula Na PtCle, the ions being sodium and PtCle, for if it were a double salt it would decompose as a mixture of sodium chloride and platinum chloride, and both metals would go to the cathode. Kohlrausch? has found that, in the electrolysis of solutions of the salt PtCl .5H,0, the weight of the cathode remains unaltered for small current densities; he therefore concludes that no platinum is deposited primarily. With greater current densities a grey deposit is obtained, which loses weight on heating and probably contains hydrogen. At the anode oxygen is first evolved, but, as time goes on, it is replaced by chlorine, the solution becoming darker in colour and acquiring a higher conductivity, showing the formation of the acid H,PtClo. Kohlrausch explains the facts by assuming the existence of compound ions of the formula PtCl.O. Osmond and Houllevigne have studied the electrolysis of solutions of salts of iron, using iron containing carbon for the electrodes. The latter observer has found that, while carbon dissolved in steel is not carried with the current but remains as a muddy deposit at the surface of the anode, combined carbon forms with the iron a complex ion, and is carried with it in the direction of the current. i Wied. Ann. LXIII. 423 (1897). 2 Journ. de Physique, 3rd series, vii. 708 (1898). CHAPTER IX. CONDUCTIVITY OF ELECTROLYTES. Ohm's law. Experimental methods. Experimental results. Consequences of Ohm's law. Migration of the ions and transport numbers. Mobility of the ions. Experimental measurements of ionic velocity. Influence of concentration. Complex ions. Connexion between the mobility of an ion and its chemical constitution. Ohm's law. THE current through a metallic conductor is, to a very great degree of accuracy, proportional to the electro- motive force applied. This relation, known as Ohm's law, may be expressed in the form that C= E/R, where R is a constant for any given conductor under fixed conditions, and is called its resistance. The law is verified if the re- sistance is shown to be independent of the current passing through it. The early experimenters, in the course of their investigations, made efforts to discover whether electrolytes also conformed to Ohm's law. It was known that, owing to the reverse force of polarization, no permanent current of moderate intensity could be maintained through an electrolyte unless the electromotive force exceeded a certain limit; but polarization occurs, primarily at any rate, at the electrodes, and it remained to see, when all reverse forces were eliminated, whether the flow of the current in the body of the liquid was in accordance with the law. Eventually F. Kohlrausch, in experi- ments to be described below, clearly proved that solutions have a real resistance, which remains constant when measured with various currents and by different methods. 198 [CH. x SOLUTION AND ELECTROLYSIS The current in a circuit containing an electrolytic cell can therefore be calculated by Ohm's law if from the total electro- motive force of the circuit be subtracted the reverse electromotive force due to the polarization of the electrodes and to any changes produced by the current in the nature and concentration of different parts of the solution. Many attempts were made to measure the resistances of Experimental electrolytes before a satisfactory method was methods. discovered. Horsford1 passed a current between two electrodes in a rectangular trough, then moved them nearer together, and determined the resistance of a wire which, when interposed in the circuit, reduced the current to its former value. Assuming that the polarization is equal in the two cases (which, owing to migration, is difficult to insure) the resistance of the wire is the same as that of a column of solution equal in length to the difference of the distances between the electrodes in the two positions. The method was improved by Wiedemann, who used as electrodes plates of the metal present in solution, and thus reduced polarization. Beetz’ used an ordinary Wheatstone bridge arrangement, getting rid of nearly all polarization by making his electrodes of amalgamated zinc placed in a neutral solution of zinc sulphate. Since the electromotive force between any two points of a given circuit is proportional to the resistance between them, the resistance of two parts of a circuit can be compared by comparing the electromotive forces between their ends. In this way Boutys examined many solutions. He placed them in inverted U tubes and passed a current through two of them in series. Tapping electrodes were constructed by putting zinc rods in zinc sulphate solution, with thin siphon tubes, filled with the same solution, to make contact where required. The electromotive forces between the ends of the two tubes were thus compared. The only polarization is at the surfaces of contact of the different solutions. i Pogg. Ann. Lxx. p. 238 (1847). ? Pogg. Ann. CXVII. p. 1 (1862). 3 dnn. de Chemie et de Physique, 1884, 111. . CH. IX 199 CONDUCTIVITY OF ELECTROLYTES Another way of eliminating the effects of polarization and migration has been used by Stroud and Henderson? Two of the arms of a Wheatstone's bridge are composed of narrow tubes filled with the solution, the tubes being of equal diameter but of different length. The other two arms are equal coils, and metallic resistance is added to the shorter tube till the bridge is balanced. Equal currents then flow through the two tubes; the effects of polarization and migration are the same in each; and the resistance added to the shorter tube must be equal to the resistance of a column of liquid the length of which is the difference in the lengths of the two tubes. At present the resistance of electrolytes is most frequently determined by means of alternating currents. This method was first successfully adapted to the purpose by Kohlrausch?, who employed the alternating currents from a small induction coil, and used a telephone as indicator. The electromotive force of polarization in the electrolytic cell is thus rapidly reversed, and never reaches its full magnitude. But, unless proper precautions are taken, a small amount of chemical decomposition can produce so much effect that, even with alternating currents, the polarization is appreciable, and the resistance as measured is found to depend on the rate of alternation. The products of the decomposition of } milligram of water on two platinum plates, each having an area of one square metre, will give an electromotive force of about one volt. The electromotive force of polarization is proportional to the surface density of the deposit; its effect can therefore be diminished by increasing the area of the electrodes, a condition obtained by coating them with platinum black. This is done as follows. A current from two accumulators or two or three Daniell cells is passed backwards and forwards between the electrodes through a solution of platinum chloride, which is now usually prepared by dissolving 1 part of platinum chloride (i.e. H,PtCl.) and 0·008 part of lead acetate in 30 parts of water. 1 Phil. Mag. [5] xLIN. 19 (1897); Proc. Phys. Soc. Lond. xv. 13 (1897). 2 Pogg. Ann. CXXXVIII.--CLIII. (1869–1874); Wied. Ann. VI.-LXIV. (1877– 1898); also Kohlrausch und Holborn, Leitvermögen der Elektrolyte, Leipzig, 1898. 200 [CH. IN SOLUTION AND ELECTROLYSIS The strength of the current is adjusted to give a moderate evolution of gas. The platinized plates obtained by this method have very large effective surfaces, and are quite satisfactory for the examination of strong solutions. They have the power, how- ever, of absorbing a certain amount of salt from the solutions and of giving some of it up again when water or a more dilute solution is placed in the cell. The investigation of very dilute solutions, hereby made difficult, has been successfully carried out by first platinizing the electrodes and then heating them to redness. This process gives a gray surface which has enough area to prevent polarization from interfering with the results, while it does not absorb any appreciable quantity of salt?. Various causes of disturbance must be taken into account or eliminated by adjustment of the arrangements; both the self- induction of the circuit? and its electrostatic capacity; may become appreciable. The most usual arrangement of apparatus is shown diagram- matically in Fig. 47. The metre bridge is adjusted till no Totoyo OOOO OOO Fig. 47. sound is heard in the telephone, when the well-known relation between the resistances of the four arms of the bridge holds good. 1 Whetham, Phil. Trans. A, cxciv. 329 (1900). 2 Encycl. Brit., Art. Electricity, or B. A. Report, 1886, 384. 3 Chaperon, Compt. Rend. cviII. 799 (1889), and Kohlrausch, Zeits. phys. Chem. xv. 126 (1894). CH. Ix] 201 CONDUCTIVITY OF ELECTROLYTES The telephone is not a very pleasant instrument to use in this way, and a modification of the method, used by MacGregor', Fitzpatrick and the present writer, is more rapid and also more accurate. The current from one or more dry cells is led to an ebonite drum, turned by a hand-wheel and cord, on which are fixed brass strips with wire brushes touching them in such a manner that the current is reversed several times in each revolution. The wires from the drum are connected with an ordinary resistance box in the same way as the battery wires of the usual Wheatstone's bridge. A moving coil galvanometer is used as indicator, and on the other end of the drum there is another set of strips, arranged to periodically reverse the con- nexions of the galvanometer, so that any residual current which flows through it is direct and not alternating. These strips are rather narrower than the first set, and thus the galvanometer circuit is made just after the battery circuit is made and broken just before the battery circuit is broken. The high moment of inertia of the galvanometer coil makes its period of swing very slow compared with the period of alternation of the current, and therefore the slight residual effects of polarization and other periodic disturbances are prevented from sensibly affecting the galvanometer. When the measured resistance is not altered by increasing the speed of the commutator, or changing the ratio of the arms of the bridge, the disturbing effects may be considered to be eliminated. IRILDNI TII11 Fig. 48. Fig. 49. . . . i Trans. Roy. Soc. Canada, 1882, 21. 2 B.Å. Report, 1886, p. 328. 3 Phil. Trans. A, cxciv. 330 (1900). 202 [CH. Ix SOLUTION AND ELECTROLYSIS The form of vessel chosen to contain the electrolyte depends on the order of resistance to be measured. For dilute solutions the shapes of figures 48 and 49 will be found convenient, while for more concentrated solutions, those indicated in figures 50 and 51. are suitable. Fig. 50. Fig. 51. The absolute resistances of certain solutions have been de- termined by Kohlrausch by comparison with mercury, and by using one of these solutions in any cell, the constant of that cell can be found once for all. From the observed resistance of any given solution in the cell, the resistance of a centimetre cube, or the specific resistance, can then be calculated. The reciprocal of this, or the conductivity, is a more generally useful constant; it is conveniently expressed in terms of a unit equal to the reciprocal of an ohm. This unit is sometimes written as a “mho," a name it is not intended to use in this book. As the temperature coefficient of conductivity is large, usually about two per cent. per degree, it is necessary to place the resistance cell in a paraffin or water bath, and observe its temperature with some accuracy. Kohlrausch expresses his results in terms of equivalent Experimental conductivity, that is the conductivity k divided results. by the number of gram-equivalents of electro- lyte per litre n. He finds that, as the concentration of solutions of monovalent salts, such as potassium chloride, sodium nitrate, etc., diminishes, the value of k/n approaches a limit, and, if the dilution is carried far enough, becomes constant, that is to say, at great dilution the conductivity is proportional to the concen- tration. In establishing this result, Kohlrausch used very pure CH. IX] CONDUCTIVITY OF ELECTROLYTES IT 203 water prepared by careful distillation. He observed that the resistance of the water continually increased as the process of purification proceeded. The conductivity of the water, and of the slight impurities which must always remain, was subtracted from that of the solution, and the result, divided by n, gave the equivalent conductivity of the substance dissolved. This method of calculation appears justifiable, for, as long as conductivity is proportional to concentration, it is evident that each part of the dissolved matter produces its own independent effect, so that the total conductivity is the sum of those of the parts, and when this relation ceases to hold, the conductivity of the solution has, in general, become so great that the part due to the solvent is negligible. Thegeneral result of these experiments can be graphically represented by plotting k/n as ordinates, and nt as abscissae ; nt is a number proportional to the reciprocal of the average dis- tance between the molecules, to which it seems likely that the equivalent conductivity will be closely related. The general forms of the curves for the neutral salt of a monovalent acid and for a caustic alkali or monovalent acid (like HCl) are shown in Fig. 52. The curve for the neutral salt comes to a limiting value, while that for the acid or alkali attains a maximum at à certain very small concentration, and falls again when the - Unitalent_acid.... --- Nentral_salt Fig. 52. dilution is pushed to extreme limits. This fall has usually been considered to be due to chemical action between the acid and 204 [CH. IX SOLUTION AND ELECTROLYSIS the residual impurities in the water, which, at such great dilution, are present in quantities quite comparable with the amount of acid. The phenomena however seem too regular to be due to the action of such impurities, for the fall begins at about the same dilution whatever the amount of impurity present. An explanation is suggested if we consider that the cases in which the fall occurs are those in which one of the ions (H or OH) of the solute is present in the solvent water?. Whatever be the cause of the phenomena we must take the maximum value of the equivalent conductivity to be the limit in the case of acids though it is possible that this method may give too low a result.. It will be seen from the tables in the appendix that the values of the equivalent conductivities of all neutral salts are, at great dilution, of the same order of magnitude, while those of acids at the maximum are about three times as great. Passing to salts of divalent acids and other more complicated electrolytes, Kohlrausch found it impossible to reach such definite limiting values for the equivalent conductivity as were given by monovalent salts. Moreover, the influence of increasing concentration was more marked, the curves sloping at much larger angles. These changes in the phenomena were still greater when, as in copper sulphate, both metal and acid were divalent, and greatest of all in such substances as ammonia and acetic acid, which have very small conductivities when dissolved in water. We shall presently return to this subject. One of the most important results of Kohlrausch's work consisted in the proof that the resistance of a given electrolyte had a definite value, which was independent of the particular method used to determine it. This amounts to a demonstration of Ohm's law within the limits of the conditions of the experi- ments. A more direct proof of the law for strong currents was given by FitzGerald and Trouton”, who showed that the measured resistance was independent of the strength of the current. i Whetham, Phil. Trans. A, cxciv. 353 (1900). ? B. A. Report, 1886, p. 312. CH. IX] CONDUCTIVITY OF ELECTROLYTES 205 The conformity of electrolytes with Ohm's law is most Consequences of instructive. Since any electromotive force, Ohm's law. however small, is able to produce a corre- sponding current, there can be no appreciable reverse electro- motive forces in the interior of an electrolyte, and no measurable amount of chemical work can be there done by the current. It follows either that the function of the current is merely directive, controlling the direction of the motions of the ions which it already finds in a state of mobility, or else that the work done in splitting up one molecule is exactly equal to that given back in the formation of the next. The first of these hypotheses was advanced by Clausiusi to explain electrolysis, and, as it is the one generally adopted, we will examine the evidence for it in some detail. If two solutions containing the salts AB and CD are mixed, double decomposi- tion is found to occur--AD and CB being formed, till a certain part of the first pair of substances has been transformed into an equivalent amount of the second pair. The proportions between the four salts AB, CD, AD and CB, which finally exist in solution, are the same under similar conditions of temperature and pressure whether we begin with AB and CD or with AD and CB. The phenomena were found by Guldberg and Waage to be fully represented by a theory which supposed that both the change from AB and CD into AD and CB, and the reverse change from A D and CB to AB and CD were always going on, and that the quantities transformed per second were proportional to the product of the active masses of the original substances and to a coefficient k, depending on the temperature and pressure, which expresses the rate at which the action proceeds when the active masses of the reagents are each unity, and measures the affinity producing the reaction. If the active masses of AB, CD, AD, CB are p, q, p', q respectively, and k and k' the two coefficients of affinity, we get for the rate of transformation of AB and CD into AD and CB kpq, and for the velocity of the reverse change k'p'q. i Pogg. Ann. cI. p. 338 (1857). 206 [CH. IX SOLUTION AND ELECTROLYSIS When there is equilibrium, these two rates of transformation must be equal and opposite, and we get kpq = k'p'' ........................(27). This equation can, as we shall see later, be obtained for dilute solutions by the principles of thermodynamics, and its results have been experimentally confirmed for many cases. It may, however, be explained as above, by a kinetic theory of the phe- nomena, and this view of double decomposition is universally admitted to be a true one. But in order that this process of chemical change in opposite directions should continually go on, it is necessary to have perfect freedom of interchange between the parts of the molecules, and to imagine that separations and reunions are perpetually occurring among them. This hypo- thesis was first advanced from the chemical side by Williamson? in order to explain the process of etherification. A study of chemical changes shows that it is always the electrolytic ions of a salt that are concerned in the reactions. The tests for a salt, potassium nitrate for example, are the tests not for KNO3, but for its ions K and NO3, and in cases of double decomposition, it is always these ions that are exchanged. If an element is present in a compound other- wise than as an ion, it is not interchangeable, and cannot be recognized by the usual tests. Thus neither the chlorates, which contain the ion C103, nor monochloracetic acid, show the reactions of chlorine; and the sulphates do not answer to the tests which indicate the presence of sulphur as sulphide. It seems certain, then, that the parts of the molecules in solution are continually interchanging, that the electrolytic ions are also the parts which enter into chemical combinations, and that the effect of a current is merely so to control the direction of these decompositions and recompositions, that, on the whole, a stream of positively electrified ions travels in one direction, and a stream of negatively electrified ions in the other. As far as we have gone, there is no evidence to show that the ions remain dissociated for any appreciable time, and * Chem. Soc. Journal, iv. 110 (1852). CH. Ix] 207 CONDUCTIVITY OF ELECTROLYTES the reasoning given above merely proves that there is freedom of interchange. This freedom may only exist in the case of those molecules which, according to the kinetic theory, at any instant happen to be moving with a velocity so much greater than the average, that, on colliding with another molecule, they produce sufficient impact to cause dissociation, and make rear- rangement possible. So much seems to follow from the truth expressed in Ohm's law and the phenomena of chemical action. There is, however, further evidence, which we shall discuss later, that the ions remain dissociated, or at all events keep a certain amount of freedom, throughout a considerable fractional part of their existence. The migration of port numbers. Kohlrausch's work on solutions of simple salts of mono- valent acids also drew attention to the the ions and trans- additive nature of their conductivity. The equivalent conductivity in such cases can be represented as the sum of two independent quantities, one de- pending solely on the anion, and the other on the cation. To examine the meaning of this result, we must remember that, as we saw in the last chapter, the experimental relations sum- marized in Faraday's laws indicate that electrolysis is to be considered as a process resembling convection, a constant stream of cations moving with the current, and a stream of anions in the opposite direction. The quantity of electricity thus conveyed will be proportional to the number of carriers and to the speed with which they travel. If we pass a current between copper plates through a solution of copper sulphate, the colour of the liquid in the neighbourhood of the anode becomes deeper, and in the neigh- bourhood of the cathode lighter in shade. This is well seen if the electrodes are arranged horizontally with the anode underneath. When the electrodes are of copper, the quantity of metal in solution remains constant, since it is dissolved from the anode as fast as it is deposited at the cathode, but if we use platinum electrodes, the amount in solution becomes continually less, since more salt is taken from the neighbour- hood of the cathode than from the anode, and the colour of 208 [CH. IX SOLUTION AND ELECTROLYSIS the solution, therefore, becomes pale more rapidly near the cathode than near the anode. This subject was first systematically investigated by Hittorf1, who examined many solutions in a manner which enabled the liquid round the two electrodes to be separately analysed after the passage of the current. Two explanations of these changes in concentration seem possible. It may be that the ions are really complex, unaltered salt being attached to the anion or solvent to the cation, so that some of the anions have the composition Cu(CuSO.) or some of the cations the composition SO. (H,0); in this way salt would be drawn to the anode or solvent to the cathode. It may be that the velocities of the ions are different, the anion, in the case of copper sulphate, travelling faster than the cation. It is possible that, in many cases, both these effects occur; and indeed, as we shall see later, the evidence indicates that such is the case. In developing the hypothesis of different ionic velocities it is certain that if the opposite ions move with equal velocities, the result of the passage of the current will be that, while the composition of the middle portion of the solution remains unaltered, the products of the decomposition, which appear at the electrodes, are taken in equal proportions from the solution surrounding the anode, and from that round the cathode. If, however, one of the ions travels faster than the other, it will get away from the portion of the solution whence it comes more quickly than the other ion enters. When the electrodes are of non-dissolvable material, therefore, the concentration of the liquid in this region will fall faster than in that round the other electrode. Let us assume that the cation drifts to the right with a velocity U, and the anion to the left with a velocity v. The velocity of the cation can be resolved into (u + v) and ] (u — v), and the velocity of the anion into 1 (v +u) and 3 (v – u). On pairing these components, we have a drift of the two ions right and left, each with a speed } (u + v), involving no accumulation i Pogg. Ann., LxxxIx. 177, xcvIII. 1, CIII. 1, cvr. 337, 513 (1853–9). IA CH. IX] 209 . CONDUCTIVITY OF ELECTROLYTES at the electrodes, and a uniform flow of the electrolyte itself without separation with a speed 1 (u — v) to the right? Thus at the cathode there is a gain of electrolyte equal to } (u — v), and a loss, due to electrolytic separation, of 1 (u + v): a total loss of v. At the anode there is a loss of 1 (u – v) and a loss of 1 (u +v), a total loss of U. The initial losses of electrolyte at the two electrodes, then, before diffusion sensibly affects the result, are in the same ratio as the velocities of the. ions travelling away from them. The process can be clearly illustrated by a method due to Or 00 00 00 00 00 00 00 00 0 o 1 Fig. 53. Hittorf. In Fig. 53 the black dots represent the one ion, and the white circles the other. If the black ions move to the left twice as fast as the white ions move to the right, the black ions will move over two of our spaces while the white ones move over one. Two of these steps are represented in the diagram. At the end of the process it will be found that six molecules have been decomposed, six black ions being liberated at the left and six white ions at the right. Looking at the combined molecules, however, we see that while five remain on the left side of the middle line, only three are still present on the right. The left-hand side, towards which the faster ions moved, has lost two combined molecules, while the right-hand side, towards which the slower ions travelled, has lost four-just twice as many. Thus we see that the ratio of the masses of salt lost by the two sides is the same as the ratio of the velocities of the ions leaving them. Therefore, on the assumption that no complex ions are present, by analysing Larmor, Aether and Matter, Cambridge, 1900, p. 290. 14 . W. S. 210 [CH. IX SOLUTION AND ELECTROLYSIS the contents of a solution after a current has passed, we can calculate the ratio of the velocities of its two ions. A long series of measurements of this kind has been made by Hittorf", Kuschel, Lenzº, Loeb and Nernst“, Bein", Hopfgartner, Kümmel?, Kistiakowsky® and others, who used various forms of apparatus arranged so as to enable the anode and cathode solutions to be separately examined after the passage of the current. One such Qao IWNE Fig. 54. apparatus used by Bein is shown in Fig. 54. Hittorf called the phenomenon the “migration of the ions,” and expressed his results in terms of a transport number, or migration constant, which gives the amount of salt taken from the neighbourhood of one electrode as a fraction of the whole amount that disappears. If there are no complex ions, it also expresses the ratio of the i loc. cit. p. 208. 3 Wied. Ann. XIII. 289 (1881). 3 Mém. Pétersb. Acad. ix. 30 (1882). 4 Zeits. f. physikal. Chemie, 11. p. 948 (1883). 5 Wied. Ann. XLVI. 29 (1892) and Zeits. phys. Chem. XXVII. 1 (1898). 6 Zeits. phys. Chem. xxv. 115 (1898). 7 Wied. Ann. LXIV. 665 (1898). 8 Zeits. phys. Chem. vi. 97 (1890). CH. Ix] 211 CONDUCTIVITY OF ELECTROLYTES I velocity of one ion to the sum of the opposite ionic velocities. Many results on the subject were collected by T. C. Fitzpatrick in his tables of “ The Electro-Chemical Properties of Aqueous Solutions," published in the British Association Report for 1893, and reprinted by permission in the appendix to this book. A more recent list appeared in Kohlrausch, and Holborn's book Das Leitvermögen der Elektrolyte-, from which is taken the table on the next page. In it results in italics are considered by Kohlrausch to have been obtained under uncertain conditions. The numbers represent the migra- tion constants for the anions. Thus CuSO4 632 means that the amount of salt taken from the cathode vessel is to the whole amount decomposed as .632 : 1, and is therefore to the amount taken from the anode vessel as '632 : 368. The concentration n gives the number of gram equivalents of salt per litre of solution. The transport numbers for cadmium iodide, which, for solutions of more than half normal concentration, are greater than unity, show that the cathode vessel loses more salt than the whole solution does. It follows that some unaltered salt must travel through the solution towards the anode, and this result at once led to the conception of coinplex ions of the type I (CDI). The changes with concentration in the transport numbers of many other substances, such as calcium chloride and copper sulphate, seem too great to be explained by a different rate of variation for the two ions of the quasi-frictional resistance which the solution offers to their passage, and suggest that complex ions may exist in many solutions. Other evidence in favour of this supposition will be given later. Bein has shown that, if a membrane be used to separate the anode and cathode solutions, a considerable effect, varying with the nature of the membrane, is produced on the transport numbers. A further step was taken in the year 1879 by Kohlrausch?, ity of who showed that a knowledge of the conduc- the ions. tivity of a solution enabled the sum of the opposite ionic velocities to be calculated. We have seen that 1 Leipzig, 1898. 2 Wied. Ann. vol. vi. p. 160 (1879). 14-2 212 XI HD] SOLUTION AND ELECTROLYSIS Transport Numbers. 0.01 0.05 0:1 02 0.02 50 0.5 = V=1/n= funds for 15 -67 ܪܬ * 3 33 100 20 10 L (CI) K Br! 0:506 •507 •507 -508 •509 •513 •514 -515 •515 •516 .614 .650 .646 •752 0.63 .67 •76 NHC) NaĈi Lici KNO, NaNOZ AgNO3 KC,H,O, Nač,ůző, .617 •69 •497 .615 528 •33 44. •620 •71 •496 •614 •527 33 •43 •626 •73 •492 •612 •519 33 43 •637 •739 -487 •611 -501 -331 •425 .640 .741 •482 •610 •487 •332 • 422 •642 •745 .479 .608 •476 •332 •421 603 585 0·528 328 | •335 •333 •417 KOH NaOH LiOH HCI •735 .82 .85 •172 •738 ·82 •861 .173 •740 .825 •873 •176 .85 •172 .890 •180 •172 .185 .200 238 •585 •64 •595 .66 .68 •710 .747 .66 62 65 -767 '995 -615 .675 •69 .69 1:00 435 •54 •70 •640 .686 •709 •72 1 1.12 434 548 •74 .696 •174 •737 .776 •865 to 2.5 .380 :71 -40 •53 •64 .632 •191 •650 .695 •718 •73 1:18 •421 •546 •75 •714 •169 .83 :41 •53 •66 •643 •188 .657 •700 •729 •745 1.22 -413 .542 •76 •720 •168 •355 : 1.28 •404 •530 •760 •565 •575 0:56 0:58 :59 .61 0:57 0.56 .63 •59 •64 •39 •52 .60 .626 :193 •170 •190 .216 CH. Ix] 213 CONDUCTIVITY OF ELECTROLYTES TYS TY we can represent the facts by considering the process of elec- trolysis to be a kind of convection, the ions moving through the solution and carrying their charges with them. Each mono- valent ion may be supposed to carry a certain definite charge, which we can take to be the ultimate indivisible unit of elec- tricity; each divalent ion carries twice that amount, and so on. Let us consider, as an example, the case of an aqueous solution of potassium chloride of which the concentration is m gram-equivalents per 'cubic centimetre. There will then be m gram-equivalents of potassium ions and the same number of chlorine ions in this volume. Let us suppose that on each gram-equivalent of potassium there reside + q units of elec- tricity, and on each gram-equivalent of chlorine ions – q units. If u denote the average velocity of the potassium ions, the positive charge carried per second across unit area normal to the flow is mqu. Similarly, if v be the average velocity of the chlorine ions, the negative charge carried in the opposite direction is mqv. But positive electricity moving in one direc- tion is equivalent to negative electricity moving in the other, so that the total current, C, is mq (u+v). Now let us consider the amounts of potassium and chlorine liberated at the electrodes by this current. At the cathode, if the chlorine ions were at rest, the excess of potassium ions would be the number arriving in one second, viz. mu. But, since the chlorine ions move also, a further séparation occurs, and mv potassium ions are left without partners. The total number of gram-equivalents liberated is therefore m (u +v). Now, by Faraday's law, the liberation of one gram-equivalent of any ion involves the passage of a definite quantity Q of electricity round the circuit. Thus, in one second, the total quantity passing, that is the current, is mQ(u + v). On com- paring this result with the first expression for the same current, it follows that the charge, q, on one gram-equivalent of either ion is equal to the quantity of electricity passing round the circuit when the gram-equivalent is liberated. We know that Ohm's law holds good for electrolytes, so that the current C is also given by — kdP/dx, where k denotes 214 SOLUTION AND ELECTROLYSIS (CH. IX the conductivity of the solution, and - dP/dx the potential gradient, i.e. the fall in potential per unit length along the lines of current flow. Thus mq (u + v)=-k k dP or U +v=-*. ..... . . . . . . . . . . . . . ...(37), mq. de *** an equation in which everything may be expressed in centi- metre-gram-second units. By measuring 1/k in ohms (an ohm being 10º C.G.S. units), q in coulombs (10-1), and writing n for the number of gram-equivalents of solute per litre instead of per cubic centimetre, we get 2 + V =- u+v=-10-6 k dp nq' duc Now q is 96440 coulombs (p. 188), so that for a potential gradient of one volt per centimetre (108 C.G.S. units), we have Utv1 = 1:037 10-2 X- .........(38), 'n which gives the relative velocity (or the sum of the opposite velocities) of the two ions in centimetres per second under unit potential gradient. These numbers, Uz and vi, measure what we may call the mobilities of the two ions. Since the transport numbers give us the ratio of the ionic velocities if no complex ions are present, we can deduce the absolute values of U, and v, from this theory. Thus, for in- stance, the conductivity of a solution of potassium chloride containing one-tenth of a gram-equivalent per litre is 0·01119 reciprocal ohms at 18° C. Therefore Uz + v1 = 1.037 x 10–2 x 0·1119 = 0·001165 cm. per sec. Hittorf's experiments show us that the ratio of the velocity of the anion to that of the cation in this solution is 5l : •49. The absolute velocity of the chlorine ion under unit potential gradient is therefore 0.000595 cm. per sec., and that of the potassium ion 0:000570 cm. per sec. Similar calculations can be made for solutions of other concentrations. The following table gives the ionic mobilities of three chlorides of alkali CH. IX] 215 CONDUCTIVITY OF ELECTROLYTES metals as multiples of 10-6 cm. per sec., per volt per cm, at 18° C. KCI Naci Lici u tu, Uy Vi utvil 2 l v uto, un l 0.0001 ·001 .01 03 1363 667 697 1348 661 688 1326 1 650 | 677 1276 625 | 650 1230 627 1165 570 595 1099 536 563 1021 496 525 920 446 603 1151 1140 1121 1070 1023 961 885 773 588 442 454 452 444 419 394 364 327 281 208 155 697 688 677 650 629 598 558 492 380 288 1060 | 364 | 697 1047 | 360 688 1023 | 346 677 971 | 321 | 650 926 301 | 625 862 600 782 | 219 563 658 171 487 468 351 337 | 81 257 118 25 93 | 262 474 116 1:0 3.0 5:0 10.0 These numbers clearly show the increase in ionic mobility as the dilution gets greater. Moreover, if we compare the values for the chlorine ion obtained from observations on these three different salts, we see that, as the solutions get very weak, the mobility of the chlorine ion becomes the same in all of them. Similar phenomena appear in other cases of simple monovalent salts; and, in general, we may say that, at great dilution, the velocity of an ion in the solution of such a salt is independent of the nature of the other ion present. From this result we may deduce the existence of specific ionic mobilities, the values of which are given in the following table for different monovalent ions in centimetres per second per volt per centimetre. 67 x 10-5 CL 70 x 10-5 Na Li 45 70 36 65 NHA NO3 OH 67 184 H 36 323 58 C2H,02 C H/02 Ag 33 , Having once obtained these numbers, we can calculate the equivalent conductivity of the dilute solution of any salt con- taining the ions referred to, and the comparison of such values 216 [CH. IX SOLUTION AND ELECTROLYSIS with observation furnished the first confirmation of Kohlrausch's theory. Some exceptions, however, are known. Thus, acetic acid and ammonia give solutions of much lower conductivity than is indicated by the sum of the specific mobilities of their ions as determined from other compounds. Experimental Oliver Lodge was the first to directly measure the velocity of transport of an ion'. In a horizontal glass measurements of tube connecting two vessels filled with dilute ionic velocity. .. sulphuric acid, he placed a solution of sodium chloride in solid agar-agar jelly. This solid solution was made alkaline with a trace of caustic soda to bring out the red colour of a little phenol-phthalein added as indicator. A current was then passed from one vessel to the other along the tube. The hydrogen ions from the anode vessel of acid were thus carried along the tube, and decolorized the phenol-phthalein as they travelled. By this method the velocity of the hydrogen ion through a jelly solution under a known potential gradient could be observed. The results of three experiments gave 0:0029, 0:0026, and 0:0024 cm. per sec. as the velocity of the hydrogen ion for a potential gradient of one volt per centimetre. Kohlrausch's number is 0.0032 for the dilution corresponding to maximum conductivity. Lodge does not mention the concen- tration of his solution, but it was probably large enough to appreciably reduce the velocity. Experiments in which the motion of other ions was traced by the formation of precipitates, gave results differing considerably from the theoretical numbers, probably owing to the indeterminate values of the potential gradient. When the current density at the cathode in a solution of copper sulphate exceeds a certain limit, copper is deposited as a brown or black hydride. C. L. Weber? attributed this to the inability of the copper ions to migrate fast enough to keep up the supply for carrying the current, part of which will consequently be conveyed by sulphuric acid formed by the action of SO, ions on the water. By measuring the limiting 1 British Association Report, 1886, p. 589. 2 Zeits. phys. Chem. Iv. 182 (1889). CH. Ix] 217 CONDUCTIVITY OF ELECTROLYTES current density and the conductivity of the solution, he esti- mated the speed of the copper ions when they could travel just fast enough to carry all the current, and hence he deduced their specific velocity. Similar methods were used for solutions of cadmium sulphate and zinc nitrate. The copper sulphate measurements were repeated with an improved apparatus by Sheldon and Downing? This method does not appear to be a very good one, for the dilution of the liquid round the cathode makes it impossible to accurately determine the conductivity of the solution concerned. This source of error will make the deduced velocities too great. The velocities of a few other ions have been directly deter- mined in another way by the present writer? Two solutions, having one ion in common, of F equivalent concentrations, different densities, different colours, and nearly equal specific re- sistances, were placed one over the other in a vertical glass tube. In one case, for example, decinormal solutions of potassium carbonate and potassium bichromate were used. The colour of the latter is due to the presence of the bi- chromate group, Cr,Oz. When a current was passed across the junction, the anions CO, and Cr,O, travelled in the direction opposite to that of the current, and their velocity could be de- termined by measuring the rate at which the colour boundary moved. Similar experiments were made with alcoholic solutions of cobalt Fig. 55. salts, in which the mobility of the ions was found to be much less than in water. The behaviour of agar jelly was then investigated, and the mobility of an ion was shown to be very little less in a solid jelly than in an ordinary liquid solution. The velocities could therefore be measured by tracing the change in colour of an indicator or the formation of a pre- cipitate. Thus decinormal jelly solutions of barium chloride Uittiunili Hill TI MWIMU Dintiiminnan ni MNO DANIEL Ulllllllltti . . 1 Physical Review, 1. 51 (1893). 2 Phil. Trans. A, CLXXXIV. 337 (1893); Phil. Mag. Oct. 1894 ; Phil. Trans. A, CLXXXVI. 507 (1895). 218 [CH. IX SOLUTION AND ELECTROLYSIS and sodium chloride, the latter containing a trace of sodium sulphate, were placed in contact. Under the influence of an electromotive force, the barium ions moved up the tube, and their presence was shown by the trace of insoluble barium sulphate formed. By keeping the conductivities of the two solutions nearly the same, discontinuity of potential gradient was avoided, and the gradient could then be calculated from the area of cross section of the tube, the conductivity of the solution, and the strength of the current as measured in a galvanometer. In dilute aqueous solutions of simple salts, the direction of motion observed at the junctions was always normal; but as the concentration was increased, in some cases, such as that of alcoholic cobalt solutions, more than one boundary line appeared, and the direction of some of these lines was occasion- ally even reversed. In order to explain these results it seems necessary to assume the existence of complex ions, unaltered salt being attached to one or other of the simple ions. The following table shows the velocities of the ions which have been experimentally determined by the methods of Lodge and Whetham. A comparison is given with their values as calculated, for the same concentration, on Kohlrausch's theory. - Specific ionic velocity in centimetres per second Name of Ion Concentra- tion of solu- tion in gram- equivalents per litre Calculated from Kohlrausch's theory Observed 0.0028 0.000048 0.07 0:1 0 Hydrogen in chlorides ... ... in acetates Copper (in chlorides) ... Barium ... ... Calcium ... ... Silver ... Sulphate group (SO2) ... Bichromate group (Cr207) Cobalt (in alcoholic CÓCl) , (, , CO(NO2),) Chlorine (in alcoholic COCI,) Nitrate group (NO3) (in alcoholic CO(NO3)2) ... ... 0:1 0:1 0:1 0:1 0:5 0.05 0:05 0.00037 0.00029 0.00046 0.00049 0.00047 0·0026 0.000065 0:00031 0.00039 0.00035 0.00049 0.00045 0:00047 0.000022 0.000044 0.000026 0.05 - 0.000035 CH. Ix] CONDUCTIVITY OF ELECTROLYTES NOTE.—The migration data for solutions of copper chloride are not known. The specific ionic velocity of copper at infinite dilution (when it would be independent of the nature of the combination) is given by Kohlrausch as 0.00031, but in a solution of the strength used it would be considerably less. The sum of the ionic velocities of cobalt chloride in alcohol, as calculated from the conductivity, is 0.000060 cm. per sec., and that of cobalt nitrate 0.000079. These numbers are to be compared with the sum of the observed velocities given in the table-namely, 0.000048 and 0·000079 respectively. These experiments, it will be noticed, depend on the pheno- mena which occur at the junction of two solutions when a current is passed across it. It was observed by Gorel that in such a case the surface of contact sometimes remained clear, giving a sharp boundary, and sometimes became blurred and indistinct. Similar results were obtained in the experiments under consideration, and shown by the writer to depend on the relative conductivities of the two solutions. The electro- motive force between two points of a circuit is proportional to the resistance, as Ohm's law indicates, and the potential gradients in the two solutions are proportional to their specific resistances. Since une ion, let us say the anion, is the same in each solution, a solution of high resistance means one in which the cation has a low velocity, and a solution of low resistance contains a fast moving cation. Now, if the current pass from the liquid of high to that of low resistance, a cation which chances to get in front of the boundary will find itself in a region of lower potential gradient, and will, therefore, drop back again into line, and if one of the faster ions find itself behind the boundary, it will have entered a region of higher potential gradient and will be once more pushed forwards. The boundary therefore keeps sharp and distinct while moving with the current. On the other hand, if the current flow from the low resisting to the high resisting liquid, a straggling slow ion will drop behind into a region of smaller potential gradient, and be still further retarded, while a wandering fast ion will enter a region where the higher electric forces will still further hasten it. The boundary will therefore become blurred and indistinct. Thus the condition necessary for the existence and i Proc. R. S. 1880 and 1881. 220 [CH. IX SOLUTION AND ELECTROLYSIS permanence of a sharp boundary is, that a specifically slower ion must follow a specifically faster ion. The general theory of such boundaries has been considered by Kohlrausch? and H. Weber?. Orme Masson has applied these results to obtain a more accurate method of experimentally determining ionic velocities®. From what has been said, it follows that a current passing from a solution of high to a solution of low resistance, adjusts the potential gradients so that the actual velocity of the specifically slow ion in the region of high potential gradient is equal to that of the fast ion in the region of low potential gradient. Masson placed a jelly solution of a colourless salt, potassium chloride for instance, in the central region of a horizontal glass tube, the ends of which were filled with jelly solutions of salts, one with a coloured anion and one with a coloured cation, these ions being specifically slower than the ions of the potassium chloride which they respectively adjoined. The solutions used for this purpose were potassium chromate with a yellow anion, and copper sulphate with a blue cation. The chromate ion and the copper are slower than chlorine and potassium respectively, and thus, if a current be passed from the copper end through the chloride to the chromate, at each end a specifically slower follows a faster ion, and the condition of stability of the boundary is fulfilled. The potential gradient is the same throughout the chloride solution, and can be calculated from the conductivity and the current strength, and therefore the speed of the colour boundaries at each end gives the velocity of potassium and chlorine under the same potential gradient. By measuring the relative velocity of these two margins, therefore, the ratio between the velocities of potassium and chlorine can be determined, and compared with Hittorf's migration constant. Other salts were examined in the same way, and the relative mobilities of different ions, thus measured, were found to agree well with Kohlrausch’s values. 1 Wied. Ann. LXII. 209 (1897). 2 Sitz. Akad. Wiss. Berlin, 936 (1897). 3 Phil. Trans. A, CXCII. 331 (1899). CH. Ix] 221 CONDUCTIVITY OF ELECTROLYTES The following table gives the mobilities of the ions, rela- tively to the value for potassium, which is put equal to 100, as determined by Masson, Kohlrausch's theoretical values for one- tenth normal solutions being appended for comparison. -. .. ... Chlorides Sulphates Kohl- rausch n = .5 I n=1 n=2 Il n=.5 n=1 n=2 n= 1 100 65.7 100 Na 100 65.4 45.2 100 100 65.8 100 66.9 47:1 100 66.9 44.7 44.4 45.2 46 NH, 96 Mg 40.5 36.9 38.7 97.9 96.1 93.6 104 ISO4 87.7 8707 B. D. Steelei has extended Masson's method by the dis- covery that, under certain conditions of concentration and potential gradient, the boundary between two colourless solu- tions, owing to the difference in refractive index, is clearly visible. He has also freed the method from the disturbing influence of jellies by placing the solution to be examined in . . . AV . 7 OM .-. . JA11101111 1 Fig. 56. 1 Phil. Trans. A, CXCVIII. 105 (1902). 222 [CH. Ix SOLUTION AND ELECTROLYSIS the limbs of the glass apparatus of figure 56, and confining it between two partitions of jelly, containing the indicator solu- tions, aqueous solutions of which are also poured into the tubes above the jelly walls and contain the electrodes. When the current flows, the indicator ions leave the jellies, and enter the liquid columns, after which their velocities cannot be influenced by the presence of the jelly. If the indicator solutions have densities greater than that of the other, the rubber stoppers closing the bottom of the apparatus are removed, and the tubes shown at the sides are inserted. The indicator ions can thus be made to enter the solution from below. Steele's results for the migration constants agree well with the best of those obtained by the method of Hittorf, and generally with those obtained by the method of Masson. From appreciable differences in certain cases it is, however, concluded that the jelly of Masson's experiments affects the two ions unequally. The following selection from Steele’s results may be given: Migration constant Salt Concen- tration Steele Masson Hittorf, etc. КСІ 0:5 1.0 2:0 0:490 0.488 0:489 0.495 0:490 0:483 0:515 NaCl 0.5 1.0 0.597 0:591 0:590 0:598 0.595 0.587 0.626 0.637 0.642 BaCl, 0.5 1.0 2:0 0:576 0.619 0.633 0.615 0.640 0.657 MgSO4 0:184 0.5 1:0 0:646 0:693 0.715 0.737 0.684 0.703 0.693 : 0.688 0.660 0.700 0-740 0.750 2:0 2.0 Steele has also calculated from his results the absolute ionic mobilities of some ions and compared the numbers with those CH. Ix] 223 CONDUCTIVITY OF ELECTROLYTES of Kohlrausch, obtaining in most cases a satisfactory agreement. As examples : Salt Concen- tration Kohlrausch 1 Steele Kohlrausch Steele KCI 0:5 2:0 0.000512 0.000466 0.000553 0.000483 0.000543 0.000494 0.000529 0.000458 Naci 0.000285 0:000250 0.000318 0.000274 0.000485 0.000418 0.000452 0:000395 2.0 BaCl, 0:5 1.0 0.000310 0.000264 0.000213 0.000330 0.000283 0.000231 0.000494 0.000405 0.000411 0.000450 0.000457 0.000398 MgSO4 2:0 0.18 0:5 10 0.000155 0.000111 0.000078 0.000054 0.000167 117 087 061 0:000301 257 221 0.000304 264 217 178 2.0 168 The agreement with theory of all experimental measure- Influence of ments of the iopic mobilities of simple mono- Concentration. valent salts, as made by different observers, is a striking confirmation of the truth of the fundamental ideas which underlie Kohlrausch's treatment of the subject. As the concentration of solutions of these salts increases, both the theoretical and the experimental mobilities are seen to dimi- nish, and still to show a satisfactory agreement. Whatever the cause of the decrease of equivalent conductivity with increasing concentration may be, Kohlrausch's theory still gives the true value of the actual velocities with which the ions on the average move through the liquid under the conditions of the experiment, though these velocities are less than those acquired by the action of the same electric forces in dilute solutions. If we still wish to express the results in terms of the specific ionic mobilities, that is, in terms of the ionic velocities (Uc and wo) at infinite dilution under unit potential gradient, we must, for these more concentrated solutions, introduce a factor a measuring the ratio of the actual to the limiting 224 [CH. Ix SOLUTION AND ELECTROLYSIS 12 . values of the sum of the ionic mobilities. Then, from equation 38, page 214, we have : a (Uc + vos) = 1:037 x 10–2k or k = 96-44 a (U. +vo). The coefficient a is thus given by the ratio between the actual value of the equivalent conductivity of the solution and its value at infinite dilution, and can readily be determined experimentally. Now there seem to be two causes which could reduce the velocities of the ions. If we look on the passage of the ions through the solution as analogous to the motion of bodies through a viscous medium, we see that the frictional forces will increase with the velocity till they become equal and opposite to the driving forces producing the motion. The ions will then travel with constant velocity, and the resistance for such minute bodies being relatively enormous, this limiting velocity will be reached practically instantaneously. An in- crease in this viscosity, or a decrease in what may be called the ionic fluidity, would therefore diminish the velocity of the ions, and consequently the conductivity of the solution. Chiefly to this cause is to be assigned the variation of ionic velocity, and therefore of conductivity, with temperature. Heating a solu- tion seems to increase the ionic fluidity to about the same extent as it diminishes the ordinary or molar viscosity. Never- theless Arrhenius has shown that there is no sudden change in the conductivity of a jelly solution at the moment when, by cooling or by the addition of more gelatine, the jelly “sets.”I While this result certainly proves that no exact connexion exists between the ionic fluidity and the molar viscosity, it does not imply that the ionic fluidity is not affected by the addition of more of the electrolyte, which might affect the molecular condition of the system. This leads to the consider- ation of another method in which the ionic velocities might be reduced. In developing the theory, the assumption is made that all the substance dissolved is actively concerned in conveying 1 B. A. Report, 1886, p. 344. CH. IX] . CONDUCTIVITY OF ELECTROLYTES 10 225 the current, though it is possible that such is not always the case. It may be that, under certain conditions of temperature and concentration, a certain fraction of the solute is in a state of inactivity, which must mean that its ions do not drift in opposite directions under the influence of electromotive forces. If, for the present, we exclude the consideration of complex ions, these inactive molecules will be unaffected by the electric forces, and will have no drift in either direction. Now, what- ever be the cause of the activity or non-activity of the solute, it is certain that the equilibrium between active and inactive molecules must be a mobile equilibrium, molecules continually passing from one state to the other? Each ion will sometimes be active and sometimes be inactive; while active it will move and while inactive be stationary, and the net result will be that its effective velocity will be reduced in the ratio of the active time to the whole time. Thus the velocities of simple ions may be reduced by an in- crease in frictional resistance, by a diminution in the fraction of the dissolved substance which is, at any moment, active, or by a combination of both these causes. In dilute solutions, the re- sistance offered by the liquid to the passage of the ions through it is probably sensibly the same as in pure water; but when the proportion of non-ionized molecules becomes considerable, we cannot assume that this is the case. If, however, no complex ions are present and the solution is dilute enough for the friction to be taken as constant, the coefficient a can be given a very simple physical meaning. The fraction which expresses the ratio of the actual to the limiting velocity of the ions must then also express the fraction of the dissolved substance which is, at any moment, electrolytically effective, and consequently the fraction of its time during which, on the average, any ion remains active. This fractional number may be called the coefficient of ionization. Thus, although we can, if we like, always put Kohlrausch's theory in the form shown in our last equation, the constant a will only have a definite physical meaning when no complex ions are present, and the solution is so dilute that the ionic 1 Whetham, Phil. Mag., July, 1891 ; Phil. Trans., A, CLXXXIV. 340 (1893). W. S. 15 226 [CE. IX SOLUTION AND ELECTROLYSIS viscosity keeps constant. This caution is necessary, for it seems to be often assumed that a, as deduced from the ratio of the actual to the limiting equivalent conductivity, always ex- presses the ionization of the solution, whatever its concentration may be, although for fairly strong solutions no convincing evidence has been adduced in favour of the assumption made. On the other hand, equation (38) given on p. 214, 26+ z = 1-037 10-2 n : in which w and V, denote the actual mobilities of the ions under the conditions of the experiment, probably holds good whatever be the concentration of the solution, and gives the simplest and most certain form of Kohlrausch's theory. Hittorf himself recognized that the migration constant of cadmium iodide requires the supposition of Complex ions. complex ions, some unaltered salt migrating in company with the iodine, as a complex anion. There is considerable evidence besides that already described that similar ions exist in many other solutions in water and other solvents? This evidence may be summarized as follows: (1) In the case of simple salts such as potassium chloride, Hittorf's transport number is independent of the concentration, but this is not so for more complicated salts, such as barium chloride or magnesium sulphate. The change is so great that it is not easy to explain it by a difference in the variation of the mobility of the two ions with concentration (2) While it is possible to assign a definite specific mobility to the ions of potassium chloride and similar salts, the velocities of the ions of more complex salts depend on the nature of the other ion present, until the dilution becomes almost infinite. (3) In direct measurements of ionic mobilities by the method of moving boundaries, the results agree better with theory for the simple salts, and when the solutions of the more complex salts are of considerable concentration, the phenomena at the boundaries become very complicated. i Whetham, Phil. Trans. A, CLXXXIV. 358 (1893); Steele, Phil. Trans. A, CXCVIII. 133 (1902); Schlundt, Jour. Phys. Chem. VI. 159 (1902). : CH. Ix] 227 CONDUCTIVITY OF ELECTROLYTES . (4) As we shall see later, the ionization as calculated from the electrical conductivity agrees better with that deduced from the freezing point in the case of simple salts than for more complicated ones. All these relations are easily explained by the supposition that, as the concentration increases, many solutions, especially of such salts as magnesium sulphate, contain complex ions, formed by the union of some unaltered salt molecules with the anion or cation. Such molecules of salt will be dragged forwards with the ions and may increase the effective resistance to their motion, thus reducing the velocity below the value given by the fraction indicated above, which expresses the ratio of the active to the total solute at any moment. The ratio of the actual to the limiting velocity then ceases to be equal to the ratio of the average active time to the whole time for each ion. The equilibrium will still be dynamical, however, and these attacbed molecules must in turn become inactive stationary molecules and active molecules, the parts of which are moving ions. The life of an ion can then be divided into four parts, (1) the time during which it is active as a simple ion, and therefore moving with nearly the velocity it would have in pure water, (2) the time when it is part of an inactive molecule at rest, (3) the time it has an inactive molecule attached to it, and is therefore moving with a velocity smaller than that referred to above, and (4) the time during which it forins part of an inactive molecule dragged along by an active ion, when it moves with the same diminished velocity but is ineffective as far as carrying current is concerned. The effective or resultant velocity of an ion is found by dividing the average distance it travels during the periods (1) and (3) by the whole time considered, for during the periods (2) and (4) it does nothing towards carrying the current. The effective velocities, as thus calculated, will be correctly deter- mined by Kohlrausch's equation: - k dp 24 + 0 = 0·01037 x x ? ded. - N . dx * But when we wish from this result to calculate the 15_2 228 [CH. IX SOLUTION AND ELECTROLYSIS individual values of 24 and V, we must use the migration constant for the given electrolyte, which has been determined by the method of Hittorf. Now the theory of Hittorf's method (page 208) assumes that the difference produced in the con- centrations of the liquids round the two electrodes is, in general, entirely due to a difference in the velocities of the two ions; though, as we stated, Hittorf recognized the action of complex ions in exceptional cases. But the differences in concentration might always be explained by the supposition that inactive solute or solvent molecules were attached to one or other of the ions. If this were the case, the division of the value of 2 + v, in the ratio of Hittorf's number would lead to an erroneous result for the individual ionic velocities. The calculated velocities would then differ from those experimen- tally determined by a greater and greater extent, as such complex ions became more numerous owing to an increase in concentration or to other causes. We may thus explain the fact that the experimental results agree less nearly with the calculated ionic velocities in solutions such as those of magnesium sulphate than in solutions of potassium chloride and similar salts. It will now be evident that, if complex ions are present, the mobility of an ion calculated from observations on solutions of different salts containing it will not be constant, since different numbers of complex ions may exist in the different solutions. Moreover, in the solutions of any one substance, the number of complexes depends on the concentration, as the change in the transport number indicates, and therefore the mobility at infinite dilution cannot be calculated unless the transport number has been determined for a solution dilute enough to secure the absence of complex ions. Experiments on transport numbers have not usually been made in very dilute solutions, and consequently the values for the mobility of such an ion as barium, found by experiments on different solutions of two or more of its salts, do not in general agree with each other. Steele points out, in this connexion, that recent transport experiments by Noyes on solutions of barium chloride and nitrate at a concentration of 0.02 normal give the same mobility to the barium ion in the two solutions. At greater CH. IX] 229 CONDUCTIVITY OF ELECTROLYTES Connexion be. of an ion and its tion. concentrations, the relative amount of salt taken from the neighbourhood of the cathode (p. 212) is increased. This result might be explained by the assumption that some double molecules of composition 2BaCl, exist, which yield the ions Ba, Cl and (BaCl2) Cl. The effects of complex ions will again be considered in Chapter XII. We may conclude, from the experimental confirmation described above, that the velocity of an ion of a tween the mobility simple salt, as calculated by Kohlrausch's theory chemical constitu- from the conductivity, really does represent the actual speed with which, on the average, the ion makes its way through the solution. We may therefore apply the theory with confidence to cases in which the experi- mental confirmation would be difficult or impossible. If we know the specific velocity of any one ion, we can, from the conductivity of very dilute solutions, at once deduce the velocity of any other ion with which it may be combined, without having to determine the migration constant of the compound, a matter often involving considerable trouble. Thus, taking the specific ionic mobility of hydrogen as 0.0032 cm. per sec. per volt per cm., we can, by determining the conduc- tivity of dilute solutions of any acid, at once find the specific velocity of the acid radicle involved. Or, again, since we know the specific velocity of the silver ion, we can find the velocities of a series of acid radicles at great dilution by measuring the conductivity of their silver salts. : By these methods Ostwald, Bredig, and other observers have found the specific velocities of many ions both of inorganic and organic compounds, and examined the relation between consti- tution and ionic mobility. A full account of such data has been given by Bredig? The velocities given by him are relative numbers calculated from the conductivities measured in terms of mercury units, and so must be multiplied by 110 x 10-7 if they are wanted in centimetres per second per volt per centi- metre. The mobility of elementary ions is found to be a periodic 1 Zeits. phys. Chem. XIII. 191 (1894). 230 [CH. IX SOLUTION AND ELECTROLYSIS 34 3:5 4 function of the atomic weight, similar elements lying on similar portions of the wavy curve. The curve much resembles that giving the relation between atomic weight and viscosity in solution. For compound ions the mobility is largely an additive property; to a continuous additive change in the composition of the ion corresponds a continuous but decreasing change in the mobility. Ostwald's results for the formic acid series give Diff. for CH, Formic acid ... ... HCO' 51.21 -19.9 Acetic „ ... ... H20202 38:31 - 4:0 Propionic , H.C202 , Butyric ... ... H_C402 308 - 2:0 Valeric „ ... ... H,C0' 28.8 Caprionic „ ... . HJC602 27.4% - Bredig finds similar - relations for every such series of compounds which he examined. Isomeric ions of analogous constitution have equal mobilities. A retarding effect is, in general, produced by the replacement of H by Cl, Br, I, CH, NH, or NO,: of any element by an analogous one of higher atomic weight (except O and S); of NH, by H,0; of (CN). by (C2O4)3 ; by the change of amines into acids; of sulphonic acids into carboxylic acids; acids into cyanamides, dicarboxylic into monocarboxylic acids; and by monamines into diamines. The additive effect is, however, largely influenced by constitution. Thus in metamerides the mobility increases with the symmetry of the ion, especially as the number of C-N unions gets greater. Reinold and Rücker have investigated the electrical re- Conductivity of sistance of thin soap films The thickness was liquid films. measured by optical means, depending on the interference of two parts of a beam of light. One part of the light passed through a tube across which several films were stretched, and the consequent optical retardation was deter- mined. On the assumption that the refractive index of a film is the same as that of the liquid in bulk, an assumption for which reasons are given, these measurements enable the ag- gregate thickness of the films to be estimated. It was found that when the films became too thin to reflect light and there- fore, like the central spot of a system of Newton's rings, looked 1 Phil. Trans. A. CLXXXIV. 505 (1893). CH. Ix] 231 CONDUCTIVITY OF ELECTROLYTES black by reflected light, no further reduction in thickness could be obtained, and the thickness remained constant for any given liquid. If some salt was added to the liquid, the thickness decreased ; thus the following table shows the thickness in micro-millimetres (metres x 10–10) of films of 1 part of hard soap in 40 parts of water with varying amounts of potassium nitrate. Optical method. Percentage of KNO, . 3 1 0.5 0 Thickness in uime 12:4 13.5 14.5 22:1 If the conductivity of the film is the same as that of the liquid in bulk, the electrical resistance of a film should give values for the thickness which agree with these pumbers. It was found that, as long as the amount of salt present was greater than about 2 or 3 per cent., the results of the two methods agreed, but that, if the amount was less, the electrical method gave a result greater than that obtained optically. Electrical method. Percentage of KNO. 3 2 1 . 0.5 0 Thickness in que 10:6 12.7 24.4 26.5 148 These results indicate that the conductivity of a thin film is much greater than that of the liquid in bulk when the concen- tration of the dissolved electrolyte is very small, but that the conductivities become identical as the concentration increases, The phenomenon cannot be explained by supposing that the effect of the surface energy is to increase the ionization, because it is in dilute solutions, where the ionization is already nearly complete, that the difference is most marked. Unless the presence of the soap has a disturbing influence, it seems that the ionic friction must be less, and the ionic mobilities greater, in the film than in the bulk of the liquid. It is worthy of note that there is evidence to show that the conductivity of . a thin metallic film is less than that of the metal in bulk. On the electron theory this is explained by the interference with the motions of the corpuscles which results when the thickness of the conductor becomes comparable with the mean free path'. i Longden, Amer. Journ. Sci. IX. 407 (1900); Phys. Rev. July & Aug. (1900). CHAPTER X. GALVANIC CELLS. Introduction. Reversible cells. Electromotive force. Effect of pressure. Concentration cells. Different concentrations of the electrodes. Different concentrations of the solutions. Concentration double cells. Effect of low concentrations. Chemical cells. Oxidation and reduction cells. Transition cells. Irreversible cells. Secondary cells or accumulators. Introduction. SINCE the invention of Volta's pile in the year 1800 many forms of battery have been introduced. An account of those now in use, and of the pur- poses to which each is specially adapted, may be found in any book on practical electricity. We shall here confine our- selves to the theory of the production of the electric current to be obtained from such cells. When two metallic conductors are placed in an electrolyte, a current will flow through a wire connecting them provided that a difference of any kind exists between the two conduc- tors in the nature either of the metals or of the portions of the electrolyte which surround them. A current can be obtained by the combination of two metals in the same elec- trolyte, of two metals in different electrolytes, of the same metal in different electrolytes?, or of the same metal in solutions of the same electrolyte at different concentrations. i An effective difference in the electrolytes can be secured by dissolving either different substances in the same solvent, or the same substance in different solvents. CH. X] . GALVANIC CELLS 233 In order that the current should be maintained, and the electromotive force of the cell remain constant during action, it is necessary to insure that the changes in the cell, chemical or other, which produce the current, should neither destroy the difference between the electrodes, nor coat either electrode with a non-conducting layer through which the current cannot pass. As an example of a successful cell of fairly constant electro- motive force we may take that of Daniell, which consists of the electrical arrangement zinc / zinc sulphate solution / copper sulphate solution / copper, the two solutions being usually separated by a pot of porous earthenware. When the zinc and the copper plates are con- nected through a wire, a current flows, the conventionally positive electricity passing from copper to zinc in the wire and from zinc to copper through the cell. Zinc dissolves, and zinc replaces an equivalent amount of copper in solution, copper being simultaneously deposited on the copper electrode. The internal rearrangements which accompany the production of a current do not cause any change in the original nature of the electrodes, and, as long as a moderate current flows, the only variation in the cell is the appearance of zinc sulphate on the copper side of the porous wall. As long as the supply of copper sulphate is maintained, copper, being more easily separated from its solution than zinc, is alone deposited at the cathode, and the cell remains constant. On the other hand, if no current be allowed to flow, slow processes of diffusion, unchecked by migration in the opposite direction, will cause copper to appear in the anode vessel, and finally to be deposited on the zinc. Little local galvanic cells are thus formed on the surface of the zinc, which then dissolves even though the circuit of the main cell is not completed. Till this deposition occurs, the cell can be left on open circuit without waste, and no zinc will dissolve if it is chemically pure. If however commercial zinc, which contains iron, be used, local action is again set up. This action can be prevented by amalgamating the zinc; probably because that process produces a uniform surface, iron being insoluble in mercury. 234 [CH. X SOLUTION AND ELECTROLYSIS The conditions necessary for the continuous production of a current are well illustrated in an experiment described by Ostwald? Plates of platinum and amalgamated zinc are sepa- rated by a porous pot, and are each surrounded by some of the same solution of a neutral salt of a metal more oxidizable than zinc, such as potassium sulphate. When the plates are con- nected together by a wire, no permanent current flows and no appreciable quantity of zinc is dissolved, for any current must primarily liberate potassium at the platinum, the potassium secondarily decomposing water. This primary process would absorb more energy than is supplied by the solution of the zinc. If sulphuric acid be added to the vessel containing the zinc, these conditions are unaltered, and still no zinc is dissolved. On the other hand, if a few drops of acid be added to the vessel in which is the platinum plate, bubbles of hydrogen at once appear, a continuous current flows, and zinc is simul- . taneously dissolved. This experiment illustrates two conditions necessary for the production of a current. In order that posi- tively electrified ions may enter a solution, an equivalent amount of other positive ions must be removed or negative ions be added; and, for the process to occur spontaneously, the possible actions at the two electrodes must involve a decrease in the total available energy of the system. Considered thermodynamically, galvanic cells must be divided into reversible and non-reversible sys- Reversible cells. tems. If the slow processes of diffusion be ignored, the Daniell cell already described may be taken as a type of a reversible cell. Let an electromotive force exactly equal to that of the cell be applied to it in the reverse direction. When the applied force is diminished by an infinitesimal amount, the cell produces a current in the usual direction, and the ordinary chemical changes occur. If the external electro- motive force exceeds that of the cell by ever so little, a current flows in the opposite direction, and all the former chemical changes are reversed, copper dissolving from the copper plate, 1 Phil. Mag. [5] xxxII. 145 (1891). CH. X] 235 GALVANIC CELLS while zinc is deposited on the zinc plate. The cell together with this balancing electromotive force is thus a reversible system in true equilibrium, and the thermodynamical reasoning applied to such systems in the first chapter can be used to examine its properties. Another reversible cell of similar type is the arrangement zinc / zinc sulphate / zinc sulphate with mercurous sulphate / mercury due to Latimer Clark. It is used as a standard of electro- motive force, giving 1.434 volts at 15° C. The very slightly soluble mercurous sulphate acts as depolarizer, depositing mercury on the cathode, when the cell works in its natural direction. Here also a reversal of the current reverses all the internal changes of the cell. Cells from which gas is lost into the atmosphere, such as Volta's original zinc / dilute acid / copper couple, and others in which irreversible processes of reduction occur, such as the Grove arrangement, zinc / dilute suphuric acid /nitric acid / platinum, form essentially irreversible systems. Moreover, it does not follow that, because an accumulator can be used to give a current in the reverse direction to the charging current, it is in the thermodynamic sense a reversible cell. This is only the case when an electromotive force greater by an indefinitely small amount than the secondary electromotive force of- the cell will reverse the current through it and the chemical actions in it also. For this to be possible, it is necessary that the whole of the energy of the charging current should be put into available energy of chemical separation, which can all be regained when the cell is discharged. Electromotive Let us now apply the thermodynamic relations, which we have established in Chapter I., to investigate the electromotive force of reversible cells. The force. solution of this problem was given in different ways by Willard Gibbs and von Helmholtz. For us the simplest method will be to use the available energy equation which was obtained on p. 29. 236 [CH. X SOLUTION AND ELECTROLYSIS 1 Let E denote the electromotive force of the cell at a temperature 0, and let a quantity q of electricity pass reversibly through the cell in the natural direction. The external work done is then equal to Eq, which therefore represents the decrease in the available energy of the system. Thus the equation (11) of available energy po=e+oa becomes Eq=e+q0 am The decrease e of the internal energy of the cell will be the same if the final state of the system is reached in any other way, as for instance by direct chemical action, the energy equivalent of which can be found by measuring the heat evolved by the reactions. Let X be the heat of reaction per gram- equivalent corresponding to the chemical changes which occur, and let q denote the number of electrical units simultaneously passed through the cell; then we get Eq=x+qe do Writing a for we have ve E=1+04 a tode ......... (39) do... as the expression for the electromotive force of the cell, where a denotes the calorimetric heat of reaction which would correspond to unit electric transfer. The same equation can of course be obtained in other ways, as for instance by putting the cell through a complete ideal reversible cycle of changes in the manner of Carnot's engine, the external work here being done by the energy of the current. It will be observed that if the temperature coefficient dE/d0 is zero, the equation shows that the electromotive force CH. x] GALVANIC CELLS 237 is equal to the heat of reaction. The earliest formulation of the subject, due to Lord Kelvin, assumed that this relation was true in all cases; as, calculated in this way, the electro- motive force of the Daniell cell, which has a very small tempera- ture coefficient, agreed with observation. The heat of reaction when one electrochemical equivalent of zinc replaces copper in sulphate solution, which is the effective process of the cell, is 2.592 calories. Multiplying by the mechanical equivalent of the calorie, 4.18 x 10”, we have 1:09 x 108 electromagnetic units, or 1.09 volts, a number agreeing with that observed. In cases in which the temperature coefficient is appreciable, the exact expression must be used. It has been experimentally confirmed by Czapski? and Gockel?, and quantitatively by Jahns; it has been verified for the Grove gas cell by Smalet, and for cells in which fused salts instead of solutions are used as electrolytes by L. Poincarés, J. Browns, and Buscemi?. It is clear, since the electrical energy is not equal to the heat of reaction in the equation, that there must be a reversible evolution or absorption of heat energy in the cell per unit electric transfer equal to the thermal equivalent of the expres- sior in de on his This reversible heat is to be distinguished from do the irreversible heat produced in a cell by the passage of a current through it against the resistance. The latter depends on the square of the current, and can therefore be reduced to any extent, as compared with the reversible heat, by lowering the strength of the current. Jahn compared the reversible heat thus calculated from the electromotive force and its tempe- rature coefficient, with that found by means of experiments with an ice calorimeter. i Wied. Ann. xxi. 209 (1884). ? Wied. Ann. XXIV. 618 (1885). 3 Wied. Ann. XXVIII. 21 (1886). 4 Zeits. Phys. Chem. XIV. 577 (1894). 5 Paris Reports, 11. 411; Compt. rend. cx. 339 (1890); Ann. Chim. et Phys. [6] XXI. 344 (1890). Q Proc. R. S. LII. 75 (1892). 7 Att. Accad. in Catania, XII. (1900). 238 [CH. X SOLUTION AND ELECTROLYSIS The following table gives some of his results: Reversible heat effect Electric Heat of Cells E.M.F. at 00. Volts Eldo reaction energy in calories in calories Calculated Observed 1•096 +0.000034 50526 50110 - 428 - 416 1.031 -0.000409 | 47506 | 52170 +5148 +4660 Cu/CuSO. 100H,01 ) ZnSO4.100H,0/ŹNS Ag/AgCl/ ZnCl, 100H,0/21 Ag/AgNO3.100H,01 Pb(NO3)2. 100H,//ºb} Ag/AgNO3.100H,O/ 21 Cu(NO3)2.100H,0/Ću) 0.932 42980 50870 +7890 +7950 0-458 21120 | 30040 +8920 | +8920 Certain mercury cells gave results not so concordant with theory, but this want of agreement was afterwards shown by Nernst to be due to an erroneous value for the heats of formation of mercury compounds. Attempts have been made by Jahn? and Gill2 to localize this reversible heat by measuring the Peltier effect at the junctions in the cell. They find that the usual thermo-electric equation, which we shall consider in the next chapter, giving the sum of the Peltier effects £()=-oay holds good within the limits of experimental error. The relation adE E=X+0 - [ ° ᏧᎾ then becomes E=1-E (7).....................(40), so that 2= E + £ ().......................(41). The relation thus verified has been applied by Jahn to the determination of heats of formation. i Wied. Ann. XXXIV. 755 (1888) and L. 189 (1893). 2 Wied. Ann. XL. 115 (1890). 3 Wied. Ann. XXXVII. 408 (1889). CH. x] GALVANIC CELLS 239 Effect of Pressure, Whenever the action of a cell causes change of volume, the electromotive force must depend on the external pressure?. In cells where metals only are de- posited or dissolved, the changes in volume are small; but when gases are evolved or condensed at either electrode, a considerable amount of external work is done. In treating this problem from the point of view of thermodynamics, we naturally employ the thermodynamic potential at constant pressure instead of that at constant volume (pp. 23 and 24). The two thermodynamic principles give, as we have seen, the relation Se = 680 + (X8x) = 089 + Edq + pov, since, in this case, the external work comprises a term pdv as well as the electrical term Ed Subtracting 8(0€ + pv) from each side, 8(e - 00 - pv)= E8q- vep-080, or, writing & for € - 00-pv, &= Edq - vdp - $80. The right-hand side is a perfect differential, and we may write 05 др =- ; hence we have relations such as (DE) o las alas lop), 5 op (og) = og lõp) = -log).' which prove that the rate of increase of the electromotive force with the pressure is equal to the decrease in volume at constant pressure per unit quantity of electricity passing, when the temperature in each case remains constant. Faraday's law shows that the volume change is proportional to the quantity of electricity, so that if y, and va be the initial and final volumes, du U - V₂ aqq and we get asE, = -0, 097p OF I Ən = V1 – V. 1 See Duhem, Le potentiel Thermodynamique, p. 1:17; and Love, Report of the Australasian Association, Sydney, 1898, p. 84. 240 SOLUTION AND ELECTROLYSIS : [CH. X For solids and liquids v, and V, are sensibly independent of the pressure, and we get by integration for the change of electromotive force with change of pressure .. E,- Ex=” – ? (P2 - pa) ............... (42). In the case of gases, if Boyle's law be assumed, we can again readily integrate the equation. Let us as usual denote by R the gas constant for one gram-molecule, so that the value of R is the same for all gases. Let each molecule of gas dissolve as n ions; let the valency of each ion be y, and let q be the amount of electric charge on one gram-atom of a monovalent. ion. The electric transfer required to liberate one gram-molecule of the gas is then gny. We thus obtain , RT (P2 dp – RT log P2...(43). E, - EL = odp= J pany - qny J P P aný Pi The decomposition of water with platinized electrodes is a reversible process, so that this equation also determines the effect of pressure on the decomposition point of water, These two relations (42) and (43) have been experimentally confirmed by Gilbaultz throughout a range of pressure extending from 1 to 500 atmospheres. The effect for a Daniell cell is about the hundredth part of that for a gas battery. Many of the results here deduced thermodynamically can be obtained in other ways. Thus J.J. Thomson has found the effect of pressure on the electromotive force of gas cells by an application of the Lagrangian function in a strictly dynamical way, and, by making a probable assumption, has also obtained Helmholtz's equation in a similar manner. Again, as we shall see later, Nernst and Planck have developed a theory of galvanic cells from a knowledge of the velocities of the ions and the osmotic pressures. C 1 Ann. Fac. des Sci. de Toulouse, v. A.S. 1891. ? Applications of Dynamics to Physics and Chemistry, pp. 86, 98. e n nie. Dis 1892. CH. X] 241 GALVANIC CELLS Concentration cells. As stated above, an electromotive force is produced whenever there is a difference of any kind at two electrodes immersed in electrolytes. In ordinary cells the difference is secured by using two dissimilar metals, but an electromotive force also exists if two plates of the same metal are placed in solutions of different substances, or of the same substance at different concentrations. Another method is to use in the same solution electrodes of different concentration. Such electrodes can be constructed by taking hydrogen in contact with platinized platinum, and making the pressure different at the two ends. . In all such cells the electrical energy is not obtained from chemical changes, but from the energy of expansion of substances from greater to smaller concentrations. For the cases in which very dilute substances, gaseous or dissolved, alone are used, the gaseous laws are obeyed, and there is consequently no heat of dilution. Thus in Helmholtz's general equation, which is appli- cable to all kinds of cell, namely dE • E=X+07, 1 vanishes, and we get , dᎬ dᎬ dᎾ . Erdo or E=; so that integrating, log E = log 0 + constant, OL E=CO........................... (44). The electromotive force is therefore proportional to the absolute temperature. This relation, it will be noticed, depends on the absence of chemical action or heat of dilution, and is only true, even for concentration cells, when the substances are so dilute that no sensible heat is evolved on further dilution. Concentration cells, in which it holds, are really heat engines, and work by using the heat energy of their surroundings. These remarks apply to all concentration cells for which the gaseous laws hold, whether the difference in concentrations is in the electrodes or in the solutions. W. S. 16 242 [CH. X SOLUTION AND ELECTROLYSİS The nature and theory of concentration cells were first fully discussed by von Helmholtz by an application of the principles of thermodynamics and a knowledge of the phenomena of vapour pressure', without any special electrolytic hypotheses, and the general accuracy of his theory was confirmed by the experiments of Moser?. Different concen- Let us consider the example mentioned, hydrogen electrodes at different pressures. If these electrodes are trations of the immersed in a solution of acid or alkali, a electrodes. current will flow, gas dissolving at the electrode of high pressure and appearing at that of low pressure. Now a thermodynamic cycle can be performed at constant temperature by allowing such a current to flow reversibly against a balancing electromotive force, taking out the gas evolved, slowly com- pressing it, and then passing it into the other electrode vessel till everything is in its initial condition. The work gained from the gas during its escape at constant pressure from the first electrode vessel is pīvz. In compressing it from pz to pz the work gained is - pdv, as was shown on p. 3. Finally in passing it into the second electrode vessel the gas does work – p2V2. The total work may be written 71 (P2 | -! pdv. * 2 JP Now 8( pv)=pdv +vop, so that / PU ſvdp = [ »). [pdu. Thus the work done during the process under consideration is always measured by vdp; and only if Boyle's law holds, so P2 11 | P2 that pv vanishes, can it also be expressed as - pdv. JPL J2 1 Wied. Ann. III. 201 (1878); Ges. Abhand. I. 840, 11. 979 ; Sitzungsber. Berl. Akad. Juli 1882. 2 Wied. Ann. III. 201 (1878). CH. x] GALVANI 243 GALVANIC CELLS Jpi Then, as before, let each molecule of the gas dissolve as n ions, the average valency of which is y; q being the electric charge on one gram-atom of a monovalent ion, the electric transfer required to liberate one gram-molecule of the gas is qny. In the complete cycle of the concentration cell, both the electrical process and the reverse operations can be performed isothermally, so that the balance of work gained must be zero, and we may write Egny + ** vdp=0. This result is general; but if the gas obeys Boyle's and Charles' laws we may put pv=RT, and obtain E=- RT 1P2 dp RT qnyl.n. Pagny loge ............(45), an equation which shows that the electromotive force of the cell described is proportional to the logarithm of the ratio of the pressures at the two electrodes. It seems that no quanti- tative experiments have yet been made on such cells, and this relation therefore remains without practical confirmation. The method of deducing it, however, will serve later on to elucidate other more complicated cases. A cell similar in theory, in which the hydrogen is replaced by mercury, has been experimentally realized. The electrodes consist of a long and a short column of mercury, each separated from the solution of a mercurous salt by parchment paper, which is impervious to the mercury in bulk but apparently allows it to pass in the form of ions. Mercury dissolves from the column of high pressure, and is precipitated beneath the column of low pressure, a corresponding electric current passing through the cell. The process can be me-. chanically reversed by raising the required quantity of mercury through a height h equal to the difference in level of the two columns, and the electrical work gained is equal to the work so expended. Thus, if A is the atomic weight in grams, Eqny= Agh, 12 being in this case equal to unity. (D 16-2 244 .[CH. X : SOLUTION AND ELECTROLYSIS Des Coudresi arranged such a cell, and obtained the following results : Pressure in centimetres E (calculated) E (observed) 36 7.2 x 10-6 volts 9:3 , 23 . 7.4 x 10-0 volts 10-5 » 21 „ . 113 Another method of varying the concentration of the elec- trodes is to use amalgams of a metal, of different proportions. Here again, the passage of material is from a concentrated to a. dilute condition; and, if we suppose that metals dissolved in each other exert osmotic pressure like that of ordinary solutions (a hypothesis which is supported by the experiments of Ramsay on the vapour pressures of amalgams and those of Heycock and Neville on the fusion points of various alloys), we can calculate the osmotic work needed to undo the changes produced by the current in exactly the same way in which we calculated the mechanical work in former cases. Assuming that the osmotic pressure is proportional to the concentration c, we get RT E= 4 any logement The electromotive forces of such cells have been determined by G. Meyer”, who finds a good agreement with theory for amal- gams of zinc, cadmium and copper. Thus for zinc amalgam in zinc sulphate solution : Temp. Cent. Ca E (observed) E (calculated) 11°:6 670.5 0:003366 0-002280 0.00011305 0.0000608 0°.0 0.0419 volts 0.0516 ., 0.0452 .. 0.0520 , 0:0416 volts 0.0497 , 0.0426 , 0.05191 60°.0 1 Wied. Ann. XLVI. 292 (1892). ? Zeits. phys. Chem. VII. 447 (1891). CH. X] 245 GALVANIC CELLS Different con- centrations of the solutions. In calculating these numbers, the value for R was taken corresponding to one gram-molecule. Now for metals dissolved in mercury, the vapour pressures show that their molecules consist of one atom each, and therefore the gram-molecule of zinc was taken as Zn or 63.5 grams. The concordance with the observed values therefore confirms the monatomic nature of the molecule of a metal dissolved in mercury. In both kinds of cell, it is seen from the equation that the electromotive force is independent of the nature of the electro- lyte. Again, the equation shows that the electromotive force should be proportional to the absolute temperature, and this result also is confirmed by the experiments. The conditions necessary to secure this result have been already considered on p. 241. Of more practical importance is the case of a concentration cell when two plates of the same metal are immersed in solutions of the same salt at diffe- rent concentrations. Take for example the cell silver / dilute silver nitrate / concentrated silver nitrate / silver. Here metal dissolves in the more dilute solution and is deposited from the more concentrated solution. When one electrochemical unit of electricity passes, one gram-equivalent of silver dissolves at the anode and an equal quantity is deposited at the cathode. In this manner the anode vessel must gain one gram-equivalent of salt and the cathode vessel lose the same amount. Now consider the motion of the ions through the solution. The current, which is exclusively carried by silver ions at the electrodes, is shared between silver ions and NO, ions in the body of the liquid. If the ionic velocities were the same, therefore, half a gram-equivalent of each would pass across the surface of contact of the solutions. In the general case, when the transport ratio of the anion is r, and that of the cation 1-r, the anode vessel will, on the whole, gain 1-(1-r) or r gram-equivalents of silver and therefore of salt, while the cathode vessel must lose an equal amount, the difference between this case and that considered on p. 208 consisting in the fact that we now have a dissolvable anode. 246 [Ch. x SOLUTION AND ELECTROLYSIS In order to return these y equivalents of salt from the dilute to the concentrated solution in a reversible manner, osmotic operations can be performed analogous to those re- quired to effect a similar change in the hydrogen electrodes described on p. 242. Let us place the more dilute solution, which has received additional salt by reason of the electric transfer, in an osmotic cylinder, of which the piston is im- pervious to the salt in question, and is backed by a large volume of the pure solvent. Let the pressure on the piston be that of equilibrium. Allow this pressure to fall by an infinitesimal amount, so that solvent enters the solution till the concentration is again exactly as it was before the electric transfer. The change in concentration is very small if a large volume of solution is present, so that the process practically occurs at constant pressure and the work gained is Pīvi, where V, denotes the change in volume, and P, the constant osmotic pressure. Now separate bodily from the solution that volume of it which contains the amount of salt transferred by the current, and reversibly compress this quantity in an osmotic cylinder till its osmotic pressure rises to P,, that of the more concentrated solution of the cell. The work done by the osmotic forces is - Pdu. Finally place this liquid in contact with the stronger cell solution, connect it through a semi-per- meable wall with the reservoir of the pure solvent, and squeeze out solvent till the solution regains its initial volume by the expenditure of work equal to P2V2. The thermodynamic cycle is then complete. Both the electrical and the osmotic processes of this cycle can be made reversible and isothermal; then the balance of external work must vanish. Denoting the electromotive force by E, and considering the electric transfer 9, we may write D C CP JP Eq+ PV -1 Pdv=0, JP which gives, as on p. 242, Eq=-vdP. JP CH. x] 247 GALVANIC CELLS Now, as before, let q be taken to represent the electric transfer needed to liberate one gram-atom of two opposite monovalent ions at the electrodes, and therefore to decompose one gram-molecule of a monovalent salt. If the salt does not yield two opposite monovalent ions, let y be the total valency of the anions or of the cations obtained from one molecule; for instance, y will be 2, whether the cations be two monovalent ions such as the two H ions of a molecule of sulphuric acid, or one divalent ion such as the Cu of copper sulphate. The total electric transfer corresponding to the decomposition of one gram-molecule of salt and the liberation of one gram-atom of each of the ions is then qy, and we have FP Egy=- vd.P..... ........(46). JP It bei It has been shown above that while one gram-atom of an ion is liberated at the electrode, the transfer of salt from the concentrated to the dilute solution is r, where r is the transport ratio for the anion. Again, as explained on p. 159, the osmotic pressures of electrolytes are abnormally high, so that, when the solutions are dilute, the usual gaseous equation gives Pu= riRT for the amount of salt under consideration, where į is van 't Hoff's osmotic factor. Substituting for v in equation (46) we have P, .dP Eqy=- RT rip or E -_P2 ,dᏢ qy J PP ........(47). ctly calcul therefore of a complicate In general, the factor ¿ is a complicated function of the concentration and therefore of P, so that this integral cannot be directly calculated. A similar expression has been con- sidered in detail by Lehfeldt?, and made the basis of a method of determining the osmotic pressures of concentrated solutions. If the two concentrations are not very different from each 1 Phil. Mag. [6] 1. 377 (1901). 248 [CH. X SOLUTION AND ELECTROLYSIS other, and the solutions moderately dilute, in certain cases no serious error will be involved in the assumption that ri is constant. The last equation then becomes by integration E=_riRTOP, ............(48). • IY Again, for these dilute solutions, the osmotic pressures are proportional to the concentrations C, and cı, and we get E-_ riRT, E=- ou loge ..................(49). Finally for very dilute solutions, i, the ratio of the actual to the non-electrolytic value of the osmotic pressure, becomes equal to n the total number of ions given by one molecule of salt. We thus reach the result Er- rnRT, C2 .................(50), ou use T "****...........(u), TY Ez which is strictly applicable to very dilute solutions only. This expression can be calculated numerically. For deci- and centi-normal solutions of silver nitrate the transport number r is the same, and has the value 0.528 (p. 212). In a cell containing these liquids, 0:528 x 2 x 8.28 x 107 x 291 x 2-303 x log10 10 96440 x1 = 0·060 108 C.G.S. units =0.060 volts. Nernst measured the electromotive force of this cell experi- mentally and found the value 0.055 volt? Considering the restrictions made in developing the equation, this number is in remarkable agreement with the theoretical result. It will be noticed that the electromotive force of the concentration cells just described, of which the arrangement silver / dilute silver nitrate / concentrated silver nitrate / silver is an example, depends on the migration ratio for the anion. 1 Zeits. phys. Chem. VII. 477 (1891). CH. x] GALVANIC CELLS 249 A second type of cell can be constructed, the formula for which involves the migration number for the cation. In the system silver / silver chloride, concentrated potassium chloride / dilute potassium chloride / silver chloride / silver, the silver chloride is very insoluble, so that the mass of it dissolved, which alone is electrolytically active, is constant, and the two silver junctions are kept always in the same condition. When an electrochemical unit of electricity passes through the cell in the direction from left to right as above, a gram- equivalent of silver dissolves at the first electrode. This metal displaces some of the silver in the chloride, and the silver so liberated forms fresh silver chloride with an equivalent of the chlorine ions of the potassium chloride. A gram-equivalent of this salt is thus removed from the more concentrated solution. At the other end of the chain, silver is deposited from the silver chloride, and a gram-equivalent of potassium chloride must therefore appear in the more dilute solution. But mean- while chlorine ions have been migrating against the current from the dilute to the concentrated solution, and if r is, as before, the migration ratio for the anion, this process involves a loss of r gram-equivalents of salt at the cathode (see p. 245). The dilute solution, therefore, on the whole, only gains 1-p gram-equivalent, and the concentrated solution must lose an equal amount. Now 1-r is the migration ratio of the cation. It will now be evident that, when we imagine the cycle of operations completed by the osmotic process described on p. 246, we shall arrive at the result RT ГР, 1 (1-1) ...........(51). qy JP, On the approximate assumptions there made we shall get un LVL .dP E - - E=-(1 – m.) IRI' logo ..........(52), qy or, for very dilute solutions, E=-(1 – m) TRT log. .(53), qy with the same notation previously used. 250 [CH. X SOLUTION AND ELECTROLYSIS From an equation equivalent to (52) the following table was constructed by Nernst?, giving a comparison between the observed and calculated values of the electromotive force of concentration cells. c; and cz denote the concentrations of the two solutions in gram-equivalents per litre. Electrolyte C2 E in volts (observed) E in volts (calculated) HCI HBr 0.105 0:1 0.126 0.125 0:125 0.0180 0.01 0·0132 0.0125 0.0125 KC 0.1. 0.01 NaCl Lici NH4Cl NaBr Na0,C,H, NaOH NH,OH KOH 0.0710 0.0926 0.0932 0.0532 0·0402 0.0354 0.0546 0:0417 0.066 0.0178 0.024 0.0348 0.0717 0.0939 0.0917 0.0542 0.0408 0:0336 0.0531 0.0404 0.0604 0.0183 0.0188 0·0298 0:1 0.125 0.125 0.235 0:305 0:1 0.01 0.0125 0.0125 0·030 0·032 0:01 Some of these results have been recalculated by Lodge, with later values for the migration numbers? In some cases the agreement is improved, in others it is made worse. The general result of the comparison is unaltered. Concentration · double cells. In the cells hitherto described, the process is complicated by the effects of migration, but these effects can be eliminated in a manner due to von Helmholtz. If a calomel cell, zinc / dilute zinc chloride / mercurous chloride / mercury, be coupled in the reverse direction with a similar cell in which the zinc chloride is concentrated, the arrangement is equivalent to the chain Zn/ dilute ZnCl,/ HgCl/ Hg / HgCl / concentrated ZnCl,/ Zn. In this double cell there is no migration from one solution of zinc chloride to the other, but a diminution of the amount of i Zeits. phys. Chem. Iv. 128 (1889). 2 Lond. Phys. Soc. Proc. XVII. 369 (1900); Phil. Mag. [5] XLIX. 351 and 454 (1900). CH. X] 251 GALVANIC CELLS mercurous chloride in the first cell, and an increase of it in the second. Mercurous chloride is very insoluble, and hence its active or dissolved mass remains constant, and the mercury surfaces in the two cells keep always in the same state. The double cell is therefore equivalent to a simple concentration cell Zn/ dilute ZnCl,/ concentrated ZnCl2 / Zn, in which the effects of migration are eliminated. Von Helmholtz originally solved the problem of the concentration cell indepen- dently of ionization hypotheses by imagining the thermodynamic cycle to be completed by evaporation from the one solution and condensation on to the other. In this way thermodynamic data only are needed, but it is now simpler to treat the subject by an application of the principles of osmotic pressure and electric ionization as above. An investigation similar to that already used holds good, but, in this case, when one gram-atom of zinc dissolves, one gram- molecule of salt is formed in the dilute solution and decomposed in the more concentrated solution, and this result is not com- plicated by migration. The transfer of salt, corresponding to unit electrochemical transfer, is therefore unity instead of r, and equation (52) becomes ¿RT ..........(54). E = 16 loge ..........(54). E= 4 LI If we use very dilute solutions of an electrolyte yielding n ions, the electromotive force of the concentration cell is » x 8.28 x 107 x 291 96440 x y x 108 01 2 x 2303 x logo = * 0:0575 x logo ..... ...(55). In the double calomel cell described above, the number of ions is three and the valency of the zinc is two, so that when the ratio of concentrations is 10 the electromotive force is 0·0863 volt. For very dilute solutions of any salt giving two monovalent ions, whatever the absolute concentrations, if the ratio of the concentrations is 10, the electromotive force is theoretically 0:115 volt. 252 [CH. X SOLUTION AND ELECTROLYSIS When the concentrations though still small are too great for the ionization to be taken as complete, an approximate result may be obtained from equation (54), iRT logela E=_ loge D, qy when the actual values of the osmotic pressures P, and P, and of van 't Hoff's osmotic factor ¿ are known. Experimental investigations on these double cells have been made by Goodwin?; the following are examples of his results. Zinc chloride / calomel and zinc chloride / silver chloride cells at 25°. Concentration of the ZnCl, solutions in fractions of normal Observed E.M.F. Observed E.M.F. of calornel cells of silver chloride in volts cells in volts Calculated E.M.F. in volts 0.2 0:1 0:02 0.02 0.01 0.002 0.001 0.0787 0.0800 0.0843 0·0861 0:0767 0.0780 0:0843 0.0847 0·0797 0·0818 0.0844 0·0853 0:01 Zinc sulphate / lead sulphate cells. Concentration of the Inso, solutions in fractions of normal Observed E.M.F. in volts Calculated E.M.F. in volts 0.2 0:1 0.02 0.02 0.01 0.002 0.0427 0.0440 0.0522 0.0453 0.0471 0.0500 By the use of the concentration double cells described in this section, the effects of migration are eliminated. Another class of concentration cells, invented by Nernst, eliminates all effects except those of migration, and thus enables measurements to be made of the potential difference which exists at the junction of two solutions, differing either in the nature or the concen- tration of their contents. These cells will be considered in a future chapter under the head of the diffusion of electrolytes. i Zeits. phys. Chem. XIII. 577 (1894). CH. X] GALVANIC CELLS 253 Effect of low concentrations. The logarithmic formulae for all these concentration cells indicate that theoretically their electromotive s force can be increased to any extent by di- minishing without limit the concentration of the more dilute solution; log P2/P, then becomes very great. This condition can to some extent be realized in a manner that throws light on the general theory of the subject. Let us consider the arrangement Ag / AgCl with normal KCl / KNO; / deci-normal AgNO3 / Ag. The concentration of silver chloride is very small in saturated aqueous solution; from the electric conductivity it has been estimated as 0.0000117 normal. It is still further reduced by the presence of the large excess of chlorine ions of the potas- sium chloride. According to principles to be explained in a later chapter, the product of the concentrations of the ions divided by the concentration of the non-ionized molecules should be a constant at each temperature, so that the lowering of solubility produced by a solution of potassium chloride of given strength can be calculated. The normal solution used in the example has a coefficient of ionization 0·756; and so the final concentration of the silver ions, in presence of deci-normal potassium chloride, which determines the amount of silver chloride dissolved, is 0.00001172/0·0756 normal. Putting in this value, allowing for the ionization 0:82 of the silver nitrate solution, and assuming, that the presence of the potassium chloride does not affect the osmotic work done by the cell, the electromotive force is calculated as 0.52 volt. This number was experimentally confirmed by Ostwaldi who also examined other cells with similar electrodes giving high electromotive forces. Thus 1. Deci-normal silver nitrate / silver chloride in 7 potassium chloride 0.51 volt 2. » / ammonia 0:54 , silver bromide in ” / potassium bromide 0.64 , | sodium thiosulphate 0.84 silver iodide in » / potassium iodide 0.91 „ „ / potassium cyanide 1:31 , , / sodium sulphide 1:36 1 Lehrbuch, 11. 882. i i ti ni con 254 [CH. X SOLUTION AND ELECTROLYSIS The effective concentration of the silver can also be reduced by adding some substance which, by combining with the silver ions, removes them as such from solution. This is shown by the high electromotive forces of the cells Nos. 2, 4, and 6 in the above list. Other metals have been used as electrodes by Zengelis, who showed that, in many cases, cells with electrodes of copper, lead, nickel, or cobalt, possessed electromotive forces which were greater the more the concentration of the ions round one electrode was depressed by the addition of a salt. Hittorf? has even shown that the effect of a cyanide round a copper electrode is so great that copper becomes an anode with regard to zinc. Thus the cell Cu /KCN/K,SO./ZnSO, Zn furnishes a current which carries copper into solution and deposits zinc. In a similar way, silver could be made to act as anode in presence of cadmium. If we know the concentration of the ions round one electrode, it is possible to calculate it round the other from observations on the electromotive force, and this has been done by Behrend The success of the theory of such cells as we are now considering confirms the natural hypothesis made in the in- vestigation, namely, that the osmotic pressure to be used in calculating the osmotic work is simply that of the migrating substance, one of the ions of which is the metal of the electrode. In the cell containing silver chloride in potassium chloride, for example, the osmotic pressure which appears in the logarithmic formula is that due to the silver chloride alone, not the total osmotic pressure of the solution round the electrode due to potassium chloride as well. Moreover, if, when the silver ions are dissolved, nearly all of them are at once converted into compound ions, such as the KAgCy, ion's of potassium silver cyanide, the effective concentration and the effective osmotic 1 Zeits. Phys. Chem. XII. 298 (1893). 2 Zeits. phys. Chem. X. 592 (1892); see also next chapter. 3 Zeits. phys. Chem. XI. 466 (1893). CH. X] 255 GALVANIC CELLS pressure are those due to the slight trace of Ag ions left-, and the solution, whether present as simple or compound ions. It seems that in deducing the formulae by the processes described on pp. 246, 249, we should imagine the osmotic work done against a piston permeable to everything except the actual salt, one of the ions of which is the dissolving electrode. This is probably legitimate, for although such a semi-permeable membrane cannot in every case be practially constructed, its existence would violate no known natural principle, and the thermodynamic reasoning based on its imaginary use would therefore still be valid. : The ideas used in developing the theory of concentration cells have been applied to the usual type of galvanic Chemical cells. * cell by Nernst and others, though in this case the basis of the investigation is more speculative. When a metal is placed in contact with the solution of one of its salts, and a current is passed across the junction and metal dissolved, changes occur in the chemical, osmotic, and electrical energies of the system. As the osmotic pressure of the solution rises, the tendency of the metal to dissolve as electrolytic ions becomes less, and it is suggested that eventually at a certain pressure no further tendency to dissolve would exist. Above this pressure the metal would tend to come out of solution and limit set to the osmotic pressure of a solution by reason of the finite solubility of the salt. With some metals it may be much too high to be ever reached, with others it may be too low. If the concentration of the solution giving the critical pressure 1 According to Morgan (Zeits. phys. Chem. XVII. 513 (1895)), potassium argento-cyanide undergoes ionization in three steps. The first, KAgCy2= K + AgCyn, is nearly complete. A small number of the complex ions AgCy, give AgCy+Cy, while to an almost infinitesimal extent occurs the third process AgCy=Ag+Cy. The mass of silver in the ionic state in a litre of a one- twentieth normal solution of potassium silver cyanide is estimated as four millionths of a milligram, whereas in a solution of silver nitrate of equivalent concentration, the quantity is 109 times as great. 256 [CH: X SOLUTION AND ELECTROLYSIS Pm ур • could be obtained, so that there would be no tendency for ions of the metal to enter or leave the liquid, it is fair to conclude that the metal and solution would be electrically neutral to each other, and that no difference of potential would exist between them. This critical osmotic pressure has been called the electrolytic solution pressure of the metal in the given solution. Nernst identifies it with the osmotic pressure of the ions of the metal in the substance of the metal itself. Such an idea is perhaps suggested by the osmotic pressure of certain metals when dissolved in mercury to form amalgams; the use of these amalgams to give electrodes of different concentrations has already been described. On this view the osmotic work done in transferring a gram-molecule of metal from the elec- trode to the solution may be calculated in the same way as on p. 246, where we calculated it when salt passed from a dilute to a concentrated solution. It will have the value / vdP, where P is the osmotic pressure of the ions in the solution, and Pm the electrolytic solution pressure of the metal. If E, is the potential difference at the surface, the electrical work is Egy, where g is the electric transfer corresponding to the solution of a gram-equivalent, and y the valency of the ions. Thus as before, Egy=- vdP. JP It is usual to go further, and make the assumption that both in the solution and in the metal the osmotic pressure obeys the gaseous laws. If this be done, we get equations (47) to (50) p. 247, in order of increasing inaccuracy, w being now unity. So far we have been considering the solution of metal at the anode. In a Daniell cell, which we may take as example, there are three junctions to be considered, two metal-liquid, and one liquid-liquid. The effect on the electromotive force of the surface of contact of the two solutions will be considered in the chapter on the diffusion of electrolytes; it is very small compared with the potential differences at the surfaces of the two metals, and may here be neglected. On the assump- tion explained above, we may apply the logarithmic formulae to S Pm CH. X] 257 GALVANIC CELLS the two metal-liquid junctions and express the electromotive force of the cell with the usual notation as 94 If we write the expression for the potential difference at one of these junctions in the form NRT. NRT log Pan- 8 Lan log P, qy ce that NRT LY qy we see that " log Pm, which includes the so-called electro- lytic solution pressure, is a mere constant for the metal at the given temperature. Writing this as M, we eliminate some of the assumptions of the preceding investigation, and apply the gaseous laws to the solutions only. The expression for the electromotive force of a Daniell cell then becomes E= M, - M, -" NRT 9Y (log P, -log P2) 1 VP = M, – M-"A log ..(56). 99 This equation may be derived directly from the principles of energetics by observing that the electric work of the cell must be equivalent to the algebraic sum of the following terms : (1) the work done in dissolving an equivalent of zinc from the electrode, its ions being produced at a standard pressure Po; (2) the osmotic work | vdP required to expand or compress the zinc ions so obtained; (3) the corresponding reversed work + vd.P required to reduce the copper ions to the standard J PO pressure; (4) the work of depositing the copper on the cathode. The equation shows that the electromotive force of a Daniell cell can be raised by diminishing the concentration of the zinc sulphate, or by increasing that of the copper sulphate. Since the third term in equation (56) is small compared with M, and M2, this effect is slight. We shall return to the consideration of the electrolytic solution pressure of the metals in the next chapter, under the head of single potential differences. W. s. 17 258 [CH. X SOLUTION AND ELECTROLYSIS In the chemical processes of oxidation and reduction, there Oxidation and occur changes in the valency of the ions, in- tion cells. dicating changes in their electric charges. The energy of these processes can be made to supply an electric current. For example, two platinized platinum plates may be placed, one in a solution of stannous chloride, and the other in a solution of ferric chloride? If the two be metallically connected, a current passes within the cell from the tin solution to that of the iron, stannic and ferrous chlorides being formed. The divalent stannous ion, taking up a third positive electric unit from the anode, becomes a trivalent stannic ion, while the equivalent amount of positive electricity is removed at the cathode by the conversion of the trivalent ferric into the di- valent ferrous ion. The gas cells with hydrogen and oxygen, or hydrogen and chlorine, as electrodes, may be classified in this group, the hydrogen being “oxidized” by its conversion into positively electrified hydrogen ions; in fact it is possible to regard all chemical cells from this point of view. Assuming that the cell may be treated simply as a reversible heat engine, Gibbs has deduced another expres- Transition cells. * sion for the electromotive force? Let 0, be the transition point, the temperature at which the chemical action which gives rise to the current would go on reversibly in either direction, and let , be the heat of reaction per electrochemical unit of mass if carried on outside the cell. Let o be the tem- perature of the cell. Now , heat-units at 0, are equivalent to a units of heat at 0, together with a with 0,-0 units of external work, as is indicated by the formula for the efficiency of a reversible engine. Thus for each unit of electricity which passes, a reversible cell being of maximum efficiency yields 0-0 24 units of electrical work, and a ă units of reversible beat. Looked at in this way, the reversible évolution of heat is seen to be of the essence of the problem. See Le Blanc's Electrochemistry, Eng. Trans. p. 235. 2 B. A. Report (1886), 388. CH. X] 259 GALVANIC CELLS Now, as we know, the available electrical work, when one unit of electricity passes, measures the electromotive force, so that (57). E =20,-0. 0 This result of Gibbs' is of great interest, for if two of the quantities 1, 01, and O be known, the third can be calculated. Cohen' has verified the equation experimentally, and used it as a means of determining transition temperatures, obtaining values which agree well with those found in other ways or by direct observation. Differentiating the equation with respect to 0, we get, since O, is constant, delete- eliminating 6, by means of the equation (57) this gives DE E-a do= or E = x + JA Thus we recover von Helmholtz's equation. Returning to equation (57), we see that at the transition point, where @ becomes 01, the electromotive force vanishes. On this fact depends one of the methods used by Cohen” for determining transition points. Let us take, as an example, the case of the two hydrates of zinc sulphate, ZnSO4.7H2O and ZnSO4.6H,O. Two vessels are filled with powdered zinc sulphate moistened with water, and connected by means of a tube filled with cotton-wool saturated with a solution of zinc sulphate. The vessels contain electrodes of zinc and are finally sealed up. The contents of one of them are now converted into ZnSO4.6H,O by heating it for an hour to a temperature higher than the transition point. The whole cell is then placed in a thermostat, and connected in series with a galvanometer, i Zeits. phys. Chem. xiv. 53 and 535 (1894). 2 Zeits. phys. Chem. xiv. 53 and 544 (1894), or see Van 't Hoff, Studies in Chemical Dynamics, Eng. Trans. p. 193. 17--2 260 [CH. X SOLUTION AND ELECTROLYSIS which is deflected, since the saturated solutions, in contact with different solids, are of different concentrations. The tempera- ture is lowered and then allowed to rise slowly. The deflection falls, and finally is reversed, the exact point at which it vanishes being the transition temperature from the higher to the lower hydrate. When the temperature is maintained above the transition point for some time, the meta-stable form of salt passes completely into the stable form, the solutions become identical and the electromotive force gradually sinks to zero. When a salt, for instance sodium sulphate, the metal of which cannot be used as an electrode, is to be examined, an electrode such as mercury in mercurous sulphate, which is unpolarizable with respect to the anion, is used. Another method of determining transition points electri- cally by the use of a concentration cell is of special value when the meta-stable form of a substance is difficult to keep for any length of time. The electromotive force of a con- centration cell depends, as we have seen, on the difference in concentration of the two solutions. Thus, if one solution be kept at a constant strength, and the other be kept saturated with salt, as the temperature slowly rises, any change in the solubility is shown by a corresponding change in the electromotive force. Now, as we saw on p. 40, the tem- perature-solubility curves for the two phases of a component cut each other at an angle at the transition point; so, although the solubility itself suffers no sudden change there, its tem- perature coefficient does. The temperature coefficient of the electromotive force, therefore, will also show a sudden change at the transition point, and the temperature-electromotive force diagram will consist of two branches, cutting each other at a sharp angle at that temperature. The cell is made up in open vessels, the solutions being kept stirred in order to insure the constant saturation of the one that is in contact with the solid. The diagram in Fig. 57 shows the electromotive forces of saturated sodium sulphate combined in a concentration cell with normal, half normal and quarter normal solutions, the weaker solutions giving the higher electromotive forces. The transition points estimated from these three cells are 33º-8, CH. X] 261 GALVANIC CELLS 33°.0 and 32°:9, the value found by other methods áveraging about 33°. The theory of this second form of transition cell Millivolts - *---- 400 500 Temperature -> 200 300 400 500 Fig. 57. has been considered by Van 't Hoff, Cohen and Bredig!, who show that the electromotive force can be calculated from the equation by using the known value of the heat of inversion. This change in the direction of the solubility curve at the transition point, it will now be clear, affects the temperature coefficient of standard cells like that of Latimer Clark, which contain a saturated solution of zinc sulphate? The transition point from ZnSO4.7H,0 to ZnSO4.64,0 is 39°, and at this temperature there is a sudden change in the temperature co- efficient of the electromotive force. When using the cell as a standard, a knowledge of the temperature coefficient is needed, and the cell would be unsatisfactory above 39º. The Weston cell, another standard, of the form cadmium / saturated cadmium sulphate mercurous sulphate / mercury, has been recommended as having a much lower temperature coefficient than the Clark, and an electromotive force of ap- proximately one volt (1.019). It has been shown, however, by i Zeits. phys. Chem. XVI. 453 (1895). 2 Barnes, Jour. phys. Chem. IV. 1 (1900). 262 [сн. Х SOLUTION AND ELECTROLYSIS solubility measurements?, and by using the Weston as an in- version cell”, that cadmium sulphate has an inversion point at 15°, which seriously interferes with its trustworthiness as a. standard of electromotive force. - Many of the cells in common use are essentially irreversible, and it is necessary to enquire how far the prin- Irreversible cells. menciples we have used for investigating the theory of reversible cells may be extended to others. It has sometimes been held that irreversible cells have no definite electromotive forces, the measured value depending among other things on the number of the ions of the metals used as electrodes which happen to be present in the liquids. On the other hand it may be argued that single-liquid polarizable cells of the type zinc/potassium sulphate / copper, are limiting cases of Daniell cells4. In accordance with the expression for the electromotive force of Daniell cells given on p. 257, namely ORT, PA E = M, - M - qy the electromotive force is independent of the absolute osmotic pressures of the two solutions; it will therefore be unchanged if the solutions be equally diluted. Now the remarks on p. 255 make it probable that the electromotive force is un- affected by the presence of a salt not containing the electrode metal, and if so, dilution with potassium sulphate solution will be equivalent to dilution with water. On this view, the initial electromotive force of the potassium sulphate cell, before polarization sensibly intervenes, should be equal to that of a Daniell, and a similar result should hold for other such cells. The errors of experiment on polarizable cells are considerable, but, as an ideal limit, the general results seem to be consistent with the required equality. 1 Kohnstamm and Cohen, Wied. Ann. Lxv. 344 (1898). 2 Barnes, Jour. phys. Chem. iv. 339 (1900). 3 Ostwald, Lehrbuch, II. 815. 4 Bancroft, Zeits. phys. Chem. XII. 289 (1893); Phys. Rev. III. 250 (1896); Taylor, Jour. phys. Chem. I. 1 (1896). CH. X] 263 GALVANIC CELLS Secondary cells Any reversible cell can theoretically be employed as an accumulator, though in practice, conditions of or accumulators. general convenience are more sought after than strict thermodynamic reversibility. The accumulator commonly used can be made by placing two lead plates in dilute sulphuric acid and passing a current between them. Hydrogen is evolved at the cathode, while the anode becomes covered with a layer of insoluble lead peroxide. As long as the metallic lead of the anode is in contact with the solution, it has been shown by C. J. Reed' that hydrogen is evolved at the cathode under a total electromotive force of about 0.5 volt, and a considerable volume of the gas can be collected if the area of the anode is large. Eventually the voltage necessary for the generation of hydrogen rises to about 2:3. This suggests that the first action at the anode is the formation of a coating of insoluble lead sulphate, which be- comes the effective electrode and yields sulphuric acid and lead peroxide on further action of the current. The cell is now in a condition to give a current in the reverse direction, during which process lead sulphate is formed at both electrodes until these become identical in constitution. In a second charging, the lead sulphate at the cathode is reduced to spongy lead, while at the anode it again gives peroxide as hefore. Not even at the beginning of the second charging is the anode a lead electrode, and there is no action until the voltage reaches about 2:3. The mass of spongy material at the electrodes is increased by continual charging and discharging, which adds to the effective capacity of the cell; and the whole preliminary process of forming the cell can be greatly hastened if the plates receive in the first place a coating of red lead, Pb,03. The main chemical action of a fully formed accumulator seems to be in accordance with the equation PbO, + Pb + 2H,80, 2PbSO4+2H,0, which read from left to right describes the discharge, and from right to left the charging of the cell. Although ozone, hydrogen peroxide, persulphuric acid, and traces of lead per- sulphate have been detected, it seems likely that the above . 1 Jour. phys. Chem. v. 1 (1901). 264 [CH. X SOLUTION AND ELECTROLYSIS equation represents the chief part of the changes. The concen- tration of the acid solution is an important factor in determining the electromotive force, which increases with increasing con- centration, since part of the available energy of the reaction is due to the dilution of the residual acid by the water formed. It is found in practice that the effective electromotive force of a secondary battery is less than that required to charge it; the energy efficiency of a lead accumulator is from 75 to 85 per cent., although from 94 to 97 per cent. of the current used in charging it can be regained. This drop in the electromotive force has led to the belief that thermodynamically the cell is only partly reversible. Dolezalek1 however has attributed the discrepancy to mechanical hindrances, which prevent the equalization of acid concentration in the neighbourhood of the electrodes, rather than to any essentially irreversible chemical action. On the provisional hypothesis that the system may be treated as reversible, the Gibbs-Helmholtz equation dE E=N+ DA has been applied. The discharge reaction for dilute solutions gives a calorimetric heat-evolution of 87,000 calories, which, on the assumption that the energy is all available, is equi- valent to an electramotive force of about 1.88 volts. This number agrees with that observed for cells filled with weak acid, and indicates that the temperature coefficient is very small, a result which has been experimentally confirmed by Streintza. The quantitative measurements, by the same observer, of dE/do for different concentrations of the acid, can be used to calculate the increase of electromotive force for a given change in the concentration. Dolezalek calculates the same increase from the vapour pressure method applied by von Helmholtz to concen- tration cells. To accomplish this we must imagine two lead accumulators, one cell A containing more concentrated acid than the other cell B. Let them be arranged to work in opposite directions. Since the electromotive force of A is greater than that of B, the combination acts as a double cell and will produce a current in the direction natural to A. The i Zeits. Elektrochem. IV. 349 (1898). ? Wied. Ann. XLVI. 454 (1892). CH. X] 265 GALVANIC CELLS chemical changes of the lead and its compounds are equal and opposite in the two cells, and the effective reaction consists in the transfer of two molecules of sulphuric acid from A to B while two molecules of water pass from B to A. The acid con- tents of the two cells thus tend to equality, and the double arrangement may be looked on as a concentration cell. The available energy is the difference between the work of mixture of pure sulphuric acid with water in the proportions of A and of B. This work can in either case be calculated if we imagine water distilled from the cell to the acid till the resulting liquid has the same composition as that in the cell, when it can be added to the cell without change of energy. Let p, and P2 denote the constant vapour pressures of water, from the liquids in A and B respectively, and p the variable pressure over the isolated acid. The work of distillation from the cell A to the acid is "vdp (p. 242), or, if we assume that the p, J ni vapour conforms to the gaseous laws, RT logo per gram- molecule, and for my gram-molecules of water RT (™ log fu dn. Thus the work of transferring one gram-molecule of H,so, from A to B is W,- W.=RTS" log in dn – RTS" log in an =RT (ng log pa –nlog pa – S™ log pdn). The actual changes in the double cell also involve the transfer of one gram-molecule of water from B to A, a process which by distillation would involve the work RT log 2. Finally we have for the electromotive force of the double cell SE= RT (no log pa – na log pa + logement - S** logpdn). The vapour pressures of sulphuric acid of various concentrations have recently been measured accurately by Dieterici', and from his results the above equation can be solved numerically. Dolezalek has measured the electromotive force E of lead cells in ice, as follows : Pi Ini } Wied. Ann. L. 61 (1893). 266 [Ch. x SOLUTION AND ELECTROLYSIS Cell Density of acid % H2SO4 Grams of water to 1 grm.-mol. H2SO4 Vapour pressure in mm. Hg 2:29 2:18 2:05 1.94 1.82 1.496 1'415 1.279 1.140 1•028 58:37 50•73 35.82 19:07 3.91 69.88 95.16 175.58 415.8 2408.4 0.796 1:438 2.900 4.150 4.574 The differences between these observed values of the electro- motive force were compared with the results of theory in two ways: by the vapour pressure equation deduced above, and by the use of von Helmholtz's equation combined with a knowledge of the heat of dilution of sulphuric acid. As measured by Thomsen, this heat of dilution may be expressed as HEB I 1.7980 H- ab . 9817860 calories when a gram-molecules of sulphuric acid are mixed with b gram-molecules of water. The results of the comparison are given in the following table. SE Double cell Calculated Observed From H From p Dolezalek Streintz 0:47 I-V I-IV II-IV II-V III–V III-IV II-III I-II IV-V 0:40 0.29 0.22 0:32 0.22 0:11 0:11 0.08 0:11 0.45 0:34 0.25 0:37 0·22 0.12 0.13 0:08 0.10 0:35 0.24 0:36 0.23 0:11 0:13 0:11 0:12 0.23 0.13 0.15 0.11 The agreement of these numbers not only confirms the theory given, but also indicates the general conformity of the lead accumulator to the thermodynamic properties of reversible systerns. CHAPTER XI. CONTACT ELECTRICITY AND POLARIZATION. Volta's contact effect. Thermo-electricity. The theory of electrons. Single potential differences at the junctions of metals with electro- lytes. Dropping electrodes. Electrocapillary phenomena. The theory of von Helmholtz. Electric endosmose. Single potential differences (continued). Electrolytic solution-pressure. Electro- chemical series. Polarization. Decomposition voltage. Polarization at each electrode. Evolution of gases. Electrolytic separations. Volta's The source of the energy of a galvanic cell is certainly the chemical action, a correction being applied for contact effect. any reversible heat which the cell absorbs from or gives up to its surroundings. The exact seat of the difference of potential, however, has remained undetermined for a century, and proved a fruitful subject of discussion. Volta located it at the junction of the unlike metals; while Faraday's work, which showed the regular and fundamental part played by the chemical processes, seemed to indicate the surfaces at which the metals were in contact with the liquids. These two views of the nature of the phenomena have continued till the present?, though it seems, from the evidence described in the last chapter and for other reasons that will be given, that a considerable difference of potential probably exists at the surface of separation between metals and electrolytes or i For a description of the phenomena of the contact effect, and an account of the Volta theory, see Lord Kelvin, Phil. Mag. July, 1898. For the other point of view, see Sir Oliver Lodge, Proc. Phys. Soc. Lond. XVII. 369 (1900); and Phil. Mag. XLIX. 351 and 454 (1900). 268 [CH. XI SOLUTION AND ELECTROLYSIS dielectrics such as air. The facts to be explained, besides those of the galvanic cell, are as follows. Dry zinc and copper brought into contact with each other in dry air become oppositely charged, and, if their surfaces are arranged parallel and very close to each other, so as to form a condenser of large capacity, these charges may be consider- able. They can be exhibited by separating the plates; the capacity is then diminished and the difference of potential is thereby increased, so that it can be indicated by an electro- scope or measured by an electrometer. By making the con- nexion between the metals through part of a potentiometer, a difference of potential in the direction opposite to that natural to the junction can be applied. Adjusting the potentiometer till, on separating the plates, the electrometer is not deflected, the natural potential difference can be determined. Another method consists in making the actual quadrants of an electro- meter of the two metals to be examined. On connecting them through a wire a deflection is observed which can be destroyed by applying an external electromotive force in the opposite direction. An electromotive force of about three quarters of a volt neutralizes the natural potential difference produced by the contact of zinc and copper. Many experiments have been made on this subject; to some of them we shall refer below. Ayrton and Perry have examined many metals, obtaining among others the following potential differences in volts?. Zinc Lead Tin Iron Copper Platinum Carbon } 0-210 0:069 0:313 0.146 0.238 } 0:113 By the summation of potential differences, a principle ex- perimentally established by Volta, we can find the contact effect between any two metals in this list by adding together the values for all the pairs of intervening metals. 1 Phil. Trans. clxxI. 15 (1880). CH. XI] 269 CONTACT ELECTRICITY AND POLARIZATION It will be noticed that in all the phenomena described it is the difference of potential in the air surrounding the two metals which is experimentally observed. Nevertheless, many physicists, following Volta, have held that this potential differ- ence in the air is due to, and measures, a natural potential difference between the metals themselves. When the metals are surrounded, except at the area of contact, with the non- conductor air, this potential difference is maintained, and can be demonstrated by means of an electrometer. In a galvanic cell it is supposed that the metallic contact between the electrodes constantly keeps up a potential difference, which is constantly tending to sink to zero by the action of the electrolytic liquid. The theory of the cell given in the last chapter suggests that the chief potential difference is to be sought at the liquid- metal surface; but it is clear that, before any such interpretation can be accepted, it must be reconciled with the phenomena of contact electricity just described. On the analogy of the cell, the most natural explanation is that the potential difference is due to the action of the oxygen of the air; and this hypothesis receives support from the possibility of approximately calcu- lating the observed Volta force as the electrical equivalent of the difference between the heats of oxidation of zinc and copper. It is perhaps not necessary to imagine actual oxidation; a sufficient cause might possibly be found in some slight modifi- cation of the film of condensed gas, which, as we have seen, seems to exist on all solid surfaces, and to be so difficult to remove. The chemical affinity of the oxygen for the zinc can be represented by supposing the film of gas to be electrically polarized, perhaps by the similar orientation of the electrically bipolar oxygen molecules. Such polarization would produce a layer of oxygen atoms straining to attack the zinc but prevented from reaching it by want of a way of escape for the correspond- ing negative charge from the metal, or of a means of approach for an equivalent positive charge. Another metal such as copper will have a different affinity for oxygen, and thus the electrical potential difference between it and the surrounding air will be different from that shown by zinc. If contact be made between 270 [CH. XI SOLUTION AND ELECTROLYSIS them, the potentials of the metals are equalized, or at any rate reduced to the small difference of true metallic contact, by a flow of electricity, which, looked at in another way, may be referred to the greater force of attraction for oxygen shown by the zinc than the copper. Modifying double electric layers are thus produced at each interface, analogous to those caused by electrolytic polarization. This process may perhaps be ac- companied by incipient chemical combination between positively electrified zinc atoms at the surface of the metal and negatively electrified oxygen atoms in the film of air. The corresponding positive atoms of oxygen would then no longer be neutralized, and would give the film of air and its neighbourbood a positive potential. The zinc and copper themselves are at the same. potential, but since the outside of the condensed film on the zinc is more intensely positive than that on the copper, there is a potential gradient through the air between them. It is this difference of potential that is observed in experiments on contact electricity. A modification of the above hypothesis has been suggested by Lodge, who imagines that, when contact is made between the metals, the negative atoms of the oxygen film facing the zinc move nearer to the metal, while the film outside the copper recedes further from it. A change is thus produced in the thickness of the two condensers formed by the zinc-oxygen and the copper-oxygen layers. Their capacities are altered in opposite senses, and an electric transfer must take place from one to the other. Now the capacities must be large, since the separating space is of molecular dimensions, and Lodge has shown that a change of about the hundred thousandth of the original thickness will produce enough electric transfer to give the observed charges to the parallel metal plates, which form a condenser of relatively enormous thickness, and hence of very :small capacity. In passing from either metal to the surrounding air, there is a sudden rise of potential, but this rise is greater for the zinc than for the copper. We can calculate the magnitude of each step of potential on the assumption that all the heat of oxidation passes into the energy of electrical contact, and that the method CH. XI] 271 CONTACT ELECTRICITY AND POLARIZATION of calculating the electromotive force of a cell, given on pp. 235, 237, is applicable to each electrode considered separately. If oxygen were removed by the metal from the film of air, its place would be supplied from the free atmosphere, so that the effective process which is possible is the oxidation of zinc by gaseous oxygen; it is therefore the ordinary heat of oxidation that is involved. The value of this heat for a gram-molecule of zinc is about 85,800 calories, and for copper about 37,200 calories. For the electrochemical equivalents, the mechanical values correspond to 1.85 and 0.80 volt. We can experimentally determine only the difference of these effects. Observation indicates about 0.7 or 0·8 volt, which is appreciably less than the calculated result. . When, instead of the insulator air, the plates are surrounded by an electrolytic conductor, the slope of potential is accom- panied by a current through the solution. At the contacts of the liquid with the metals, the natural potential difference is constantly tending to be again set up by the chemical affinity; thus a constant current is maintained and zinc is actually dissolved. The probability that the contact effect depends on the chemical action or affinity of the surrounding medium will be much increased if it can be shown that the magnitude of the effect depends on the nature of the medium. Many experiments, such as those of Bottomley, indicate that no change is produced by working in vessels at high exhaustion, or by placing the metals in an atmosphere of hydrogen, though a reversal of the sign of the potential difference was obtained by J. Brown by replacing the air by hydrogen sulphide or ammonia?. The film of gas which clings to a solid is ex- ceedingly difficult to remove, and it now seems likely that its persistence explains the negative results so often found. From a recent research by Spiers?, in which extraordinary precau- tions were taken to remove the film of gas, it is clear that the difficulties of getting rid of it have been greatly undervalued, and that, when it is really disturbed, large changes in the 1 Proc. R. §. XLI. 294 (1887). ? Phil. Mag. XLIX. 70 (1900). 272 [CH. XI SOLUTION AND ELECTROLYSIS magnitude of the Volta force are produced. More work on this point is very desirable, but in such a case, a few experiments that yield a positive result, and indicate a probable reason for the negative results of others, seem to carry great weight. The effect of small changes in the nature and condition of the surfaces has been recently studied by Erskine-Murray?, who showed that the potential was increased by polishing and burnishing, and diminished by a film of oxide. There would certainly be less affinity between gas and a partially oxidized metal than between gas and a clean metal, and we should naturally expect the potential difference to be reduced by oxidation. The phenomena of thermo-electricity have an intimate connexion with the subject now under conside- Thermo- electricity. ration? Let us imagine a condenser composed of two plates of different metals, separated by a layer of dielectric and connected by means of a wire of a third metal. In applying the principles of thermodynamics to this system, there are two irreversible processes to be considered; the conduction of heat along the metals, and the frictional generation of heat by the flow of the current. The latter effect, being proportional to the square of the current, will be negligible when the current is very small, and can therefore be considered to be eliminated under ideal conditions. The conduction of heat may be neglected if it proceeds inde- pendently of the current, except for the reversible Thomson effect considered below; this independence it is necessary to assume. In order to explain the phenomena of the reversal of thermo-electric currents when one of the junctions of certain metallic circuits continually rises in temperature, Lord Kelvin has imagined a convection of heat by the passage of the current. Thus the heat absorption per unit quantity of electricity may be written as o&T for a current passing up the temperature- gradient, where o may be called the specific heat of electricity, i Phil. Mag. xlv. 398 (1898). ? See for instance, Larmor, Aether and Matter, p. 306. CH. XI) 273 CONTACT ELECTRICITY AND POLARIZATION OTT and denotes possibly a differential effect, depending on an inequality in the properties of streams of oppositely moving ions. The corresponding heat absorption for a second metal may be expressed as oʻST. Now let us consider a complete circuit of these two metals, T, and T, being the temperatures of the junctions. Let II, and II, be the heat evolved by unit electric transfer at the junctions of the temperatures T, and T, respectively; II, and II, are called the Peltier effects. Then, considering unit electric transfer round the circuit, the energy and entropy principles lead to the results E = II, – II,+/-(6-0) dT ...........(58), O and and TI. PT2 10 T'J2. TT (59). T By differentiation, equation (59) gives ta (9)+70=0, whence we obtain īdī, or Π Δ.Ε T=dT Thus, while the Peltier effects depend on the temperature coefficient of the total electromotive force of the circuit, in equation (58) for E, the Peltier effect appears as a local electromotive force at the junction. Each electron as it passes across, introduces an energy effect qII which involves a re- versible evolution or absorption of heat. The Peltier effects have been experimentally determined, and their electrical equivalents, which measure the contact potential differences at the metallic junctions, are calculated as a few millivolts only, values much too small to explain by themselves the observed Volta effects, without taking account of similar effects at the surfaces of the surrounding dielectric. W. S. : 18 274 [CH. XI SOLUTION AND ELECTROLYSIS electrons. According to the corpuscular theory of electric conduction, the passage of a current through a metal The theory of is is accompanied by the transfer of electrons in its line of flow. In each metal, the cor- puscles or electrons are present in a certain concentration on which depends the conductivity of the material, and may perhaps produce something of the nature of osmotic pressure. On the analogy of Nernst's conception of electrolytic solution characteristic pressure has been imagined at the surface of one metal in contact with another. The better conducting metal in which the corpuscles are more concentrated, will send electrons into the other metal till the equilibrium of the various tendencies prevents further transfer. The electrostatic effect thus produced is the explanation on this view of the potential difference of contact. We may thus imagine two metals in contact to be in a certain sense a concentration cell, the difference of concentration being that of the electric corpuscles in the two materials. On this view, the contact potential difference is analogous to the electromotive force of the cells previously described. There is however a vital difference between the two cases. A con- centration cell is a system in an unstable state; if a current passes through it, the difference of concentration is changed, and the electromotive force altered. Two metals in contact, on the other hand, possess a constant difference of corpuscular concentration, which must re-establish itself if disturbed. In this case, then, there is no source of energy available for the production of a current; and, consistently with this result, the total electromotive force of a circuit of several metals at the same temperature is found to vanish. Nevertheless, if we accept the idea of corpuscular osmotic pressure, the transfer of corpuscles from one side to the other of a metallic interface will involve the loss or gain of osmotic work. The energy change thus produced may be but another aspect of the contact difference of electrical potential; it may be a complicating effect, which will alter the relation of that potential difference to the Peltier effect of reversible heat production. CH. XI] 275 CONTACT ELECTRICITY AND POLARIZATION ve wi540 Pound 12 W OLUOW ww Single potential differences at the junctions of metals with Many attempts have been made to determine experimentally the single potential differences at the individual differences at the junctions in a circuit containing electrolytes as well as metals. In a galvanic cell, for example, electrolytes. . there must be at least two such junctions, and the problem is to separate their effects and measure the step of potential at each. The measured electromotive force gives the sum of all the single potential differences, but the impossibility of directly connecting the electrolyte with an electrometer without introducing another metallic junction throws difficulties in the way of observing them individually. If a method could be devised capable of application to one such junction, the combination of that junction with any other would enable the value for the other to be calculated from the total electromotive force as observed in the usual manner. Two possible diagrams of the distribution of potential in a simple galvanic circuit are exhibited in Fig. 58. The diagrams are supposed to be drawn completely round the surface of a MATUN MILOTION : ATITIN. Cu K |||||||||| Zn cu E Zп си Fig. 58. Fig. 59. cylinder and then unrolled, so that the two vertical lines marked Zn denote the same zinc plate, considered to be at the zero of potential. Beginning at the left end of the figure, there is a sudden rise of potential at the surface. of the zinc, the , 18–2 276 [CE. XI SOLUTION AND ELECTROLYSIS potential difference of the electric double layer being denoted by the vertical rise of the dotted line. Passing through the cell there is a downward potential gradient due to its resistance to the current. At the surface of the copper plate, there is another discontinuity of potential, upwards or downwards according as the natural potential difference at the copper-electrolyte surface has a sign opposite to or the same as the zinc-electrolyte junction. These two possibilities are indicated in the two diagrams of the figure; the external electromotive force of the cell, the same in each case, being represented by the vertical height EE'. Since both metals are oxidizable, though not with the same readiness, we should expect the potential difference with the liquid to have the same sign for copper as for zinc, though generally received experiments described below indicate opposite signs. Leaving the copper plate, there is another potential gradient conforming to Ohm's law in the external circuit, till, at the outside surface of the zinc, the potential again falls to zero. If the external circuit be broken, the natural potential differences at the surfaces of contact remain unaltered, but the Ohmic potential gradients are destroyed. The resulting dia- grams are shown in Fig. 59, in which EE now denotes the total electromotive force of the cell, as measured on open circuit. Thus it will be seen that a determination of the electromotive force of the cell only tells the value of EE', the algebraic sum of two effects. The absolute values of these two effects remain undetermined; it is even uncertain whether they have the same or opposite signs. Since the current passes from metal to electrolyte at the surface of the zinc, and from electrolyte to metal at the surface of the copper, both junctions help to drive the current if the signs of the two effects are different, while, if the signs are the same, the copper plate reduces the natural electromotive force of the zinc electrode. For circuits containing metals and dielectrics only, Volta's law of the summation of potential differences is a necessary consequence of the principle of the impossibility of perpetual motion, but if electrolytes connect the metals, the possible chemical action gives a source of energy, and Volta's law cannot: be assumed to hold good without experimental demonstration. CH. XI] 277 CONTACT ELECTRICITY AND POLARIZATION Again, the potential difference between copper and zinc in air is probably due to the more or less complete transverse orienta- tion of bipolar molecules at the metal / air interfaces, but for å metal / electrolyte junction, besides the corresponding molecular orientation, due to the essential difference in the nature of the two materials, there is a superposed potential difference due to the presence of a double sheet of electrolytic ions in the neighbourhood of the surface. If a small external electromotive force be applied across the junction in the direction opposite to that of the natural potential difference, the number of ions in the double layer is altered, and, by proper adjustments, the ionic effect might be destroyed. The natural potential difference, due to the molecular orientation, however, will probably not sensibly be affected. On the other hand, when a current flows, chemical changes occur, and the molecular layer may in time be disturbed. The electromotive force of a galvanic cell may possibly involve the potential differences due to the molecular arrangement at the various junctions, as well as those due to the distribution of ions. It seems probable, however, that the methods commonly used for determining single potential differences at the junctions of metals and electrolytes give the differences due to the ionic layers only. If so, before the experimental methods can be considered to solve the problem of the location of the effective potential differences in a galvanic cell, it is necessary to prove that Volta's summation law holds with regard to the molecular potential differences, so that its total effect in the circuit vanishes. We must now pass to the consideration of the attempts that have been made to determine these single potential differences. The results are still doubtful and unsatisfactory, but, never- theless, a somewhat full account of the subject will be given, for it has produced much experimental investigation, and further light is greatly to be desired. It is generally believed that the single potential difference at the common boundary of mercury and an electrolyte has been satisfactorily determined by experiments on capillary electrometers and by others in which mercury was allowed to drop into a solution. Nevertheless, uncertainties arise in the 278 [CH. XI SOLUTION AND ELECTROLYSIS interpretation of the phenomena, and doubt may well be felt about the results deduced. Another method of investigation has been adopted by Exner and Tuma, and by Exnerl, and although it is open to criticism we will first briefly consider it as it illustrates the difficulties inherent in the subject. The introduction of the dropping electrode is due to Lord Dropping Kelvin, and was applied by him to determine electrodes. the difference of potential between the earth and any point in the atmosphere. If a conductor is constantly giving off a stream of particles into the surrounding dielectric medium which is at a potential different from that of the conductor, each particle carries away an electric charge until the potential of the conductor is made equal to that of the conducting boundary of the insulator if the latter is itself unelectrified. By connecting the conductor with an electro- meter, the potential of the dielectric at the point of emission of the particles is determined. The particles may be drops of water or mercury, the products of combustion of a flame, or the smoke from a slow-burning match. For measuring the high voltages observed in meteorology, any of these arrange- ments are trustworthy, but when the differences of potential to be observed are one volt or less, the conductivity due to com- bustion restricts the method to the use of some kind of drop. In examining the junction of a metal with an electrolyte, Exner connected the metal to earth and to one quadrant of the electrometer, while the electrolyte was joined by means of a thread moistened with the same solution to a cylinder of , filter paper also soaked in the liquid. The cylinder forms a virtually closed conductor, and the inside of it is therefore an equipotential region, and is assumed to have the potential of the surrounding electrolyte. A funnel having a capillary end is filled with mercury which falls in drops starting within the cylinder. The stock of mercury in the funnel is connected with the other quadrants of the electrometer. In this way the mercury gradually assumes the potential of the air inside 1 Sitzungsber. Kais. Akad. Wien, xcvII. 917 (1889); C. 607 (1891); CI. 627 and 1426 (1892). CH. XI) 279 CONTACT ELECTRICITY AND POLARIZATION the moistened cylinder, except for any natural difference of potential between the air and the falling drops of mercury, 1 In order to correct for these effects, Exner arranged a null experiment in which the mercury drops formed inside a cylinder of carbon or platinum connected with the earth, and the reading of the electrometer then obtained was taken as zero. Now in doing this, any natural difference of potential between platinum and air is neglected, and thus all the results of the work are in error by a constant amount which should be added to or subtracted from them. The error may be small, but there is no means of estimating its magnitude. Moreover, if there is any natural potential difference between the electrolyte and the air, it also is included in the numbers obtained; in fact, by the principle of the summation of electromotive forces, we see that, when electric transfer ceases, the total electromotive force of the circuit mercury / air / solution / metal / air / metal/ mercury must vanish. To secure this result, the solution / metal inter- face is polarized by a double ionic layer; if the necessary double layer were too intense, there would presumably arise a continual leakage current, maintained by the energy of the falling drops. Another form of application of Lord Kelvin's dropping electrodes furnishes one of the methods in common use, to which reference has already been made, for the examination of the electric phenomena at the junction of mercury with an electrolyte. Von Helmholtz pointed out that a potential difference at such a junction would be produced by a double layer of electricity over the surface, the two opposing faces being oppositely charged-on the side of the electrolyte by the congregation of ions as explained above. Such a system would take time to reach its final state, and he concluded that if mercury were allowed to drop rapidly from an orifice beneath the surface of a liquid electrolyte, the double layer would not be established, and the stock of falling mercury would be brought to the same potential as the electrolyte. The 280 [CH. XI SOLUTION AND ELECTROLYSIS apparatus might therefore be used in connexion with an electro- meter as is the dropping electrode in meteorology, the other quadrants being joined to a quantity of mercury at rest in the same electrolyte. A difference of potential of about 0.8 or 0:9 volt is obtained between the dropping mercury and the mercury at rest in dilute sulphuric acid; but it has been pointed out by Exner and by Brown' that the result is complicated by the electromotive force of the cell composed of the mercury with the clean surface newly exposed by the drop as it forms, the electrolyte, and the mercury, tarnished or affected in some way. by the action of the solution, which is at rest in the bottom of the vessel. This part of the observed electromotive force may depend on potential differences of the type due to the regular orientation of bipolar molecules. It would be set up almost instantaneously at the interface, and thus would not be elimi- nated by the action of the falling drops. Again, Warburgº has suggested that owing to the formation of mercury salts in electrolytic solutions containing dissolved oxygen, an explana- tion of the phenomenon might be found in the electromotive force of the concentration cell, . mercury / dilute mercury salt / concentrated mercury salt / mercury, since differences of concentration at the electrodes will be produced by the passage of a current. It seems likely at all events that both these effects are involved in the current which will flow through a connecting wire from the standing to the falling mercury. In examining the results of researches on mercury dropping electrodes, these inherent difficulties should be borne in mind. A third explanation of the dropping electrode is given by. Nernst's theory of electrolytic solution pressure. The solution pressure of mercury is very low, and mercury ions tend to be deposited as metal on a mercury surface, even from a very dilute solution of one of its salts. As the drops form, mercury ions are absorbed by their newly exposed surfaces, and negative 1 Phil. Mag. [5] XXVII. 384 (1889). 2 Wied. Ann. XXXVIII. 321 (1889). CH, XI 281 CONTACT ELECTRICITY AND POLARIZATION ions are attracted to the ionic layer of the electrolyte next the interface. These negative ions are carried down with the drops as they fall; they enable mercury ions to redissolve in the lower parts of the solution when the drops coalesce with the standing mercury and the area of contact is diminished. This explanation involves a loss of mercury salt in the upper regions of the solution, and a corresponding gain below. Such changes of concentration have actually been observed by Palmaer by electrical and chemical methods in an unsaturated solution of calomel, through which mercury was allowed to drop". Experiments have been made by different observers on electrodes dropping mercury directly into electrolytic solutions, with results that did not agree very well among themselves. If the orifice be within the electrolyte, the time of fall of the mercury as a continuous jet allows the ionic potential difference of the interface to partially establish itself, but Paschen”, who investigated the subject in 1890, came to the conclusion that concordant values -could be obtained by making the mercury jet emerge from the orifice into air, but break into drops just as it reached the surface of the electrolyte. His experiments on liquid amalgams, however, seemed to indicate that even in this way the mercury or amalgam is not completely deprived of its electric charge on entering the solution. It is commonly assumed that in experiments on such mercury dropping electrodes the total potential difference be- tween the falling mercury and the solution is destroyed. There are observations, however, by G. Meyer and S. W. J. Smith 4 which make such an interpretation difficult to accept. We shall see later that, from a knowledge of the ionic mobilities, Nernst and Planck have calculated the rates of diffusion of electrolytes and hence the difference of potential between the solutions of two electrolytes in contact with each other. On their theory, and indeed on almost any possible view of the phenomena, there can be no potential difference between dilute 1 Zeits. phys. Chem. xxv. 265 (1898); XXVIII. 257 (1899); XXXVI. 664 (1901). 3 Wied. Ann. LVI. 680 (1895). Phil. Trans. CXCIII. A (1900). 282 SOLUTION AND ELETCROLYSIS [CH. XI equivalent solutions of potassium chloride and iodide, which are ionized to the same extent, and contain ions possessing equal mobilities. The potential difference between either of these two solutions and a mercury dropping electrode should also vanish, and the electromotive force of the cell dropping mercury / KCI / KI / dropping, mercury should be zero. Its observed electromotive force is given by Meyer as 0·284 and by Smith as 0.262 and 0.256 volt. This result apparently indicates that part of the potential difference at a mercury-electrolyte interface depends on the nature of the anion; it is not eliminated by the action of a dropping electrode, and is therefore probably established with much greater rapidity than the part of the potential difference which is so eliminated. The surface tension of the area of contact between the Electro-capillary mercury and a solution is affected by its elec- phenomena. trical state. If the surface be increased, an electric transfer is produced, and, conversely, if an external electromotive force be applied across the junction, the area tends to change, owing to an alteration in the effective surface tension. These phenomena have been applied by Lippmann' to the construction of capillary electrometers, of which several forms are in frequent use. In one variety, a vertical glass tube is drawn to a very fine capillary. R' TT The tube is partially filled with mercury, and the lower portion immersed in an electrolyte, usu- ally dilute sulphuric acid, in which is placed another quan- Fig. 60. tity of mercury. The capillary forces tend to raise the mercury surface in the little tube, and are balanced by the pressure of the long column. When the mercury in the vertical tube and i Pogg. Ann. CXLIX. 561 (1873); Ann. de Chim. Phys. [5] v. 494 (1875). Onn Earth JUL CH. XI] 283 CONTACT ELECTRICITY AND POLARIZATION the mercury below the electrolyte are connected with two conductors at different potentials, such as the opposite poles of a galvanic cell, a change is produced in the level of the surface of contact in the capillary tube. A microscope with a micrometer eyepiece may be arranged to view the capillary, and, for small differences, the change in level is found to be proportional to the applied difference of potential. The move- ment is slow, and the final position of the meniscus is not reached for an appreciable time, probably owing to the high values of the electrical resistance of the column of electrolyte in the capillary, and of the frictional resistance to the move- ment of liquid through such a narrow tube? Burch? has shown that, while the applied electromotive force is a small fraction of a volt, the electrometer behaves as a condenser of good insulation, retaining its charge for several hours when disconnected from the cell. On the other hand, when the applied voltage is greater, electrolysis at the surface seems to occur, and the charges leak away. If, during the process of charging, the cell be disconnected before the final position of the meniscus is reached, the movement at once stops, and, in any case, the instrument is quite dead beat, and never oscillates about its position of equilibrium except as the result of mechanical disturbance. An explanation of these phenomena, based on Lippmann's The theory of observations, has been given by von Helmholtz, von Helmholtz. on the assumption that no electrolysis occurs. Any natural potential difference between two bodies implies an electrification over the boundary, in such a manner that an electric condenser of minute thickness is formed, with its parallel faces oppositely charged. This electric double layer will produce an electrostatic surface energy e, the value of which is {CA II”, where C is the capacity of the double layer per unit surface, A the area of contact, and II the potential difference across the layer. Now if II be kept constant, and 1 Phil. Trans. CLXXXIII. A, 104 (1892). ? Proc. R. S. LXX. 221 (1902). 3 Wied. Ann. XVI. 35 (1882), Faraday Lecture, Chem. Soc. Jour. (1882); see also Larmor, Phil. Mag. [5] xx. 422 (1885), and S. W. J. Smith, loc. cit. 284 [CH. XI SOLUTION AND ELECTROLYSIS the area be increased, we have for de dА the value 4CTI?. This increase in available energy is obtained from the chemical energy which maintains the natural potential difference. The electric layer on either side of the interface tends to expand under the mutual repulsion of the different parts of its charge, and thus tends to increase the area of contact; it therefore acts in a sense opposite to that of the ordinary surface tension So. The total surface tension S will be S = S. - *CTI? On the assumption that the only effect of the potential differ- ence is to produce such an electrostatic effect, So will be independent of II, and the total observed surface tension will reach a maximum when II is zero. Nevertheless, it is possible that the potential difference may affect the nature of the surface chemically or otherwise, and thus change S, the ordi- nary surface tension. The maximum value of S will, in this case, not necessarily imply that the potential difference of the double layer is zero." The visual methods, by which attempts have been made to determine the total natural potential difference between mercury and an electrolyte, really give, on the view advocated above, only the part of that total due to the ionic double layer. If we assume that the electrostatic effect is the only result of changing tbe ionic difference of potential by apply- ing an external electromotive force, and that the analogy with the condenser still holds good, the natural ionic potential difference will be equal and opposite to that which must be applied externally in order to reach the maximum value in fact found that the curves drawn between the external electromotive force and the reading of a capillary electrometer, are roughly parabolic; with dilute sulphuric acid, the maximum versely, when the surface of separation is stretched, a current flows to supply the charges for the increased area of the double layer of electricity, and Pellatfound that this current ceased i Comp. Rend. civ. 1099 (1887). CH. XI] 285 CONTACT ELECTRICITY AND POLARIZATION when an external electromotive force of 0.97 volt acted against the natural potential difference. By using liquid amalgams, the same electrolyte can be compared with mercury and what is effectively a different metal. Rothmundi and others have compared the difference of the values thus measured with the electromotive force of the cell amalgam / electrolyte / mercury, finding concordant results. Rothmund gives the following as the voltages required to give the maxima of surface-tension : Mercury in normal sulphuric acid solution Mercury hydrochloric , Lead amalgam sulphuric , Bismuth , sulphuric' Tin hydrochloric Copper sulphuric Cadmium sulphuric Zinc sulphuric 2 Thallium , » hydrochloric , +0.926 volt +0.560 +0.008 +0.478 +0.080 +0.445 -0.079 -0.587 , +0.089 , In the experiments with mercury, the acids were saturated with their mercurous salts, and when using amalgams a trace of the salt of the metal was added to the solution. Cells were · then arranged with these amalgams in combination with the corresponding mercury electrodes. amalgam cell Lead Bismuth Tin Copper Cadmium Zinc Thallium 9 » » » Observed E.M.F. 0.923 0.437 0.534 0.458 1.090 1.472 0.652 Calculated E.M.F. 0.918 0:448 0:480 0:481 1.005 1.513 0:471 12 The results of these experiments, unlike those on cells with dropping electrodes above described, on the whole favour the view that the electromotive force of a cell is the sum of the 1 Zeits. phys. Chem. xv. 1 (1894). 286 [CH. XI SOLUTION AND ELECTROLYSIS single potential differences at its electrodes as determined by the capillary electrometer, and that any permanent part of the total potential differences due to the orientation of bipolar molecules is not involved. On the other hand, there is evidence to show that in general the result of an applied electromotive force on the surface tension is not merely the electrostatic effect con- templated by the Helmholtz theory, but depends also on the chemical nature of the electrolyte. The capillary electrometer may be imagined to consist of a very small condenser, composed of the mercury-electrolyte double layer in the capillary, arranged in series with a large condenser formed of the similar surface in the outer vessel. Such a small condenser will be charged by an electric transfer which does not appreciably affect the large one, and the varia- tion of the potential difference at the capillary electrode is the same as the variation of the external electromotive force. The Lippmann-Helmholtz theory rests on two hypotheses. It assumes that the electrometer circuit may in truth be treated as a system of condensers, and it assumes that, as explained above, the only effect of the potential difference, whether natural or applied, is the electrostatic one. To increase the surface tension, and thus to reduce the natural electrification, of the interface between mercury and an electrolyte, an external electromotive force has to be applied from the solution to the metal. The natural ionic double layer must therefore consist of negative anions, chlorine for example, in the electrolyte, and a corresponding positive charge, perhaps represented by positive electrons, on the surface of the mercury. On applying a gradually increasing reverse electromotive force, we may imagine that the chlorine ions diminish in number and finally disappear; the surface tension then reaches a maximum. Beyond this point, positive metallic ions would be driven up to the interface, and a reverse double layer would arise. If this polarization exceeded a certain limit, a current would flow, and an amalgam might be formed. On the original Helmholtz theory, which took no account of differences between ions, and assumed that the reverse layer was similar to the first one, the CH. XI] 287 CONTACT ELECTRICITY AND POLARIZATION : experimental voltage surface-tension curves should be a single parabola. Observation shows, however, that there is usually a slight want of symmetry between the ascending and descending branches of the curves, possibly indicating the effect of the chemical nature of the ions. The result of this effect on the surface energy of the interface has been considered by van Laar? When an electric transfer oq occurs, the change in surface energy will be given by the expression Sci-O (SA). as € = əqdq=ão oq, o denoting the electric charge per unit area. The surface tension will be altered by a term de/aA. Now as. de Jooq ƏS A = SA="ão The complete expression for the surface tension thus becomes =8–6 OS q=S-06 - 2002 ..................(60). Whichever side of the electric double layer is positive, its effect is opposite to that of the natural surface energy, and the term oas/ao is always negative, but there is no reason to suppose that its numerical value will be the same when it represents the effect of anions and cations on the electrolyte side of the double layer. The total electrocapillary curve therefore consists of parts of two parabolas which meet at the point for which o=0 and y=S. Only the ascending branch has a maximum which is in general near, but not at, the point of intersection. Since the concentration of the ionic layer is always small, the variation of available surface energy can be formulated, and van Laar, by determining the constants of his detailed equa- tions, finds that they represent the experimental results of S. W. J. Smith with great accuracy. On this confirmation of CITY 1 Kon. Akad. Wetens. Amsterdam, March, 1902, p. 560. 288 [CH. XI SOLUTION AND ELECTROLYSIS his theory, van Laar concludes that the capillary electrometer does not give a trustworthy means of measuring single potential differences. In the work on electrocapillary phenomena to which we have referred, S. W. J. Smith finds indications that, on changing the potential difference by external means, a leakage current will flow owing to the tendency of the electrode to revert to its original condition, so that the condenser analogy cannot be complete. He finds that a very high resistance in the potentiometer circuit changes the indications of the electro- meter. As we said on p. 281, on almost any view of the pheno- mena there can be no difference of potential between dilute they are equally ionized and contain ions of equal mobilities. The electromotive force of the cell mercury / potassium chloride / potassium iodide / mercury ought therefore to agree with the sum of the two potential differences, mercury / potassium chloride + potassium iodide / mercury, Surface tension - - - - - com Applzed Electromotive Force kell Fig. 61. as determined by the capillary electrometer. If the latter values are estimated from the maxima of surface-tension, their 1 Phil. Trans. cxcii. A, 47 (1900). CH. XI] 289 CONTACT ELECTRICITY AND POLARIZATION sum for semi-normal solutions is 0.162 volt, while the cell gives 0:394 volt. Similar discrepancies occur in other cases. For these two solutions, Smith gives curves like those of Fig. 61, in which abscissae represent applied electromotive forces, and ordinates arbitrary scale readings of the electro- meter. While, in their ascending portions, the two curves have different slopes, they become parallel when they descend. It is probable that the effects of the ionic polarization are then the same for both. Let E be the external electromotive force required to give the same surface tension to the capillary surface of the potassium chloride solution as E' gives to the iodide solution. Then on the parallel parts of the curves, E- E' is very nearly constant. Let II and II' be the natural potential differences between mercury and the chloride and iodide solutions respectively. On the first hypothesis of the ordinary electrometer theory (the condenser analogy), the potential differences between the solution and the capillary meniscus for two points of equal surface tension, one on each curve, are E-II and E' - II' respectively. On the second assumption, that the sole change is an electrostatic one, and the potential differences are the same in the two cases because the surface tensions are the same, we have E- II = E' – II', II – II' = E - E' = a, where a is an observable quantity, measured by the horizontal distance between the parallel portions of the curves. If there is no potential difference between the two solutions when in contact, the electromotive force of the cell mercury / potassium chloride / potassium iodide / mercury is also II – II', and should thus be equal to a. The first four results in the following table give a comparison between the electromotive forces of such cells and the values calculated (1) by the method just described, (2) by estimating the maxima of the curves. W. S. 290 [CH. XI SOLUTION AND ELECTROLYSIS Calculated E. M.F. Solutions Observed E.M.F. of mercury cell normal KCl and KI TO » » » 399 •350 -337 ·169 •162 •122 •162 20 " 3940 •3503 :3381 •1670 -9588 9578 K'C and KCNS •938 KCl and Na2S 19 •581 •581 •944 Here again we have results which suggest that the electro- static theory is insufficient. The maximum of surface-tension seems to depend on the nature of the anion, and, if that maximum be taken as a means of determining the natural potential difference, the electromotive force of a cell with two electrolytes having different ions apparently cannot be calcu- lated from the two single potential differences at its electrodes. The last two lines of the table indicate the same relations in solutions where both anion and cation are different, the greater discrepancies being explained by the uncertainty regarding the contact potentials of the two solutions. Electrocapillary curves for equivalent solutions of potassium, sodium and hydrogen chlorides, which contain the same anion, coincide within the limits of experimental error throughout both the ascending and descending portions. Hence it is concluded that the effect of the anion is considerable as long as the reverse applied electromotive force is less than the natural potential difference; but the nature of the cation seems to have no appreciable influence on the potential difference throughout the whole range covered by the experiments. Assuming that the Nernst theory gives the true potential difference between two solutions, Smith, however, remarks that, although the slope of the lower portion of the 'descending curve varies little with the concentration of the solution, the absolute value of the surface tension for a given potential difference does show such variation. Thus the tension does not depend on the electrostatic effect alone even when the influence of the anion has presumably disappeared; there CH. XI] 291 CONTACT ELECTRICITY AND POLARIZATION 291 ( is also a cation effect, which becomes evident as the solution grows increasingly positive with regard to the electrode, and the cation therefore tends to enter the mercury and form an amalgam. On the other hand, the anion effect increases as the electrode becomes more positive, and thus tends to dissolve. Warburg's theory of these phenomena can be extended to the capillary electrometer on the same lines as to the case of dropping electrodes?. When an external electromotive force is applied, Warburg traces the increase of surface-tension to the action of the polarizing current. This current removes from the neighbourhood of the meniscus the trace of mercury salt which always dissolves from the metal into solutions containing dissolved oxygen. The salt is slowly replaced by diffusion, and the actual change in concentration is the resultant of the two opposite effects. Owing to the minute quantity of salt in the capillary tube and the slowness of the compensating diffusion, the exhaustion may be very complete. The concentration cell which is formed may thus have a considerable electromotive force. The surface-tension will reach a maximum when the whole of the mercury ions are removed from the solution near the meniscus. In order to explain the descending branches of the surface-tension curves on Warburg's theory, it has been suggested that, as the electromotive force rises, an amalgam is formed with a surface-tension naturally lower than that of mercury. On Nernst's conception of electrolytic solution pressure, electrocapillary phenomena will be interpreted as follows. The low pressure of mercury causes positive ions to enter it even from a dilute solution. The mercury thus acquires a positive charge. An external electromotive force applied to an electro- meter from solution to metal causes a temporary current, which carries more mercury ions across the interface. In the capillary tube this process at once dilutes the solution, and therefore, in accordance with the logarithmic formulae of Chapter X., makes the mercury more anodic to the electrolyte and eventually stops the current. If the concentration of the mercury ions in the solution falls to the value corresponding to the solution pressure 1 Wied. Ann. XXXVIII. 321 (1889); XLI. 1 (1890). 192 292 [CH. XI SOLUTION AND ELECTROLYSIS of the metal, the potential difference disappears; if it falls below that value, the potential difference is reversed, the mercury becomes negative to the solution, and draws cations to the electrolyte side of the double layer. On the theories of both Warburg and Nernst, when the external electromotive force is removed, the processes of dif- fusion should gradually reduce the differences of concentration and the displacement of the meniscus of the electrometer. Burch has found, however, that a new and good electrometer will show the same deflection of the meniscus for many hours when charged to a small fraction of a volt and then left on open circuit with its electrodes insulated from each other. Such observations indicate that for small electromotive forces, the instrument acts as a condenser of good insulation. Never- theless, it seems certain that the changes of concentration contemplated by Warburg and Nernst must occur in some cases. It is possible that it is to the influence of such effects that are due some of the discrepancies which appear in the results of experiments on the potential differences at the surfaces of contact of mercury with electrolytes. Electric Another set of electrocapillary phenomena, like those we have been considering, probably depend on the endosmose. natural potential differences at the surface of separation of two unlike substances--in this case an electrolyte and an insulator. If an electric current be passed through a vessel divided into two compartments by means of a porous partition and filled with some solution, we shall find that, in general, besides the changes in concentration at the electrodes which were described on p. 207 under the head of migration, there is a bodily transfer of the liquid, usually in the direction of the current, through the porous plate. To this phenomenon the name of electric endosmose is given. It has been experi- mentally studied by Wiedemann? and Quincke?. If the pressure be kept constant on both sides of the partition, the volume of liquid which flows through, as measured 1 Elektricität, II. 166. 2 Pogg. Ann. CXIII. 513 (1861). CH. XI] 293 CONTACT ELECTRICITY AND POLARIZATION by the overflow, is proportional to the total electric transfer, and is independent of the area and thickness of the plate; it varies much with the nature of the solution, being greater with liquids of high specific resistance, and, in solutions of different concentrations of any one substance, is approximately propor- tional to the specific resistance. If the liquid is not allowed to overflow, the pressure on one side of the porous wall will increase. The final pressure is directly proportional to the electromotive force between the faces of the partition, and therefore to the current through it; for a given current it varies inversely as the area of face of the porous wall and directly as its thickness. In this case, the flux of liquid due to the electric forces must be equal and in the opposite direction to that caused by the difference of hydro- static pressure. Considering the porous wall to consist of a collection of capillary tubes, we can apply Poiseuille's laws to the reverse flux under the hydrostatic forces, and this expla- nation has been supported by Quincke, who proved that the pressure produced by electric endosmose through a capillary glass tube was inversely proportional to the fourth power of the diameter of the tube. The pressures were considerable with distilled water, but ceased to be perceptible with liquids of high conductivity such as solutions of salts and acids. A detailed theory of the subject has been given by von Helmholtzł, on Quincke's hypothesis of a constant potential difference between the liquid and the walls of the capillary tubes. The electric charge which resides on the outermost layer of liquid and forms the inner face of the electric double layer, will be acted on by the external electromotive force and the skin of liquid will therefore be dragged through the tube. If a difference of pressure is allowed to develop, one current of liquid is drawn forwards along the walls, and an opposite one flows down the centre of each tube under the action of the hydrostatic forces. The final pressure is reached when these two currents of liquid convey equal volumes per second in opposite directions. From these ideas von Helmholtz deduced the observed facts of electric endosmose, and calculated that 1 Wied. Ann. VII. 337 (1879). 294 SOLUTION AND ELECTROLYSIS [CH. XI the contact potential differences involved were of the order of one volt. A modification of the theory has been given by Lambi, allowing for a slight slip between the liquid and the walls of the tube. In a similar manner is explained the motion through liquids of fine particles of clay or other material under the influence of an external electromotive force, a phenomenon which has been studied by Quincke and others?. It has been suggested by W. N. Shaws that electric endosmose constitutes an essential part of the mechanism of electrolysis, the motion of the liquid being due to the drift of complex ions made up of an ion of the salt attached to a large number of solvent molecules. The inverse proportionality between the concentration of a solution and the endosmotic effect, shows that, in very dilute solutions, such complex ions must contain many hundred or thousand water molecules; and it seems more likely that, in accordance with the usual view, electric endosmose is an independent phenomenon, not directly connected with the electrolytic process. t is possible that the results of experiments with capillary electrometers may be influenced by electric endosmose as soon as any current flows and a potential gradient established along the capillary tube. From Quincke's observations above de- scribed, however, it seems probable that the measurements would not appreciably be affected. Single potential differences continued. It is evident from what has been said in the sections preceding the last, that there is some doubt whether the experiments on dropping elec- trodes and on capillary electrometers really enable the natural potential difference, which is involved in the electromotive force of a galvanic cell containing a mercury- electrolyte surface, to be calculated even approximately. Never- theless, since many useful determinations of other single potential i B. d. Report, 1887, 495. 2 Wiedemann's Elektricität, II. 181. 3 B. A. Report, 1890, 202. CH. XI] 295 CONTACT ELECTRICITY AND POLARIZATION VA differences, which, at all events, are relatively exact, rest on such measurements, in the present condition of the subject we must provisionally accept the value of about +0.92 volt as the potential difference between mercury and dilute sulphuric acid, the mercury being positive to the acid. The step of potential as thus measured is in the opposite direction to that which occurs at the surface of a zinc plate. Results are obtained for other metal-electrolyte surfaces by subtracting this number, or another similarly estimated for mercury in contact with some other electrolyte, from the total electromotive force of galvanic cells arranged in the manner 1c metal / electrolyte / mercury. Such indirect determinations will contain as a constant error any deviation of the primary measurement from the true value, but, as relative numbers, serving to compare the metals among themselves, they will retain their importance. In making such experiments, it is usual to employ what is known as a normal electrode, consisting of a quantity of pure mercury covered by a layer of mercurous chloride and a solution of potassium chloride of normal concentration, that is, a solution containing one gram-equivalent per litre. An indiarubber tube ending in a glass tube leads from the solution and is filled with it (Fig. 62). Contact can thus be made between the potassium th Fig. 62. chloride and any other liquid. This electrode as measured by Lippmann's method gives a potential difference of 0.56 volt, the mercury tending to come out of solution and be deposited 296 [CH. XI SOLUTION AND ELECTROLYSIS as metal. The chlorides can of course be replaced by other substances when their potential with respect to mercury is known. Thus a soluble sulphate, with mercurous sulphate as depolarizer, has been used. Assuming that we may neglect the small effects at the junction of the metals, and at the surfaces of contact of unlike solutions, if such surfaces are present, the measured electromotive force of the combination metal / electro- lyte / normal electrode enables the potential difference at the surface metal / electrolyte to be calculated by subtraction. In this manner, Neumann measured the single potential differences for many metals in contact with either normal or saturated solutions of their salts. The following are some of the most important results?. Acetate -0.522 Metal Zinc Cadmium Thallium Iron Lead Hydrogen Copper Silver Mercury Sulphate -0.524 -0.162 -0.114 -0.093 Nitrate -0.473 -0.122 -0.112 Chloride :-0503 -0.174 -0.151 -0.087 +0.095 +0.249 +0:115 +0.238 +0.515 +0:974 +0.980 +0.615 +1.055 +1.028 +0·079 +0.150 +0.580 +0.991 - In this table positive signs have been assigned to those metals which show a positive potential relatively to the liquids surrounding them. Assuming the accuracy of these results as absolute numbers, it follows that such metals tend to come out of solution, and the natural potential difference at their surfaces helps to drive a current in the direction to effect the deposition. Spontaneous separation of these metals, or solution of negative metals, however, will only occur if means are available for the simultaneous addition of opposite ions, or the removal of an equivalent quantity of similar ions. The numbers show that the electromotive forces of the cells used depend on the nature of the acid ion present, but Neumann also prepared centinormal solutions of many different thallium salts, and found sensibly equal values. In these solutions the ionization may be taken 1 Zeits. phys. Chem. Xiv. 229 (1894). CH. XI] 297 CONTACT ELECTRICITY AND POLARIZATION as complete, but it remains to be seen whether or not under such conditions the equality would extend to salts of all metals. There is some evidence to suggest that the variations of electro- motive force with the acid ion are to be traced to the presence of mercury, cells in which two other metals are used being usually free from such discrepancies? The table on the last page gives a fair idea of the single potential differences calculated from the fundamental experi- ments on mercury, and, for slightly oxidizable metals such as silver, it will be seen that the method leads to numbers which have an opposite sign and an even larger numerical value than those obtained for very oxidizable substances such as zinc. The intimate connexion which exists between the electromotive force of a cell and the calorimetric heats of the resultant chemical actions, when allowance is made for the usually small reversible heat effects, has already been considered on p. 236. It seems reasonable to apply the same relations to each individual part of the circuit, and we should expect that metals which are only acted on with difficulty and have small beats of oxidation, would show a very much smaller potential difference than very oxidizable metals with large heats, though probably a difference of the same sign; in fact the potential diagrams of the cell represented by the second parts of Figs. 58 and 59 seem à priori more likely to correspond to reality than those shown in the first parts. Moreover, in correlating these phenomena with those of the Volta contact effect between metals in air, it is probable that there will at all events be a general agree- ment between them. It is unlikely that metals would show a difference of sign in their potential differences with air, if that difference is due to actual oxidation or to an affinity which tends to oxidation. On the other hand, Nernst's theory of electro- lytic solution pressure offers a possible explanation of the difference in sign as usually accepted. Whatever be the final outcome of the problem, we may take Neumann's numbers and similar results as true relative values, though a constant error 11 i Paschen, Wied. Ann. XLIII. 590 (1891); Taylor, Journ. Phys. Chem. I. 1 and 81 (1896). 298 [CH. XI SOLUTION AND ELECTROLYSIS Electrolytic solution pressure. electrolytic solution pressure to be calculated. In the last chapter it was shown that, on the analogy of the junctions between two liquids," the potential difference between a metal and a solution might be expressed in the form log -m, R being the gas constant for the gram-molecule of the metal, Pm the solution pressure of the metal, P the osinotic pressure of its ions in the electrolyte, q the charge on the monovalent: gram-equivalent, and y the valency of the ions. The potential difference can be observed, and the osmotic pressure is approximately known from the concentration of the solution. Thus the electrolytic solution pressure can be calculated; the following are some of Neumann's values in atmospheres recalculated by Le Blanc. Zinc 9.9 x 1018 Hydrogen 9.9 x 10-4 Iron 1.2 x 104 Mercury 1.1 x 10-16 Lead 1.1x10–3 Silver 2:3 x 10-17 pressure of the solution at which it would show no potential difference with the metal. Nernst extends this idea, and identifies Pm with a characteristic property of the metal itself, which, on the analogy of the vapour pressure of a liquid, is taken to measure the tendency of the metal to diffuse in the form of electrolytic ions in the liquid surrounding it. The legitimacy of this extension is still a matter of discussion, and, as indicated on p. 257, by writing the formula as RT log Pm/qy – RT log P/qy, or M – RT log P/gy, . we may treat the part of the expression referring to the metal simply as a function of its properties of unknown form. Accepting provisionally, however, the solution pressure hypo- thesis, the absolute values given above are still open to ob- jection, not only as based on the mercury-electrolyte difference of potential, but in another way. The formula from which they are calculated is transferred from that deduced on the assumption of the ideal gaseous laws for the junction between two liquids, and the extension of these laws to the very high pressures here dealt with is clearly unjustified. CH. XI] 299 CONTACT ELECTRICITY AND POLARIZATION In the derivation of the theory for liquid junctions on p. 246, it is shown that the electromotive force is measured by the integral ſud P. Lehfeldt has calculated the value of this integral on the assumption that the deviation from the gaseous .laws in solutions is represented by an expression of the form of van der Waals' equation for gases. Putting iRT P= v-2 JP we have, since in concentrated solutions i is nearly unity, Egy= 1 ModP = RT log 1 p +6 (P.m – P). Applying this to the case of zinc in normal zinc chloride solution, we may put 22 atmospheres for P, and 0.5 volt for E; b is assumed to be the volume of a gram-molecule of the salt in the solid state, about 46 cubic centimetres. The value of the solution pressure Pm can then be calculated, and comes out about 2 x 104 atmospheres, instead of about 1019, as deduced from the simple logarithmic formula. It is clear that such considerations as these enable the deviations of concentrated solutions from the ideal gaseous laws to be estimated, and Lehfeldt has calculated the osmotic pressures of such solutions from measurements of the electromotive forces of concentration cells. We shall reconsider the hypothesis of solution pressure under the head of electrolytic diffusion. Electro- chemical series. It was one of the objects of the early experimenters to arrange the metals in order in an electro- chemical series. The two tables of potential differences, set forth on pp. 268, 296, are quantitative solutions of this problem under given conditions. Whereas it was formerly thought that the metals occupied the same relative positions in all circumstances, it is now obvious that the potential differences which they yield will depend on the nature of the surrounding medium, and, if that medium is a solution, on the concentration of the dissolved substance, though if a table of electrolytic solution pressures could be calculated, it would enable the effects of concentration to be eliminated. 300 [CE. XI SOLUTION AND ELECTROLYSIS The general accuracy of the theories explained above indicates that a metal immersed in the solution of one of its salts should be the less electropositive as the concentration of its ions in the solution increases. If the metal dissolves as a compound salt, as do gold and silver in cyanide solutions, it may be that the metal can exist in the solution in the form of simple ions in very small quantity only? In accordance with this result, the electromotive force of such metals as gold and silver in solutions of cyanides is very high, and places them in a position in the electrochemical series different from that which they occupy when the metals are studied in contact with solutions of their own salts or the corresponding acids. As stated in the last chapter, Hittorf found that in the cell Cu / KCN / K2SO4/ ZnSO4/ Zn, copper is dissolved when a current flows. The contact potentials of different metals with cyanide solu- tions have also been studied by von Oettingen? and by Christys The latter observer traces the influence of the concentration of a solution of potassium cyanide on its potential difference against gold, and shows that the rate at which gold dissolves when shaken with the liquid is a function of this potential difference and also of the amount of dissolved oxygen. As a " combination of these two effects, the rate of solution of the gold reaches a maximum at a concentration of ten to twenty per cent. of potassium cyanide, and then again decreases as that proportion is exceeded. Polarization. Another aspect of the subject now under consideration is : given by an examination of the phenomena of a polarization. As we said in Chapter VIII., it requires a certain minimum electromotive force to drive a permanent current through an electrolyte between electrodes which are not dissolved. If a single Daniell's cell be connected through a galvanometer with two platinum plates immersed i See footnote p. 255. ? Journ. Chem. and Metallurgical Soc. South Africa, 1899. 3 Amer. Inst. Mining Engineers, Trans. xxx. (1899), reprinted as Bulletin oj Depart. Mining, etc., Univ. of California. CH. XI] CONTACT ELECTRICITY AND POLARIZATION 301 in dilute sulphuric acid, the galvanometer is at first deflected. The current, however, rapidly falls off, and soon sinks nearly to zero. If the platinum plates are now disconnected from the cell, and joined with each other through the galvanometer, they will send a current through it in the reverse direction. The plates are said to be polarized. The electromotive force of polarization, in the case we have chosen, soon diminishes, so that in order to measure its maximum value, the connexions must be rapidly reversed. Raoultz found that a speed of reversal of one hundred alternations a second was enough to secure this result. The best method of experimenting is to use a tuning-fork commutator which vibrates very rapidly. If the electromotive force is gradually raised from a very small value, the reverse force of polarization is also found to rise, keeping equal to that applied, until a nearly constant limit is reached. A further rise in the applied electromotive force causes little or no more increase in the polarization, and the current through the solution can then be calculated from Ohm's law by taking as the effective electromotive force the value found by subtracting that of polarization from the force externally applied. Decomposition voltage. The phenomena of polarization have been very fully studied by Le Blanc?. There is a certain decomposition " value for the applied electromotive force, beyond which a permanent current flows. Le Blanc found that the decomposition voltage can be easily and exactly determined for salts from which a metal is precipitated, the current starting from that point to rise proportionally to the electromotive force; but for other salts, as well as for acids and alkalies, the measurements are more uncertain. The following decomposition values were found with platinum electrodes for salts from which the metal is pre- cipitated; the salts were mostly in normal solutions. 1 Ann. Chim. Phys. IV. 2. 326 (1864). 2 Zeits. phys. Chem. VIII. 299 (1891); or Le Blanc's Elektrochemie, Eng. Trans. p. 247. 302 [CH. XI SOLUTION AND ELECTROLYSIS SALTS. 2:35 volts 1.80 Zinc sulphate Zinc bromide Nickel sulphate Nickel chloride Lead nitrate Silver nitrate 2.09 Cadmium nitrate Cadmium sulphate Cadmium chloride Cobalt sulphate Cobalt chloride 1.98 volts 203, 1.88 » 1:92 , 1.85 1.78 , 1:52 , 0-70 Whereas the values given in the above table for metallic salts vary from metal to metal, the values : for acids and alkalies show a maximum decomposition point, which is approached by most of these compounds and exceeded by none. ACIDS. 1.67 volts 1•69 » 1:57 volts 1:51 » 1.70 1:31 » 1:72 Sulphuric Nitric Phosphoric Monochloracetic Dichloracetic Malonic Perchloric Dextrotartaric Pyrotartaric Trichloracetic Hydrochloric Hydrazoic Oxalic Hydrobromic Hydriodic 1.29 0.95 1.66 , 1.69 0.94 , 0:52 , 1.65 1.62 aric BASES. Sodium hydrate 1.69 volts Potassium hydrate 1.67 , Ammonium hydrate 1.74 , Methylamine (normal) 1.75 » Diethylamine (normal) 1.68 volts Tetramethyl ammonium hydrate (} normal) 1.74 · Acids and alkalies which evolve hydrogen and oxygen on electrolysis, show the maximum decomposition voltage nearly independently of the concentration of the solution. For acids which are more easily decomposed, the numbers increase on dilu- tion with a simultaneous change in the nature of the products. The use of other non-oxidizable electrodes such as gold or carbon instead of platinum, leads to different numerical results, though the relations between them remain unaltered. The differences may be explained by remembering that, although the resultant chemical process is in each case the liberation of CH. XI] 303 CONTACT ELECTRICITY AND POLARIZATION hydrogen and oxygen, the production of bubbles of gas at the surface of a metal, which does not occlude the gas, is an essentially irreversible operation depending on conditions which may well vary from metal to metal?. each electrode. The electromotive force of polarization evidently consists of two parts, one depending on the electrical Polarization at work done at the anode, and the other on that at the cathode. In order to examine these separately, an arrangement due, to Fuchs was used by Le Blanc? The tuning-fork commutator is adapted to a double U-tube apparatus shown in Fig. 63. The primary ilih dih Fig. 63. or polarizing current is passed from Q between the electrodes a and b. If the electrode b is to be examined, the bent glass tube of the normal electrode described on p. 295 is inserted at C, and the effect of the cell so formed is balanced by an adjustable electromotive force at M, an electrometer being used as indicator. The potential difference between the plate b and the liquid can then be found by subtracting that of the normal electrode and that at the contact of the two solutions at c. As the primary current from Q is increased from zero, it is found that the electromotive force of polarization is at first nearly equal to that of the primary current, but it gradually comes to 1 In this connexion reference may be made to a paper by Nernst and Dolezalek [Zeits. Elektrochem. May 10, 1900]; and another, containing a criticism on it, by C. J. Reed [Journ. Phys. Chem. v. 1 (1901)], on the “Gas Polarization of Lead Accumulators.” 2 Zeits. phys. Chem. XII. 333 (1893) ; XIII. 163 (1894); also Electrochemistry, p. 244. 304 [CH. XI SOLUTION AND ELECTROLYSIS a nearly constant value, though Le Blanc states that no exact final limit is ever reached. When the solutions which deposit metals are examined in this way, Le Blanc finds that at the decomposition point the polarization potential difference at the cathode is equal to the potential difference which a plate of the metal itself gives if placed in contact with the solution, both, of course, depending on the value taken for the fundamental mercury-electrolyte difference of potential. The polarization at a junction is thus exactly correlated with the single potential difference, which can be measured by experiments on capillary electrometers or dropping electrodes. If, as previously explained, we refer the total potential difference to a combination of molecular and ionic effects, Le Blanc's results indicate that electrolytic polari- zation is an ionic phenomenon—a natural result to anticipate. As the external electromotive force is gradually increased from zero, the measured potential difference at the cathode, like the total electromotive force of polarization, rises also, approaching a limit, though the electromotive force necessary to reach this limit is often less than that required to give the maximum polarization of the whole apparatus which includes the anode also. The limit seems to be reached when the deposit of metal on the electrode is enough to cover its surface with a continuous layer. The converse phenomenon has been studied by Oberbeck?, who deposited small quantities of the metal of a salt solution on a platinum plate, and then measured the potential difference between the plate and a solution of the same salt placed in contact with it. As the amount of deposit was increased, this potential difference rose, and finally reached the value found for a solid plate of the metal. As a final result of all these investigations, it is concluded that the deposition and solution of metals from solutions of their salts are reversible processes. The single potential differences, exhibited in Neumann's table on p. 296, may therefore also be taken as measuring the polarization when the metal is electrolytically deposited from its solution in the salts there indicated. i Wied. Ann. xxxi. 336 (1887). CH. XI] 305 CONTACT ELECTRICITY AND POLARIZATION Evolution • In considering the total effects of polarization the anode also has to be taken into account. When the anode is of platinum or a similar metal, gas is usually evolved there, and it thus becomes of great importance to determine how far the conditions of reversibility hold good in the evolution of gas at an electrode. As we have seen, a minimum electromotive force is required to continually electrolyse a dilute solution of sulphuric acid in water; when gold or bright platinum electrodes are used, about 1.7 volts are necessary. The reverse electromotive force of polarization is, however, only 1.07 volts, and as is well known, if the hydrogen and oxygen are collected in tubes and kept in contact with platinum electrodes, an arrangement called Grove's gas battery is obtained, which furnishes a secondary electromotive force of 1:07 volts, and will yield a current as long as any gas remains. Thus the development of gas at a bright platinum surface is an irreversible process. When, however, the electrodes are coated with platinum black by previously passing a current backwards and forwards between them through a solution of point was 1:07 volts; so that, with platinized electrodes, the process is reversible. The difference is explicable when we remember that platinum occludes a large amount of gas. The platinized electrodes absorb the gases when slowly developed, and when the plates become saturated, if parts of them are outside the liquid, they can gradually give up the gases by diffusion without the formation of bubbles. Thus, if an external electromotive force of 1.07 volts be applied, the system is in equilibrium, while, if the applied electromotive force exceeds or falls short of that value by an infinitesimal amount, an in- definitely small current will flow one way or the other, and the gases are slowly- set free or dissolved. The arrangement is therefore reversible, and the thermodynamic treatment of the effects of pressure, etc., on the electromotive force of the oxy-hydrogen gas battery, which was given on p. 240, applies equally to their effects on the reverse electromotive force of polarization in the decomposition of water between platinized W. S. 20 306 [CH. XI SOLUTION AND ELECTROLYSIS electrodes. We may therefore in this case also write the equation then deduced, RT 19 P1 E = qu 108 po' where R is the usual gas constant for one gram-molecule, T the absolute temperature, q the charge of electricity passing when one univalent gram-ion is liberated, y the valency of the ions, and pand P, the pressures in the two cases considered. Now if p, be gradually reduced, the value of this expression can be made as great as we please, and thus, at a certain very low pressure, the reverse electromotive force must vanish, and below this pressure actually be reversed, so that water would decompose spontaneously. This critical pressure will be so low that it is quite out of reach of experimental confirmation; in fact the vapour pressure of the water itself would prevent its ever being reached. The information that the decomposition of water could theoretically be effected at a low pressure by a very small electromotive force is exceedingly striking, for the heat developed by the direct chemical combination of oxygen and hydrogen at constant pressure is nearly independent of the absolute value of that pressure. It furnishes a good illustration of the want of proportionality between the heat of chemical union and the electromotive force when other transformations of energy are involved, and shows the need of the second term in von Helmholtz's equation, p. 236, TOODE E=X+0 de Let us now return to the case when gold or bright platinum electrodes are used instead of platinized ones. As we have said, the decomposition point is then 17 volts, while the reverse electromotive force is still only 1:07 volts, showing that the process is irreversible. Bright electrodes have very little power of absorbing gas; consequently if an electromotive force be- tween 1:07 and 1.7 volts be applied, the gases cannot be removed from the electrodes nearly fast enough by diffusion, and, when the solution in the neighbourhood of the electrodes becomes saturated with dissolved gas, the evolution will cease. CH. XI] 307 CONTACT ELECTRICITY AND POLARIZATION Slow diffusion from the liquid into the air and back through the liquid will however go on, and this process allows more gas to be evolved, while a slight leakage current continually flows, as indicated by the galvanometer.' In order to produce a permanent large current and a constant evolution of gas in appreciable quantities, it is necessary to raise the electro- motive force till it is able to cause the formation of bubbles at the surface of the electrodes, a process which involves an amount of work depending on the surface-tension, the state of the electrodes and other uncertain and irreversible conditions. That these conditions vary with different kinds of electrode is shown by the unequal potential differences needed to liberate hydrogen at cathodes of platinum, gold, lead, copper, etc. In such cases, when bubbles of gas are formed, part of the available energy of the chemical action is not expended on electrical separation; thus the reverse electromotive force, which depends on the free energy of this separation, is less, and the process is not reversible. 02 Electrolytic separations. It will be noticed that the 1.7 volts needed to evolve oxygen and hydrogen at bright platinum electrodes is the maximum value of the decomposition point of solutions of acids and alkalies (p. 302). This fact is explicable if we consider in detail the process of electro- lysis in such cases. All the ions in the solution, of whatever nature, are acted on by the electric forces, and must therefore all carry the current by moving through the solution; as, indeed, was shown by the experiments of Hittorf. At the electrode, however, if more than one kind of ion is present, that kind will first be deposited which has the lowest deposition value. Now we shall find later that in water, even when pure, a certain number of hydrogen and hydroxyl ions are always present, and unless they are removed in some way, these ions will cause hydrogen and oxygen to be evolved before any substances in the solution which possess higher deposition voltages can appear at the electrodes. Now for acids and alkalies, the electrolytic processes allow this preferential action to occur. The hydrogen ions derived 20_2 308 [CH. XI SOLUTION AND ELECTROLYSIS from the electrolyte in one case, and its hydroxyl ions in the other, travel to the electrode at which they can respectively be converted into neutral hydrogen and oxygen. Thus wbile in the interior of the solution the current is almost entirely carried by the ions of the acid or the base, the transmission from the solution to the electrode is effected primarily by the ions of the water. From solutions of some salts also, hydrogen and oxygen are evolved; but here the conditions are different. Alkali is developed at the cathode, and its hydroxyl ions, combining with some of the hydrogen ions of the water, enormously reduce the number available. Thus the potential difference required to liberate the hydrogen at the electrode is increased, in accordance with a relation to be afterwards deduced and already used on p. 253 to explain the high electromotive forces of certain concentration cells. Returning to the consideration of acids and alkalies, we see that the decomposition voltage of such of them as contain ions of higher values than hydrogen and hydroxyl cannot rise above the potential difference which liberates hydrogen and oxygen. Those acids on the other hand, which, like hydrochloric, contain an anion of low deposition point, show a smaller decomposi- tion value when present in fairly concentrated solutions. As the concentration falls, it becomes difficult for the diffusion of the acid in solution to replace fast enough the chlorine ions which are removed from the layer of liquid in contact with the electrode. Increasing numbers of hydroxyl ions are therefore used to convey the current into the electrode, and this causes a rise in the polarization, which in dilute solutions reaches the maximum 1:7 volts. From strong solutions of hydrochloric acid the gases evolved are hydrogen and chlorine, but as dilution proceeds, the chlorine is gradually replaced by oxygen from the hydroxyl. This rise in the polarization is well seen in the following table, due to Le Blanc. 2 normal hydrochloric acid, decomposition point 1.26 volts 9 1:34 2 , 16 32 » » » » » » » » 1:41 , 1.62 , 1.69 , CH. XI) 309 CONTACT ELECTRICITY AND POLARIZATION The products of the continuous electrolysis of any mixed solution; containing two metals, depend on conditions more complicated than those which control the initial decomposition voltage of the solution or the polarization at one electrode. It is evident that the conditions determining the appearance of a second kind of ion of higher deposition point depend on such things as the current density, the transport numbers for the different ions present, the rate of diffusion of the dissolved substances, the existence and intensity of convection currents in the liquid and any mechanical mixing or stirring. The initial decomposition voltage of a solution, however, does not involve these dynamical problems, and solely depends on the potential differences required for the liberation of the ions first appearing at the two electrodes. If we accept the logarithmic expression for the electrolytic solution pressure, it is easy to see that two ions can only be simultaneously liberated by an electromotive force E when, with the usual notation, - Pmo RT. P. RT. p. - log D 99, P ay, log P, or, for two monovalent ions, when - Pi_Pm ľmi D7 f2 Pm ma that is, when the partial osmotic pressures of the two ions in the liquid are in the same ratio as their solution pressures- Even if this result be only a rough indication of the conditions of the problem, it serves to show that enormous differences in concentration would be necessary in order that the two metals of different deposition-voltages should be deposited together from a well-stirred solution, by a current of small intensity. Experiments confirming these conclusions have been made by Sand on mixed solutions of copper sulphate and sulphuric acid, in which convection was prevented. He finds that copper, which, at a copper electrode, has a deposition value lower than that of hydrogen by about 0.507 volt, is first liberated at the i Nernst, Zeits. phys. Chem. XXII. 541 (1897); Sand, Proc. Phys. Soc. Londo XVII. 496 (1901). 310 [CH. XI SOLUTION AND ELECTROLYSIS cathode. As the current is increased, hydrogen also appears; but this is due to the exhaustion of copper from the layers of solution in contact with the electrode which proceeds more rapidly than the replacement effected by the diffusion of the salt. By efficient stirring it is possible to prevent any evolu- tion of gas in cases where, without stirring, over sixty per cent. of the electro-chemical equivalents liberated would be hydrogen. Electrolysis has long been used to separate metals from each other. The theory of this process will now be clear. Let us suppose that we have a mixed solution of zinc and copper sulphates. The deposition point of copper is -0.515 volt, and that of zinc +0.524 volt. Thus if the total electro- motive force applied be enough to give a potential difference at the cathode greater than – 0·515 volt but less than +0.524 volt, copper only will be deposited, for although its deposition point rises as the amount of copper gets less, this change is very small, and all traces of copper which could be detected by chemical analysis will be removed from the solution before the deposition point rises to that of zinc. If the electromotive force at the cathode be now increased above + 0.524 volt, the zinc likewise can be separately removed from solution. Even without this adjustment of electromotive force, if the solution be kept well stirred to prevent the local exhaustion of one metal at the electrodes, complete separation can be nearly effected. For, as we have seen, as long as there is any of the metal of lower deposition point present, none of the other is liberated. This principle is used in a process of copper refining. A plate of pure copper forms the cathode in a bath of copper sulphate. The anode is a thick plate of impure copper, pro- bably containing metals both less and more easily deposited than copper. The bath is stirred, and when the current flows, copper and all more oxydizable metals are dissolved, while the less oxydizable metals, such as gold and silver, fall to the bottom of the vessel, for while copper is present in excess the current will dissolve it rather than more resisting metals. In the neighbourhood of the cathode, however, there will be a large excess of copper together with other metals, such as zinc, more CH. XI] 311 CONTACT ELECTRICITY AND POLARIZATION easily oxydizable and therefore of higher deposition points. As long as any copper is near, therefore, none of the other metals are deposited, and pure copper is obtained at the cathode. On the other hand, by increasing the current density, it of solution next the electrode faster than either stirring or diffusion will replace it. The other metal must then also be used by the current, and, by proper adjustment of conditions, it is possible to deposit alloys, the percentage composition of which can be altered by varying the current density. CHAPTER XII. THE THEORY OF ELECTROLYTIC DISSOCIATION. Introduction. Osmotic pressure of electrolytes. Additive properties of electrolytic solutions. Dissociation and chemical activity. The mass law. Equilibrium between electrolytes. Thermal properties of elec- trolytes. Heat of ionization. Dissociation of water. The function of the solvent. Hydrolysis. Conclusion. Introduction. inn THROUGHOUT our investigation of the electrical properties of solutions we have constantly been led to infer that the ions of electrolytes are to a certain extent independent of each other. The flow of the current is in accordance with Ohm's law, and as we have already pointed out, that law implies freedom of interchange between the parts of the dissolved molecules. The existence of specific coefficients of mobility as characteristic properties of certain ions in very dilute solutions, involves the idea of inde- pendent migration, and suggests that the freedom of the ions from each other persists during the greater part of the time, and is not merely a power of interchange at the moments of molecular collision. If it were only a momentary freedom, the convective passage of the ions in opposite directions through the liquid, indicated by Faraday's law, would be explained by a continual handing on of the ions from molecule to molecule. The ions would work their way along by taking advantage of the intermolecular collisions, and the ionic velocities would depend on the frequency of these collisions; a frequency, which, as indicated by the kinetic theory, depends on the square of the concentration. Now, as we saw on page 213, the conductivity CH. XII] 313 THE THEORY OF ELECTROLYTIC DISSOCIATION of a solution varies as the product of the concentration and the relative ionic velocity; on this view, then, the conductivity will be proportional to the cube of the concentration. The facts described on page 203 do not bear out this result. In dilute solutions, the conductivity is proportional to the concentration, and, as the concentration rises, the conductivity increases at a slower rate. It is difficult to see how these relations could hold except as a consequence of an almost complete migratory free- dom of the ions of dilute solutions, and very strong evidence is thus obtained in favour of a theory of ionic dissociation. Preconceived ideas would not, perhaps, lead us to expect that substances, which, like the mineral salts and acids, show great chemical stability when solid, should almost completely be dissociated into their ions when dissolved in water. It must, however, be remembered that it is precisely these bodies which possess the greatest chemical activity, that is to say, most readily exchange their parts with those of other substances. ·That. a solution of hydrochloric acid, for example, does not ex- hibit the properties of dissolved hydrogen and chlorine, though it has been urged as an objection, is not a valid argument against the theory of dissociation, for the ions are certainly in conditions differing from those in which the atoms of the same elements exist in their usual state. Whether or not there is combination between the ions and the solvent, and whatever be the exact relation between the ions and the charges they carry, we are at least certain that a definite quantity of elec- tricity has to pass between an ion and the electrode before the substance can be liberated in a normal chemical state, say as gaseous hydrogen or chlorine. The energy associated with a substance when ionized must therefore be very different in quantity and character from that associated with it when in its normal chemical condition, and there is no reason to assume identity of properties in the two states. It has been suggested that, if really dissociated from each other, the two ions of a dissolved salt would generally diffuse at different rates, and ought therefore to be separable. If such separation occurred, however, electrostatic forces between the ions would at once arise and increase till further division was 314 [CH. XII SOLUTION AND ELECTROLYSIS prevented. Nevertheless, some separation should undoubtedly occur, and, as a matter of fact, a volume of water in contact with the solution of an electrolyte is found to take, relatively to the solution, a potential of the same sign as the charge on the ion which has the greater mobility and therefore the quicker rate of diffusion. The phenomena involved will be studied in Chapter XIII. An experiment described by Ostwaldi is instructive in connexion with this subject. A membrane of copper ferro- cyanide can be prepared which will allow potassium chloride in solution to pass through it, but is quite impermeable to barium chloride. Now, according to the theory, the chlorine ions of this salt will again pass, since they could do so in the first case, but the electric forces will prevent any considerable separation from taking place. If, however, we place some substance like copper nitrate on the other side of the membrane, the chlorine ions, which diffuse in one direction, are replaced by nitric acid ions, which diffuse in the other. In this way electrostatic charge is prevented, and the process will continue till we soon find nitrate mixed with the barium chloride, and chloride mixed with the copper nitrate. The salts cannot have directly reacted, for neither alone can pass through the membrane, but the exchange is readily intelligible on the hypothesis that the ions possess migratory independence. The dissociation required by the theory is a separation of the ions from each other, securing complete migratory indepen- dence. There is nothing to suggest that the ions are free from all chemical combination. As pointed out in the chapter on theories of solution, the hypothesis of electrolytic dissociation is entirely independent of any particular view as to the nature of solution or the physical mode of action of the osmotic pressure. All that is required to interpret the electrical phenomena is the freedom of the migrating ions from each other; they may quite possibly be combined in some way with the solvent. If we take a chemical view of the nature of solution, it is in fact necessary, as shown on page 174, to imagine such combinations between CU 1 B. A. Report, 1890, p. 332. CH, XII] 315 THE THEORY OF ELECTROLYTIC DISSOCIATION the ions and the solvent in order to explain the abnormal osmotic pressures of electrolytes. We may perhaps represent what occurs by supposing that double molecules, such as NaCl. 2H,0, are formed, and dissociated into Na.H,0, and Cl. H,0, complex ions analogous to those described on pages 226—229, for the existence of which there is definite evidence. On the other hand it may even be that a double decompo- sition goes on, as suggested by Reychlert, a molecule of sodium chloride, for example, decomposing with water thus : Na Cl + HOH = Na OH + HCI.. The water here is separated into parts which are non-electrical; a positive molecule of the composition NaOH, and a negative : * - and molecule HCl are consequently formed. These molecules are not the same as ordinary soda and hydrochloric acid, which themselves are imagined to react with water in accordance with the equations Na OH + HOH = NaOH + HOH + # Cl + HOH = HOH + HCI. The acid, by the interchange of its hydrogen, becomes nega- tively electrified, and produces a positive molecule of water which acts as the cation; the alkali itself becomes a positive ion, and produces a negative molecule of water to form the anion. This hypothesis may not accurately represent the facts --the suggested decomposition of water under the action of dissolved electrolytes into non-electrical hydrogen and hydroxyl cannot readily be accepted—but it does not seem to be contra- dicted by any of the electrical relations; and it is from the consideration of this and other similar ideas that we may hope to ascertain the essential features of the dissociation theory. i Outlines of Physical Chemistry, Eng. trans., London and New York, 1899, p. 216. 316 [сн. XII . Osmotic pressure of elec- trolytes. In solutions of electrolytes the osmotic pressure and the correlated effects, the depression of the freezing- point and the lowering of the vapour pressure, are abnormally great. When an organic body such as cane sugar is dissolved in water, the osmotic pressure effects of dilute solutions are found, approximately at any rate, to agree with the values deduced by Van 't Hoff's theory. The osmotic pressure of dilute dissolved gases can be deduced by the principles of energetics either from the observed solubility relations, or from general molecular theory, and the reasonable extension of the results to solutions of other substances is justi- . fied by experimental measurements in many different solvents, examples of which, due to Raoult, are given on pages 156 and 157. Such theoretical and experimental considerations prove that, when water is used as solvent, the lower series of values, obtained with organic solutes, are normal; it is the higher values characteristic of electrolytic solutions, which need further explanation. As long as a solution is dilute enough for the particles of solute to be outside each other's sphere of action, theory indicates that the osmotic pressure of a number of dissolved I same number of gaseous molecules would exert at the same temperature when confined in a volume equal to that of the solution. Thus the osmotic pressure effects of dilute substances must depend on the number and not on the nature of the dissolved molecules. When experiments yield abnormally small values, it follows that the number of the solute molecules is less than that indicated by the chemical formula weight; it is then natural to conclude that aggre- gation of molecules to form complexes has occurred. When, on the other hand, abnormally great values are obtained for solutions of electrolytes, it is necessary to infer that the number of solute particles is increased, and that some of their molecules have dissociated. Attempts have been made to explain the phenomena by an association of solvent molecules instead of a dissociation of those of the solute, but the general theory indicates that it is the volume and not the state of molecular CEL. XII] 317 SY THE THEORY OF ELECTROLYTIC DISSOCIATION 1 2 aggregation of the solvent that is involved ; moreover, in the particular case of vapour pressure which led to the idea of the association of the solvent, the equations of page 128 clearly show that such an association would not affect the osmotic pressure. As soon as Van 't Hoff? made known his investigations on osmotic pressure they were applied to the theory of electrolytic dissociation by Planck² and by Arrhenius®. Planck showed that the abnormally great osmotic pressure effects of electrolytes, when considered from the point of view of thermodynamic theory, required the hypothesis of some form of electrolytic dissociation. Arrhenius pointed out that the amount of dis- sociation thus existing in a solution might be estimated by two independent methods; it might be determined by the com- parison of the actual equivalent conductivity with its value at infinite dilution, or by the measurement of the osmotic pressure effects, of which the importance had been recognized by Van't Hoff. • The depression of the freezing-point has been more thoroughly investigated than the other correlated properties, and as the experimental error is probably less, a comparison may rightly be instituted between the results of this method and the electrical ones. Following Arrhenius, let us suppose that every electrolytically active molecule produces an abnor- mally great osmotic pressure, and that its effect is proportional to the number of ions into which it can be resolved. Thus the effect of an active molecule of potassium chloride should be twice that of an inactive one, and the effect of a molecule of potassium sulphate, which in dilute solutions yields two K ions and one SO, ion, should be three times that of an undisso- ciated molecule. If then, in a certain solution, we have m inactive and n active molecules, each of the latter giving k ions, the total i Kongi. Svenska Akad. Handl. XXI. 38 (1885); Zeits. phys. Chem. I. 481 (1887). 2 Wied. Ann. XXXII. 499 (1887). 3 Zeits. Phys. Chein. I. 631 (1887); Eng. trans. Harper's Science Series, iv. 47. 318 [CH. XII SOLUTION AND ELECTROLYSIS. osmotic pressure produced will be proportional to m + kn, whereas the normal osmotic pressure would be proportional to m +n. By measuring the conductivity we can, for the dilute solutions of simple salts (see p. 225), find the fraction of the number of molecules which is at any moment active. Let us call it a. Then, on Arrhenius' theory aan a= m + n' = = so that, if the ratio of the actual osmotic pressure to the normal. is called i, · m + kn '=1+ (k – 1) a...............(61). mtn This same ratio can also be found by direct experiment on the depression of the freezing-point, for by Van 't Hoff's equation we know the normal value, and if t be the observed depression for a solution of one gram-equivalent per litre, t is i = 1:86 We can thus compare the value of į as directly determined by observations on the freezing-point, with its value as calcu- lated from the conductivity. The table on the opposite page is part of that given by Arrhenius? for aqueous solutions. It will now be seen that there are two relations involved in the dissociation theory. Firstly, the number of ions into which a molecule must be resolved in order to explain its electrical behaviour when completely dissociated in a very dilute solution should be the same as the number required to give its observed osmotic pressure; secondly, in dilute solutions of simple salts, where the phenomena are not obscured by complex ions or changing ionic viscosity, as the concentration rises, the abnor- mally great osmotic pressure should diminish with the coefficient of electric ionization. Since the publication of Arrhenius' original paper, the results of which were accepted as a rough proof of the approximate accuracy of both these relations, a great quantity of experimental work has been undertaken ; some of it must now be passed in review. i Zeits. phys. Chem. II. 491 (1887). CH. XII] 319 THE THEORY OF ELECTROLYTIC DISSOCIATION Substance dissolved | ¿ calcu. No. of gram. i observed lated from per litre ing-points tivities I a coeffi- | cient of conduc. lionization A. Non-Conductors. Methyl alcohol CH,OH 0:1 0.485 0.97 0.125 0.62 0.90 0.96 1.00 0.97 Ethyl alcohol C,H,OH 1:01 Phenol C.H.OH 14.1.00 0 0.101 0.216 0:558 0.0445 0.0947 0:316 0.809 1:01 1.05 0.96 0.96 0.93 1.08 1.11 1:12 1:34 1:43 Cane Sugar C12H22011 1.90 B. Electrolytes. Lithium hydrate LiOH Acetic acid CH2COOH 1.86 1:01 1.98 1:39 1.05 1:04 1:01 1:38 1:27 1:01 *01 •00 .17 Phosphoric acid 1:22 1.00 1:32 1.25 1:20 1.88 1.84 •08 •07 .88 .84 .82 Sodium chloride Naci 1.82 .74 1.74 1.86 1.81 Silver nitrate AgNO3 .86 .81 0·127 0:317 0.135 0:337 0·842 0:077 0.146 0:319 0.0467 0:117 0·194 0:539 0.056 0:140 0:341 0.0364 0:091 0.227 0.455 0.0476 0.119 0.199 0:331 0.0393 0·112 0.254 0.523 0.973 2:00 1.93 1.87 1.85 2:02 1.90 1.77 2.68 2:35 2.21 2:04 2.74 2.62 1.73 .73 2:45 72 -66 Potassium sulphate di K2804 5.9 Calcium chloride CaCl2 71 .67 2:18 2:06 2:52 2:42 2:34 2:24 1:41 1:34 1.27 1•22 .62 41 •34 2.73 1:33 1.15 1:03 0.94 0.92 Copper sulphate .27 .22 To investigate the first relation it is necessary to measure the electrical conductivity and the freezing-point of solutions 320 [CH, XII SOLUTION AND ELECTROLYSIS. so dilute that the ionization may be taken as complete, or, at all events, that its value at infinite dilution may be estimated. The freezing-point experiments are complicated by sources of error pointed out in Chapter VI. In Raoult's booki on “Cryoscopie” are given the results obtained by Loomis at a concentration of 0:01 gram-molecule of salt to 1000 grams of water, i.e. 0:01 normal, as in themselves trustworthy and in accordance with the best of other results known at the time. The following are the molecular depressions of the freezing- point for certain substances in aqueous solution, the concentra- tion being expressed as gram-molecules of solute per thousand grams of water. Potassium hydrate Hydrochloric acid Potassium chloride Sodium chloride 3.71 3.61 3.60 Nitric acid Potassium nitrate Sodium nitrate: Ammonium nitrate 3.73 3:46 3.55 3.58 3.67 4:49 5:04 Sulphuric acid Sodium sulphate Calcium chloride Magnesium chloride 5.09 5.08 Magnesium sulphate 2.66 Zinc sulphate 2.90 In the first group are substances which are shown by the electrical properties to yield in solution two monovalent ions. On the dissociation theory, therefore, the osmotic pressure effects should, at high dilutions, have double their normal value. The normal value for the molecular depression of the freezing- point is 1.857, as calculated from the osmotic pressure theory, and confirmed by experiments on dilute aqueous solutions of non-electrolytes (see page 147). Twice this value is 3.714, a number to which all the observed molecular depressions of substances in group 1 closely approximate. The electrical behaviour of bodies in the second group similarly indicates dissociation into three ions, producing a theoretical molecular depression of 5:57. The experimental numbers differ from this value by perhaps 10 per cent., but the error is in the right direction since the electrical conductivities at the concentration i Paris, Oct. 1901. CH. XII] 321 rn THE THEORY OF ELECTROLYTIC DISSOCIATION used by Loomis in these freezing-point experiments, namely, about 0:01 normal, show that the ionization is still far from complete in the salts containing divalent ions. The corre- sponding error is still greater in the salts of the third group, which yield two ions, both divalent; the molecular depression should be again 3.714, greater by about a third than the observed values. All discrepancies are thus of the kind to be expected from a consideration of the electrical phenomena; and the first group, the salts of which are about 95 per cent. ionized at the concentration used in the cryoscopic experiments, yield very concordant results. In the investigation of the freezing-points of very dilute solutions carried out by E. H. Griffiths, to which reference was made on pages 147 and 158, results for salts with divalent ions have not yet been published. The molecular depression of potassium chloride at a concentration of about 0:0003 normal was found to be 3.720, exactly double, within the limits of experimental error, the number given by an equivalent solution of cane sugar. At this concentration the conductivity indi- cates that 99.7 per cent. of the salt is dissociated. Thus the evidence at present available goes to support the accuracy of the first relation of Arrhenius' theory in the case of aqueous solutions. The observed depressions never appreciably exceed the theoretical values, and the discrepancies in the other direction are readily explicable by incomplete ionization. In fact consideration shows that the relation can only be exact for those solutions which reach a definite limit of equivalent con- ductivity as the dilution is increased ; it is only these solutions that are fully ionized. Passing to solutions in solvents other than water, we find that sufficient data are not available to decide whether the same relation between the electrical and the osmotic pheno- mena holds good. The difficulties of experiment are much increased, and no observations on osmotic pressure effects seem to have been made on solutions in which the dilution was carried far enough to secure a constant value for the equivalent conductivity and so justify the assumption of complete ioniza- tion. In many aqueous solutions, such as those of acetic acid W. S. . 322 [CH. XII SOLUTION AND ELECTROLYSIS and ammonia in particular, complete ionization cannot be ex- perimentally reached; and, without definite evidence, we cannot assume that it is ever obtained in another solvent. Measure- ments on stronger solutions are of little use, for as soon as the dissolved particles come within each other's sphere of influence their change of available energy by dilution will not be inde- pendent of the nature of the solvent, and the thermodynamic deduction of the gas-value for the osmotic pressure ceases to be valid. Moreover, for non-aqueous solutions, we have little know- ledge of such electrical constants as the transport numbers, and it is not safe to conclude that the ions are of the same nature as in water. In alcoholic solutions, at any rate, what little evidence is forthcoming indicates that complex ions are very numerous, even at moderate dilutions, (see pages 195 and 218), and any such complexity must diminish the number of dissolved par- ticles, and consequently the osmotic pressure effects. Kahlen- berg, however, states that solutions of diphenylamine in methyl cyanide show abnormally low molecular weights, and yet are not conductors of electricity? Such a result perhaps indicates a dissociation yielding products which are not electrically charged, or a non-electrical double decomposition with the solvent. Until further observations have been made it is im- possible to say whether or not the first relation suggested by the dissociation theory holds for non-aqueous solutions. The second relation enuuciated by Arrhenius indicates that the coefficient of ionization measured electrically should agree with its value calculated from the osmotic pressure effects; but this relation can only hold within very narrow limits of con- centration. The thermodynamic theory of osmotic pressure is valid only when the solute particles are beyond each other's sphere of influence, and any further addition of solvent can consequently not affect that part of their available energy which is due to their connexion with the solvent. For greater con- centrations, the osmotic pressure will depend on the nature of the solvent and of the solute, and on the interaction between them. Again, if complex ions are present, and, in any case, as 1 Jour. Phys. Chem. v. 344 (1901) ; VI. 48 (1902). CH. XII] 323 THE THEORY OF ELECTROLYTIC DISSOCIATION soon as the concentration becomes great enough to affect the ionic fluidity, the ratio of the actual to the limiting equivalent conductivity, as shown on p. 225, ceases to measure the fraction of the number of molecules which are resolved into indepen- dent ions. Moreover, except in solutions of such simple salts as potassium chloride, etc., there is some doubt whether the limiting value of the equivalent conductivity has ever been reached, and if not, even in dilute solution, the electrical measurements do not give the true coefficient of ionization. Nevertheless, experiments on these lines are of great interest; confirmation of the relation for dilute aqueous solutions of simple salts would be valuable evidence that the Arrhenius relation gives, in such cases, a complete explanation of the phenomena, and the amount of divergence in other cases would supply useful indications of the nature and amount of the dis- turbing influences. It must be clearly recognized that, while the dissociation theory requires the agreement in the numbers of the ions indicated by the electrical and osmotic methods in the few cases in which the conductivity phenomena show the ionization to be complete, it is far from suggesting that the first relation holds in other cases, or that the second relation exists except for a limited range of concentration of salts which in dilute solution are fully ionized. As soon as the concentra- tion begins to increase, the complications we have indicated are appreciable, and the relation between the electrical and the osmotic values of the ionization coefficient must become more and more inexact. Stress is laid on these restrictions because the relations under consideration have played a great part in the history of the dissociation theory, and the want of quanti- tative agreement in the results of the two lines of research has often been adduced to deny the claims of the theory to give a true explanation of the difference between electrolytic and non-electrolytic solutions. It may here be pointed out that relations, which are true when the system possesses the properties of dilute matter, must be expected to begin to fail at much smaller concentra- tions in the case of electrolytes than of non-electrolytes. On the supposition that the forces between atoms and molecules I. 21-2 324 [CH. XII SOLUTION AND ELECTROLYSIS are electrical, the force between two electrically bipolar mole- cules will quickly diminish as the distance between them increases—probably as the fourth power. The force thus rapidly becomes insensible beyond a certain small range, the sphere of molecular action; but the force between two dis- sociated ions is of a different order. Here we have positive and negative charges which are not permanently connected to opposite charges to form molecular doublets. The forces will be more of the nature of those between small isolated electrified bodies, and their variation with distance will approximate to the law of inverse squares; their range is greatly increased, and ionic influence will not rapidly vanish beyond a definite limit in the same way as do the intermolecular forces. We might expect, for example, that, for cane sugar, the molecular depression of the variation of concentration than for the solution of a metallic salt, even when the latter is corrected for ionization. It is possible that, as the concentration increases, the electric forces between the dissociated ions become sensible before any re-com- bination can occur; if so, the ionic velocities, and therefore the conductivity, would be reduced before the ionization ceases to be complete, and the coefficient a of p. 224 would not represent the ionization even at great dilution. On the other hand, the osmotic pressure effects might be affected also at about the same concentration, though not necessarily to the same extent, and perhaps any such inter-ionic electric forces as are here contemplated may, for the purposes of the properties we are considering, be truly reckoned as combination. At all events, the forces would interfere with that complete migratory independence of the opposite ions as regards each other which may be taken as the meaning of complete ionization. References to cryoscopic determinations on solutions of electrolytes have been made in the chapter on freezing points, pp. 153 to 158. Many of the results have been compared with the ionizations as measured by Kohlrausch at 18° or Ostwald at 25°; but to obtain a satisfactory basis of com- parison, the electrical data also must be deterinined at the freezing point. CH. XII] 325 THE THEORY OF ELECTROLYTIC DISSOCIATION Experiments at 0°, on solutions of moderate dilution, have been made by R. W. Wood, Archibald”, and Barness, the limiting values of the equivalent conductivity being estimated by reference to Kohlrausch's data. Other experiments were made by Kahlenberg and Hallº and by the present writers, who carried the dilution far enough to reach the limiting equivalent conductivity of simple salts. The experiments were planned in connexion with those of Griffiths on freezing points, and were made in a platinum cell similar to his apparatus. The results showed an appreciable difference when the ionizations were determined at 0° and at 18º. The following values were obtained from smoothed curves drawn between the cube root of the concentration and the equivalent conductivity, and represent the inost probable numbers for the ratio u/ Mor of the actual to the limiting equivalent conductivity throughout the range of concentration employed. The values for magnesium sulphate were obtained later from experiments in a glass cell. It will be seen that definite limits were found for the equivalent conductivities in the cases of potassium chloride and permanganate and of barium chloride. In these solutions, therefore, complete ionization was reached at the concentrations indicated. In the cases of the other salts used, potassium bichromate and ferricyanide and copper sulphate, no exact limit was found, and the value of the equivalent conductivity corresponding to complete ionization had to be estimated by exterpolating the curves. For sulphuric acid which, as at 18°, reaches a maximum equivalent conductivity at a certain dilution, and then falls off again as the concentration is still further diminished, the maximum was taken as the limit, a mode of procedure which, however, almost certainly leads to too high values for the ionization coefficients. i Zeits. phys. Chem. XVIII. 3 (1895); Phil. Mag. [5] XLI. 117 (1896). 2 Trans. Nov. Sco. Inst. Sci. x. 33 (1898). 3 Ibid. x. 139 (1899); Trans. Roy. Soc. Canada, 11. 6 (1900). 4 Jour. Phys. Chem. v. 339 (1901). 5 Phil. Trans. A. cxciv. 321 (1900); Zeits. phys. Chem. XXXIII. 344 (1900). 326 [ch. XII SOLUTION AND ELECTROLYSIS Equivalent conductivities at Oº, referred to the limiting values as unity. n=number of gram-equivalents of solute per thousand grams of solution. KCI KMnO4 BaCl, {H,804 | CuSO4 MgSO4 | 1K2FeCy6 | 3K,Cr,0, 1.000 1.000 1.000 1.000 0.999 0.998 0.996 0.991 0.985 0.876 0.942 0·0215 0·0272 0.00001 0.00002 0.00005 0.0001 0.0002 0.0005 0.001 0:002 0.005 0:01 0.015 0.02 0.03 0.0464 0.0585 0.0794 0.1000 0·1260 0:1710 0.2154 0.2466 0.2714 0:3107 1.000 1.000 1.000 0.999 0.998 0:996 0.992 0.987 0.976 0.962 0.952 0.944 0.932 1.000 1.000 0:998 0.995 0:990 0.980 0.969 0.953 0.925 0.896 0.876 0.864 0.998 0.993 0.981 0.967 0.947 0.908 0.863 · 0.807 0.717 0.983 0.976 0.963 0.950 0.932 0.899 0.864 0.814 0.720 0.659 0.618 0.587 0:545 1.000 0-993 0.971 0.928 0.880 0.848 0:822 0.993 0.986 0.971 0.955 0.944 0.934 0.991 0.980 0.952 0.929 0:902 0.880 0.870 0.864 0.863 0.858 0.853 0.847 0.961 0:944 0.919 0.876 0.834 0.591 0:557 CH. XII] 327 THE THEORY OF ELECTROLYTIC DISSOCIATION The investigation has lately been extended in glass appa- ratus to greater concentrations, and the following smoothed values have been obtained :- dor KCI BaCl, CuSO4 MgSO4 •929 913 •888 •843 813 778 742 20 932 .917 .896 .874 •858 •855 •856 •860 311 •368 -464 •585 •737 •794 1.000 1.063 1.145 1.260 •40 •50 •861 •833 .823 •710 •512 -468 -405 •348 294 •275 230 .218 •208 •194 •545 -493 .433 •373 •315 •295 213 •188 •149 ·090 1.0 794 -786 1.2 699 •665 •657 •645 •632 1.5 2:0 The first column under KCI, like those under all the other salts, gives the value of u do when the concentration is ex- pressed in terms of gram-equivalents of salt per thousand grams of solution. In the second column under KCl, the concentra- tion is expressed per thousand grams of solvent. This method, if applied to the other salts would, in a similar way, reduce the calculated results. The corresponding freezing point experiments are not yet completed, and an exact comparison of the two lines of research is not possible. If, however, we accept Griffiths' result for potassium chloride as establishing the first relation, namely, the agreement between the numbers of the ions at infinite dilution as estimated in the two ways, we can take 1.858 k, where k is the number of the ions, as the limiting value of the molecular depression, and calculate the ionization a from cryo- scopic determinations on stronger solutions. The following comparisons with the electrical measurements described above may be given, n being expressed in gram-molecules of salt per thousand grams of solvent. 328 [CH. XII SOLUTION AND ELECTROLYSIS Potassium chloride. KCl = 74:59. 8T|n a (Raoult) ullos .906 ·0291 .0585 •1173 2368 .4813 1.000 3:342 3.466 3:416 3:376 3.328 3.286 .864 .837 .816 •790 •767 •929 .908 .883 .854 •825 794 a (Loomis) a (Jones recalculated) •992 .932 .919 ·005 07 •02 ·05 •1003 2012 -4048 •937 •911 •881 .849 .821 •783 .976 •962 •942 •913 •888 •860 •832 .855 •835 •803 In the annexed diagram, the smooth curve W denotes the electrical values of u do, and the dotted lines indicate the 2.06 - --- w....... ... ný .5 1-0 ionizations as deduced from the cryoscopic observations of Raoult (R), Loomis (L), Jones (J), and Ponsot (P). The cross CH. XII] 329 THE THEORY OF ELECTROLYTIC DISSOCIATION shows the concentration at which Griffiths found complete ionization. Accepting his result, it follows that Jones' numbers, at great dilution at any rate, are too high, while the complete difference of Ponsot's curve from those of other observers makes it unsafe to lay stress on his experiments. We are thus left with the results of Raoult and Loomis, and the lower part of Jones' curve as a basis of comparison with the electrical measurements. As a general conclusion, we may perhaps say that there are indications that the electrical and cryoscopic curves approach each other at greater dilutions, and perhaps also at greater concentrations. Throughout the range at which a direct comparison can be made, however, there is a considerable difference between the two sets of results. This difference is greater than has been usually supposed. The electrical curve, deduced from conductivity measurements made at 18°, which has generally been adopted as the basis of com- parison, lies below the curve for 0° given in the diagram, and happens nearly to coincide with the cryoscopic results. The question cannot be regarded as settled, but the evidence at present available indicates that the ionizations as measured in the two ways become consistent only at extreme dilution, even in simple salts such as potassium chloride. The divergencies between the cryoscopic results of different observers, considerable in the case of potassium chloride, be- come even more conspicuous for more complicated salts, and in the present position of the subject no useful purpose would be served by a detailed examination. It seems that, in some cases at any rate, the curves cross each other at moderate concentration, the electrical becoming lower than the freezing point results. In barium chloride solutions, the change occurs within the range of comparison given by Loomis' experiments; it is possible that some of the agreements that have been obtained may depend on accidental conjunctions of this nature, and would fail at lower and higher concentrations. More accurate determinations of the freezing points are needed before such comparisons as these can be taken as a satisfactory basis for theoretical generalizations. Collections of 330 [CH. XII SOLUTION AND ELECTROLYSIS Barium chloride. Loomis n=2M ST/M и/ию •843 •832 LA 4.99 4.95 4:761 4:676 4.627 •781 -759 •745 .865 .831 •778 •742 710 40 A the present data have been made by MacGregori and Kah- lenberg? Passing as before to solutions in solvents other than water, we again find the difficulties of experiment much increased. Many observations have been made, but very seldom has the dilution been pushed to such extremes as are necessary to produce complete ionization in aqueous solutions. The phe- nomena seem to be more complicated, and sometimes the equivalent conductivity increases with concentration even in fairly dilute solutions: Limiting values of the equivalent conductivity for salts of the alkali metals dissolved in methyl and ethyl alcohol have however been obtained by increasing the dilution by Fitzpatrick“, Völlmers, and Zelinsky and Krapiwin. For solutions in these solvents, then, it is possible to calculate the dissociations at moderate dilutions by deter- mining the ratio of the equivalent conductivities. To compare these results with the osmotic values, it is necessary to use the vapour pressure or the boiling point method, as the freezing points of these solvents are very low. A collection o, it 1995 by apare i Trans. Nova Scotia Inst. Sci. x. 211 (1899–1900); Phil. Mag. [5] L. 505 (1900). 2 Journ. Phys. Chem. v. 339 (1901). 3 Kahlenberg, Journ. Phys. Chem. v. 342 (1901). 4 B. A. Report, 1886, p. 328; Phil. Mag. XXIV. 378 (1887). 5 Wied. ann. LII. 328 (1894). 6 Zeits. phys. Chem. xxi. 35 (1896). CH. XII] 331 THE THEORY OF ELECTROLYTIC DISSOCIATION of results of such comparisons has been made by A. T. Lincoln”, who gives the following tables from boiling point experiments by Woelfer, and conductivity experiments by Völlmer. Ionization Salt Concentration in per cents. From boiling point From conductivity Solutions in methyl alcohol. Lithium chloride 0:45 0.63 Potassium iodide 0:36 0.61 Sodium iodide 0:44 0.87 Potassium acetate 0:48 0:48 Sodium acetate 0.40 0:49 0:57 0.79 0.74 0.63 0.63 Solutions in ethyl alcohol. Lithium chloride 0.9 0:35 Potassium acetate 1•07 0.18 Potassium iodide 0.78 0.29 Silver nitrate 0:53 0.65 Sodium iodide 2.14 0.27 0.68 0:51 Sodium acetate 0.97 0.01 0:32 0-27 0:49 0:38 0:45 0.56 0.24 In alcoholic solutions, what little evidence is available indicates that complex ions are very frequent even at moderate dilutions (see pp. 195 and 218), and the above results show that, as we should expect, the disturbing factors have greater influence than in aqueous solutions. The results for sodium iodide suggest that better agreement would be obtained at smaller concentrations. Experiments, summarized in Lincoln's paper, on acetone by Carrara, Laszozynski, and Dutoit and Aston, and on pyridine by Laszozynski and Gorski, indicate limiting values for the equivalent conductivities of the iodides of the alkali metals when dissolved in these solvents? Lincoln's measurements on 1 Journ. Phys. Chem. III. 457 (1899). 2 Carrara, Gazz. Chim. Ital. XXVII. 1. 207 (1897); Laszozynski, Zeit. Elektrochem. 11. 55 (1895); Dutoit and Aston, Compt. rend. cxxv. 240 (1897); Laszozynski and Gorski, Zeit. Elektrochem. IV. 290 (1897). 332 [CH. XII SOLUTION AND ELECTROLYSIS silver nitrate in pyridine show no sign of reaching a limit, but his greatest dilution was only 784 litres per gram-molecule?. Many other solvents give conducting solutions, but, in them, limiting values of the equivalent conductivity have seldom or never been obtained. A general account of the work that has been done on non-aqueous solutions will be found in Lincoln's paper. Cases in which the boiling or freezing points of con- ducting solutions indicate molecular weights equal to or greater than the normal have been pointed out by Kahlenberg?. Such phenomena probably indicate association of the non-ionized solute molecules. Additive properties of electrolytic solutions. Many attempts have been made by chemists to trace con- nexions between the physical properties of compounds and their chemical constitution. Details can be found in any book on physical chemistry. The general result may be summarized by saying that, while some properties, such as the atomic volumes, the atomic heats, and the power of magnetic rotation of the plane of polarization of light, seem to be permanent characteristics of the elements and keep nearly the same values even when those elements change their state of combination, such additive relations are limited to a few properties, and never seem to be more than approximations. In solutions of electrolytes, additive relations are applicable to many more properties, and are much more accurately true. The explanation of these results by means of the hypothesis of the practical independence of the constituents of the solutes 1 A detailed study of this solution would be useful, for in it Faraday's law has been confirmed by Skinner (B. A. Report, 1901, p. 32); from boiling point experiments Werner concluded that the molecular weight is nearly normal (Zeits. Anorg. Chem. xv. 23 (1897)); while, between dilutions of one and forty litres, the transport numbers for the cation have been found by Schlundt to be: 1 litre, 0.326 ; 2 litres, 0.342 ; 10 litres, 0.390; 40 litres, 0:440 (Jour. Phys. Chem. VI. 168 (1902)). This rapid change indicates the existence of complex ions. Schlundt remarks that, as a rule, the experiments of Hittorf and others show that the transport number for the cation increases rapidly with dilution in solutions of salts which show a marked affinity for the solvent. 2 Journ. Phys. Chem. v. 342 (1901). CH. XII] THE THEORY OF ELECTROLYTIC DISSOCIATION · 333 was suggested by several observers, even before the develop- ment of the electrolytic dissociation theory. That theory indicates that when the ionization is complete, the difference between any physical property of a solution and the cor- responding property of its solvent should be compounded additively of the differences produced by the two ions. When the ionization is not complete, the differences referred to must be similarly compounded of those produced by the undis- sociated molecules and the dissociated ions. It should thus be possible to express the numerical values of the various properties in terms of the state of ionization, by means of an expression of the form P= Pw+K (1-a)n + Lan where P is the numerical value of any property, such as the density, etc., Pw the value of the same property for the solvent under the same conditions, n the molecular concentration of the solution, a the ionization coefficient, and K and I two constants independent of the concentration. MacGregor has supported this equation for many properties of dilute solutions by tabulating known data?. An extended account of the additive relations of salt solutions will be found in Ostwald's Lehrbuch der Chemie. A short summary only is here attempted. Valson” found that the specific gravities of salt solutions could be calculated from a table of moduli of the elements of the substance dissolved, the modulus for each element being experimentally determined. The relation is better investigated, however, by considering the specific volume instead of its reciprocal the specific gravity, and Groshaus: found that the molecular volume of the dissolved salt was, in dilute solution, the sum of two constants, one determined only by the acid and the other only by the base. The densities and thermal expan- sions of solutions have since been redetermined by Bender“, who confirmed Valson's conclusions. The thermal expansion of i Phil. Mag. [5] XLIII. 46 and 99 (1897). % Compt. rend. LXXIII. p. 441 (1874). 3 Wied. Ann. xx. p. 492 (1883). 4 Wied. Ann. XXII. 184 (1884); XXXIX. 89 (1890). 334 . [CH. XII SOLUTION AND ELECTROLYSIS salt solutions is more uniform the more the concentration is increased, the curved temperature-volume diagram for water becoming more straight as salt is added. Ostwaldı has measured the volume-changes accompanying the neutralization of bases by acids, and shown that, here again, additive relations appear. The subject has been fully discussed by Nicola. Similar phenomena appear when we study the colour of a salt solutions, which is found to be produced by the super- position of the colours of the ions and the colour of the undis- sociated salt. If the absorption spectra of a series of coloured salt solutions containing a common ion are examined, the additive character of the colour is well seen, the absorption bands due to the common constituent being unaffected by the presence of the other part of the salt. The light transmitted through a solution is composed of all those rays which have been absorbed by neither constituent. Anhydrous cobalt chloride is blue, while in cold aqueous solution all cobalt salts are red. Red, then, is the colour of the cobalt ion, and only appears when the salt is more or less dissociated. When cobalt chloride is dissolved in alcohol, the conductivity is very low, showing very incomplete ionization. The colour is, accordingly, the blue of the undis- sociated salt. If we slowly add water to this solution, the ionization gradually increases, and the colour changes to purple and then red. An aqueous solution, boiled with potassium cyanide, is decolorised, for a cobalti-cyanide, K,Co(CN)., has been formed; the ions of this compound are 3K and Co(CN)6 ; the free cobalt ions no longer exist, and the solution ceases to respond to the usual tests for cobalt. That the red colour is really due to the ionization, and not to a hydrate formed between the cobalt salt and the solvent, is indicated by the additive nature of the phenomena; for, like many other pro- perties, the colour of non-electrolytes depends on the consti- tution and is not additive. The use of indicators, which show the presence of acids or bases by a change in colour, depends upon similar phenomena. Thus para-nitrophenol is a weak 1 Lehrbuch, or Solutions, p. 257. 2 Phil. Mag. XVI. 121 ; XVIII. 179 (1883–4). 3 Ostwald's Lehrbuch; Zeits. Phys. Chem. IX. 584 (1892). CH. XII] 335 THE THEORY OF ELECTROLYTIC DISSOCIATION acid, very little dissociated. The addition of an alkali, soda for example, causes the corresponding salt to be formed. This is largely dissociated, and the intensely yellow colour of the ion C.H_NO2.0 is at once seen. A rise of temperature generally reduces the dissociation of a salt in solution, and increases the number of combined molecules -the accompanying increase of conductivity being brought about by a still greater reduction in the viscosity which the solution opposes to the motion of the ions. We should expect, therefore, on heating a coloured solution in which this temperature relation exists, that the colour would become more like that of the undissociated salt. Thus anhydrous copper chloride is a yellow solid, and the combination of this with the blue of the copper ion produces the green colour of the strong solution. On adding water the colour gets more blue, but on heating it goes back to green. Other cases have been described by J. H. Gladstone? Similar additive relations have been traced in the refraction coefficients, which were found by Gladstone to be additive properties in solutions of active-i.e. dissociated—salts, in the optical rotatory powers, in the surface tensions, and in the viscosities of salt solutions; while Perkin, from the phenomena of magnetic rotation, concluded, without reference to the disso- ciation theory, that salts were dissociated into acid and base. The thermal capacities are complicated in that a change of temperature usually causes a change in the state of dissociation to an amount dependent on the nature of the substance; but, in completely dissociated solutions, the thermal capacity is also an additive property?. The rapidity and ease with which reactions occur between solutions of electrolytes are in sharp contrast and chemical with the difficulty and delay usually experienced in producing chemical changes in organic sub- stances. The close connexion between chemical activity and Dissociation and chemical activity. 1 Phil. Mag., 1857, [4], XIV. p. 423. 2 Marignac, Ann. Chim. et Phys., 1876, [5], VIII. p. 410. 336 [CH. XII SOLUTION AND ELECTROLYSIS electrolytic conductivity was noticed by Hittorf, and Arrhenius, who afterwards investigated the subject, was able to establish definite numerical relations. The existence of specific coefficients of affinity, which are characteristic properties of individual acids and bases whatever the reaction in which they are engaged, is clearly recognized in modern chemistry. The relative strengths of these affinities may be measured in different ways with consistent results. If one acid acts on the sodium salt of another, some of the sodium salt is decomposed, and, unless its acid is removed from the sphere of action by evaporation or precipitation as fast as it is formed, eventually certain quantities of both sodium salts and both acids will be left in solution. The relative amounts will finally be the same whichever possible pair of components we use as reagents. The final composition of the solution cannot, in general, be ascertained by chemical means, for the addition of a new substance would alter the equilibrium. Physical methods of investigation have therefore been employed. Thomsen determined how much of the sodium salt of one acid was decomposed by another, by measuring the heat evolved during the action. He thus measured the ratio in which the base is shared by the acids—a ratio which may be said to express their relative avidities. Ostwaldı also investigated the relative avidities of acids for potash, soda, and ammonia, and proved them to be independent of the base. The method employed was to measure the changes in volume caused by the action. The results are given in column I. of the table which follows, the avidity of hydrochloric acid being taken as one hundred. Another method is to allow some acid to act on an insoluble salt, and to measure the quantity of substance which goes into solution. Determinations have been made with calcium oxalate, which is easily decomposed by acids, oxalic acid and a soluble calcium salt being formed. The avidities of acids relative to that of oxalic acid are thus found, so that the acids can be compared among themselves. Their relative avidities as thus measured are given in column II. of the table. A property of acids, at first sight unconnected with the i Lehrbuch der Allg. Chemie. CH. XII] 337 THE THEORY OF ELECTROLYTIC DISSOCIATION avidity, is their accelerating influence on such actions as the “inversion” of cane sugar, which consists in its transformation into dextrose and laevulose. It has long been known that strong acids produce much greater accelerating effects than weak acids, the acid itself being in all cases unchanged. The relative strengths of acids as thus determined agree with their avidities for decomposing the salts of other acids. Another instance of accelerating action is seen in aqueous solutions of methyl acetate, which, if allowed to stand, undergo a very slow decom- position into alcohol and acid. This process is much quickened by the presence of a little dilute foreign acid, though the accelerator remains unchanged. It is again found that the influences of different acids on this action may be taken as specific coefficients of affinity. The results of this method are given in column III. Finally in column IV. the electrical conductivities of normal solutions of the acids have been tabulated. A better basis of comparison would be the ratio of the actual to the limiting conductivity; but, since the conductivity of acids is chiefly due to the hydrogen, the limiting value is nearly the same for all, and the general result of the comparison would be unchanged. As we have already noticed, the electrolytic conductivities of solutions of different mineral acids attain approximately equal values and their ionizations are nearly complete. Similar phenomena are observed in the case of their chemical affini- ties. The values of the affinity for hydrochloric, nitric and other strong acids are practically the same, and cannot by any means be increased. Ostwald has found that the introduction of oxygen, sulphur or a halogen, which increases the affinity of a weak acid (compare acetic acid with the three chloracetic acids), has no effect on the affinity of strong acids. The limit has evidently been reached, and the whole substance obtained in a state of activity. In each column of the following W. S. 22 338 [CH. XII SOLUTION AND ELECTROLYSIS Acid III IV 100 102 100 100 110 92 100 99.6 65.1 68 4.0 67 2.5 1.7 1.0 04 Hydrochloric Nitric Sulphuric Formic Acetic Propionic Monochloracetic Dichloracetic Trichloracetic Malic Tartaric Succinic 1.2 1.1 7.2 74 1:3 0:3 0:3 4:3 23.0 68.2 0:3 5:1 34 18 82 4:9 25:3 62:3 1:3 2:3 30 50 1.2 5:3 6:3 2:3 0.5 0:1 0.2 0:6 Similar methods can be used for determining the relative strengths of bases. The avidities can be compared by sharing an acid between two bases competing for it; and their in- fluence on the rate of saponification of methyl acetate gives the accelerating power? Since the velocity of the hydroxyl ion is less than that of the hydrogen ion, the conductivities yield a less accurate method of comparison than in the case of acids, and the ionizations have therefore been calculated for the concentration of one-fortieth normal, at which the accelerating power was measured. Base Accelerating power Ionization hydroxide 97 Lithium Sodium Potassium Ethylammonium Ammonium 97 97 16 2:5 The difficulties and the experimental errors of some of these chemical measurements are very considerable, and, in many cases, the solutions of the acids given in the table are not of comparable concentrations. Nevertheless, the remarkable general agreement of the results is quite enough to show the intimate relation which exists between the chemical activity of i J. Walker, Physical Chemistry, London, 1899, p. 277. CH. XII] 339 7 THE THEORY OF ELECTROLYTIC DISSOCIATION The mass-law. electrolytes in aqueous solution and their electrical conductivity. For solutions in other solvents no such numerical data are available. Kahlenberg has shown that chemical reactions which are practically instantaneous occur in non-electrolytic solutions in benzene? As an example, dry hydrochloric acid gas passed into a solution of copper oleate in benzene produced at once a heavy brown precipitate of copper chloride, though the solution, even at the instant of reaction, showed no more conducting power than did the pure benzene. Again, an insulating solution of stannic chloride in benzene mixed with the solution of copper oleate, gave instantly a copious precipitate. It seems, then, that electrolytic ionization is not in all cases the mode of operation of rapid chemical action, and that the encounters between two molecules must sometimes be accompanied by chemical interchanges. The phenomena of reversible chemical action have already been considered from a kinetic standpoint on pp. 205 and 206. The results can also be obtained by an application of the principles of energetics. The most direct way to treat the problem is to consider the increase of available energy due to the appearance of new molecules or atoms of given species during the process of chemical change?. This increase in free energy will involve two terms; one expressing the work a done in forming the particle at the temperature chosen and at a standard pressure, and, another giving the work required to bring by isothermal operation the new substance when formed to the actual pressure at which the system exists. If the system is a gas or dilute solution, the second term will be of the form RT log p/po, where p is the actual and po the standard pressure. Thus the change in the available energy of the system is a + RT log 6C, an expression already used on p. 26, where a is a function of the temperature T, R is the gas constant per gram-molecule and has the same value for all kinds of dilute matter, C is the final number of molecules of the given species per unit volume, and b is a constant expressing the dilution of the molecules at the standard 1 Jour. Phys. Chem. vi. 1 (1902). 2 Larmor, Phil. Trans. A. cxc. 276 (1897). Q 222 340 [CH. XII SOLUTION AND ELECTROLYSIS pressure and at the existing temperature. A reaction in the system involves the disappearance of 'molecules of some of the species present, and the appearance of others to an equivalent amount. When equilibrium is reached, the change of available energy arising from a further slight transformation of the kind considered must vanish; thus ni (az + RT log b,C1) + ng (az + RT log b2C2) +... =0, or, RT (log bınıb,2 ... + log 0,11 ,92...)=-(Nīdy + n2da + ...), where ny, N2, ... are the numbers of the molecules of the different types which are involved in the reaction, reckoned positive when they appear, negative when they disappear. We then see that CNC,M2... = K ......... ............(62), K being a function of the temperature alone. This expression is the mass-law of chemical equilibrium, originally derived by Guldberg and Waage from statistical considerations. This law of mass action has been applied to reversible chemical actions such as the dissociation of gaseous nitrogen peroxide and the like processes, and has been found to lead to results in accordance with the observed facts. It has been extended to electrolytic dissociation by Ostwald. For a binary electrolyte such as potassium chloride, it is natural to suppose that the change consists in the dissociation of one molecule into two ions; in this case in the equation of equilibrium 124 will be – 1, and Ny and nig will each be + 1, so that the equation becomes C-4C,C,= K . . . . . . . . . . . .........(63), or, since the concentration of the two ions must be the same, C-C2 = K .......... ............ (64), where C, denotes the molecular, and C, the ionic concentration. This result is explained on kinetic principles by assuming that the rate of dissociation is proportional to the active mass Cy of the remaining molecules; and that the rate of recombi- nation varies as the frequency of collision between the ions, a frequency which is proportional to the product of the active masses of the ions, that is to C,2. For equilibrium, the two rates of transformation must be equal, and we regain the mass equation. CH. XII 341 THE THEORY OF ELECTROLYTIC DISSOCIATION or Considering one gram-molecule of electrolyte dissolved in a volume V of solution, the ionization being a, we have (79) (9) *=K, V (1-a)=K ......................(65). This equation is called Ostwald's dilution law. It should represent the effect of dilution on the ionization of binary electrolytes; and, for small concentrations, when the ioniza- tion may be measured by the ratio of the actual equivalent conductivity to its value at infinite dilution, an experimental confirmation of its accuracy should be possible. Many observa- tions show, however, that the law fails to express the ionization of strong acids and salts, though Ostwald has confirmed it with considerable accuracy in the case of weak acids with small coefficients of ionization. For such bodies 1 -a is nearly equal to unity, and only varies slowly with dilution. The equation then becomes ū=K, or Q=VVK ........................(66), so that the molecular conductivity should be proportional to the square root of the dilution. If we determine a for a number of solutions of different strengths, and use our results to calculate K, we may expect the values obtained to be con- stant. The following table is given by Ostwald: Acetic acid. 씨 ​Moo K ·0000180 179 64 128 256 512 1024 4.34 6.10 8.65 12:09 16.99 23.82 32:20 46:00 0119 •0167 ·0238 0333 ·0468 ·0656 ·0914 •1266 182 179 179 180 180 177 342 [CH. XII SOLUTION AND ELECTROLYSIS V is the number of litres containing one gram-molecule; the molecular conductivity (in mercury units), and Mco its maximum value which is calculated as 364 from the velocities of the acetic acid ion and of hydrogen, determined by Kohlrausch from the conductivity of sodium acetate and mineral acids. The following are further examples of Ostwald's experi- ments. Cyanacetic acid. 100_ Moo 21.7 29:1 128 256 512 1024 78.8 105:3 139.1 176.4 219.1 260:9 297.3 38.4 48.7 60.5 72.0 82:1 0.00376 373 374 361 362 361 368 Formic acid Acetic , Monochloracetic acid Dichloracetic Trichloracetic , K='0000214 ·0000180 ·00155 051 1.21 Propionic acid Butyric » Isobutyric , Isovaleric , Caproic » .0000134 ·0000149 ·0000144 •0000161 ·0000145 If we have once determined the constant K for any elec- trolyte, we can, by the help of the equation, calculate the conductivity for any dilution. Ostwald considers that this constant, K, gives the “long sought numerical value of the chemical affinity.” If we choose states of dilution V, and V, for two different substances, such that the products V,K, and V K, are equal, then , and therefore a, must be the same for both. If we alter both dilutions in the same ratio, the products V,K, and. V,K, are still equal, so that the dilutions at which two substances are dissociated to the same extent are always pro- portional, whatever the absolute values of the dilution. This was experimentally discovered by Ostwald before he had applied the theory of dissociation to electrolytes. CH. XII] 343 THE THEORY OF ELECTROLYTIC DISSOCIATION As already stated, the dissociation of highly ionized electro- lytes does not conform to Ostwald's dilution law. The failure occurs not only in the case of acids and alkalies, when the con- ductivity curves are abnormal, but also in solutions of normal salts. Thus Ostwald gives the following numbers calculated from Kohlrausch's measurements for potassium chloride. a K 0.60 10 20 0:41 100 0.873 0:903 0.956 0.939 0.994 500 1000 0.21 0:18 0:16 Rudolphi has given an empirical relation which seems to hold for such cases, though no physical meaning has been attached to it. The equation is - -K, or 11 –a)2 V NV (1 - x) The values of the first constant for potassium chloride are: V 10 20 100 500 1000 0.866 0.890 0.942 0.974 0.980 1.68 1.61 1:54 1.61 1:54 Van't Hoff shows that equally good results are obtained from the equation (1 –a) Vz=K, or (i 2)y=K'. Thus for silver nitrate at 25° the comparable constants are : Ki (Rudolphi) K' (Van 't Hoff) 64 0·828 0.875 0.899 0.926 0.947 0.962 1.00 1:16 0.92 1:06 1.10 1:14 1:11 1:16 1:06 1.07 1.08 1.09 128 256 512 1 Zeits. phys. Chem. XVII. 385 (1895). 2 Zeits. phys. Chem. XVIII. 300 (1895). 344 [CH. XII SOLUTION AND ELECTROLYSIS Van't Hoff's equation can be deduced by the kinetic method on the assumptions that the number of molecules dissociating is proportional to the square of the whole number of undissociated molecules, and that the number of ions recombining is propor- tional to the cube of the whole number of ions, the equation of equilibrium being C = K'. Kohlrausch points out that Van't Hoff's formula, if written in the form = constant, or = constant, and divided on each side by C7, becomes C, constant Cat denotes the average nearness of the molecules, so that, if y be the average distance between them, we get the very simple relation =r x constant, the ratio between the ionic and the molecular concentrations being proportional to the average distance between the undis- sociated molecules. Turning from these empirical relations, let us consider once more Ostwald's original dilution equation, which extends the chemical law of mass action to the dissociation of electrolytes. In deducing the law by the application of thermodynamics, the restriction to dilute systems is necessary, in order that the reacting particles may be beyond each other's sphere of influence, and the change with dilution of available energy be thus independent of the nature of the solvent. Now, as we pointed out on p. 324, on the hypothesis that chemical forces are of electrical origin, the influence of a dissociated ion will extend far beyond the range at which the forces between the non-dissociated molecules cease to be sensible. A solution containing dissociated ions will therefore fail to show the properties of dilute matter at a much less concentration than will the solution of a non-electrolyte. It is not surprising, there- at which it is tested. It is possible that it would only be applicable at dilutions so great that most solutions of strong electrolytes would be almost completely dissociated; in fact, as already stated, it is possible that, as the concentration increases, the electric forces between the dissociated ions would become sensible sooner than any combination could occur. In the case of weakly dissociated bodies, like acetic acid, the number of ions at moderate concentrations is enormously smaller than for strong acids and salts; it is possible, also, that the presence of a large quantity of undissociated solate affects the properties of the medium and diminishes the electric forces between the separated ions. Such solutions, therefore, show the phenomena of dilute systems at comparatively high concentrations, and conform to the dilution law. The application of the mass law as hitherto considered is concerned only with substances which dissociate into two ions. For salts or acids, which, like barium chloride or sulphuric acid, may be expected to give three ions, equation (62) on p. 340 becomes C3° – K, and we get a3 V? (1a)=K, for the dilution law. If a is small we may write a=ºV2K ........................(67). In the case of weak polybasic acids, succinic for example, the ionization at high concentrations conforms to the law for mono- basic acids, and varies with the square root of the dilution in accord with equation (66) on p. 341. This behaviour indicates that the ions are H' and HA', where A denotes the acid group, and the dashes the valency of the ion. When about half the molecules are dissociated, some begin to produce three ions, and, at greater dilutions, the dissociation becomes normal in agreement with equation (67) above, indicating H', H', and A" as the ions. From strongly ionized bodies three ions are 346 (CH. XII SOLUTION AND ELECTROLYSIS usually formed at more moderate dilutions, as shown by the conductivity and the depression of the freezing point, though, as we have seen, some of them may be linked with solute or solvent molecules to form complex ions. For these bodies, as for the corresponding binary compounds, the theoretical dilution law fails. between When solutions of two electrolytes are mixed, there will, in general, be a change in the amount of ion- Equilibrium ization in both. For particular concentrations of bodies which conform to the dilution law, however, we can show that no such change occurs, and the solutions can be mixed without affecting the number or nature of the ions, or the mean conductivity. Any two solutions which fulfil these conditions were called by Arrhenius isohydric. Let us, as the simplest case, consider two simple electrolytes which possess one ion in common, such as two acids HA, and HA,. Let the coefficients of ionization be a, and 22, and the dilutions V, and V, respectively. Then, for the two solutions T = K, and a2 -02) =h2. (1-a7) V- If the solutions be isohydric, we can mix them without changing the ionizations; the total volume becomes V. + V2, and the number of hydrogen ions az + Oy. For the acid HA in the mixed solution, since the number of A ions remains unchanged at az, we have by equation (63) on page 340, . (a, tas) az (1-2)(Vi+V.)=K. Dividing this equation by the first, we get (Qz+az) Vi az + Qg Vi+V =l, or (Vi+ V.) az V 8 Thus Or - .....(68) Now ay/V, and az/V, are the respective concentrations of the hydrogen ions in the two isohydric solutions HA, and HA,. It follows, then, that solutions of electrolytes containing a common CH. XII] 347 THE THEORY OF ELECTROLYTIC DISSOCIATION ion are isohydric when the concentration of the common ion in the different solutions is the same. Two solutions with a common ion will so act on each other when mixed that they become isohydric, for then alone will the undissociated part of each be in equilibrium with the dissociated ion common to both. In deducing this result, the dilution law has been used; the investigation therefore only applies in the case of electrolytes which conform to that law. Nevertheless, similar principles probably hold in other cases, and we may use our conclusion to qualitatively elucidate the interaction of solutions of any two acids. If the solution of a strong acid like hydrochloric be mixed with that of a weak acid like acetic, equilibrium can only occur when the two acids are isohydric and the concen- tration of the hydrogen ions the same for both. In order to secure this condition, it is necessary that a large amount of the feebly dissociated acetic acid, and a small amount of the highly dissociated hydrochloric, should exist. Now when dilute hydrochloric acid is mixed with dilute sodium acetate, acetic acid is formed, and this process continues till the two acids are isohydric, and the dissociated hydrogen ions in equilibrium with both. A large quantity of undissociated acetic acid must therefore be formed, and consequently most of the acetate be decomposed. This replacement of a weak acid by a strong one is a matter of common observation in the chemical laboratory. As indicated on p. 336 however, it must be noticed that the relative strengths of two acids can only be determined when both remain within the sphere of action ; if one of them is removed by precipitation or evaporation, it will be completely replaced, irrespective of the relative strengths. The theory of isohydric solutions can also be applied to investigate the effect on the solubility of one salt of adding to its solution a quantity of another salt containing an ion common to both. Nernst has pointed outi that in all likelihood the equilibrium between a solid salt and its solution is primarily an equilibrium between the crystals and the undissociated dissolved molecules, which on the other hand, are themselves i Zeits. phys. Chem. IV. 372 (1888). U 348 [CH. XII SOLUTION AND ELECTROLYSIS in equilibrium with the dissociated ions. Under constant external conditions, therefore, we may conclude that the amount of the undissociated solute present in the liquid is not changed by adding more of either of its ions. In order to simplify the theory as much as possible, let us consider the case of a sparingly soluble salt, silver bromate for example?. The concentration of the silver ions can be increased by adding a soluble silver salt, and that of the bromate ions by adding a soluble bromate. Let us add a quantity of silver nitrate. The quantity of undissociated silver bromate is unchanged, and must still be in equilibrium with the silver and bromate ions. According to the mass law, the product of the concentrations of these two ions must be equal to the concentration of the undissociated salt multiplied by a constant; in this case the product must itself be constant. By increasing the number of the silver ions, then, the concentration of the bromate ions must be diminished in the same ratio. A bromate ion can only be precipitated in company with some positive ion; thus silver bromate, formed by the combination of its ions, is deposited to restore equilibrium. The effect of adding the silver nitrate therefore is to reduce the solubility of the silver bromate proportionally to the quantity of nitrate added. The effect of a soluble bromate is exactly similar, and the solubility of the silver bromate is lowered to the same extent as by an equivalent quantity of silver nitrate. This account of the subject has been quantitatively confirmed'. A solution of silver bromate, saturated at 24°:5, contains 0:0081 gram-equivalents per litre. Assuming that the salt is practically completely dissociated, the product of the concentrations of the two ions is 0.0081%, or 0:0000656. To such a solution, a quantity of silver nitrate was added sufficient to give a 0:0085 normal solution of the nitrate when dissolved in the volume of water which contained the bromate. Assuming complete dissociation for the silver nitrate also, let us calculate x, the total quantity of silver bromate which remains dissolved. The concentration i The details of the calculations which follow are taken from Walker's Physical Chemistry (1899), p. 294. CH. XII] 349 THE THEORY OF ELECTROLYTIC DISSOCIATION of the bromate ions is 2, and that of the silver ions 0.0085 + X. Thus, (0.0085 + x) x = 0.0000656, whence @=0:0049. An experimental measurement showed that the solubility was actually reduced from 0:0081 to 0:0051 normal. If the cal- culation be corrected for the changes in the ionization of the salts indicated by conductivity determinations, the theoretical number becomes 0:00506, even nearer to the observed result. Two sparingly soluble salts, shaken up with the same quantity of water, each reduce the solubility of the other. The saturated solutions of thallium chloride and thallium thiocyanate have concentrations of 0.0161 and 0.0149 normal respectively. If u and y denote the solubility of the two salts respectively each in presence of the other, the concentration of the Cl ions is x and that of the SCN ions is y, while the sum x + y gives the concentration of the thallium ions. We thus obtain ac (x + y)= 0.01612 and y (x + y)= 0·01492 whence we calculate that x is 0:0118, and y is 0·0101; direct experiment gives 0:0119 and 0.0107 for the same quantities. These results justify the use of the principles here involved in such cases as the electromotive force of concentration cells, etc., examples of which we have already considered (pp. 253, 254). Owing to the failure of the mass law for solutions of strong electrolytes, we should expect these results, which depend on the same principles, to be limited in their application. The concordance between theory and experiment in the cases given, indicates that, for very slightly soluble salts, the theory is justified. This result is of great interest, for it shows that at great dilution, when the ions are beyond each other's spheres of influence, the mass law holds for strong electrolytes. Attempts have been made to use this solubility method to determine the ionization of the salt added, but consistent results are obtained only when the salt precipitated is very slightly soluble? 1 Arrhenius, Zeits. phys. Chem. XI. 391 (1893). 350 [CH. XII SOLUTION AND ELECTROLYSIS These principles are often used in the chemical laboratory to precipitate salts from solution in a state of purity. Thus sodium chloride can be separated from a strong solution by the addition of hydrochloric acid, a very soluble substance also containing chlorine ions. The product of the concentrations of the ions of sodium and chlorine exceeds the equilibrium value, and salt is precipitated. The problem of the equilibrium of two electrolytes which have no common ion is much more complicated. When, for example, the solutions of two salts M 4, and M2A, are mixed, the final system will contain the ions M, M., Ā, and Ā,, together with undissociated molecules of M4A1, M,A,, M,A, and M,A1; the equilibrium to be investigated is that which holds between all these bodies under the conditions of the experiment. Of the four salts, any two which contain a common ion can be treated by the methods already adopted. Thus a solution of M_A, can be made isohydric with one of M_42. M2A, with regard to the other ion, and the solution of M,A, can be made isohydric with that of M.Ag. The conditions which must hold between the volumes of the four isohydric solutions to secure that their equilibrium is not disturbed when they are mixed, can be investigated on the assumption that they all conform to Ostwald's dilution law. For one of them, say M,A1, we have with the usual notation, an? = K. If all the solutions be now mixed without change of equili- brium, the number of the M, ions will increase in the ratio of (V + V)/V, where V, is the volume of the isohydric solution of M24, in which the concentration of the M, ions must be the same. The volume in which the M, ions are now contained is, however, Vi+ V + V: + V&, so that the concentration of the M ion is Vi+V a(V + V) Vi Vu+ V, + V + VaVi(Vi+ V + V: + V.) CH. XII] 351 THE THEORY OF ELECTROLYTIC DISSOCIATION Thus Similarly the number of A, ions is increased in the ratio (V + V)/V1, and its concentration becomes a(V + V) Vi (Vi+ V+ V: + V)' where V, and Ve are the volumes of the isohydric solutions of M.A, and M2A, respectively. The new equilibrium of the salt MA, will thus be given by the equation a(V,+ V) a(V + V) V (V + V, + V + V): V(V, + V + V + V) , 2= K. 1-a Vi+V,+V+ VA Hence by the dilution law a® (V. + V)(V+ V) (1-a) V(V+ V + V: + V) (1-a) Vi (Da + V) (V,+ V3) Vi(V + V + V + V.) which reduces to VV = V,V, ........ .......... (69), an equation giving the relation which must hold between the volumes of the four isohydric solutions, in order that there should be no disturbance in equilibrium when mixture occurs. In words, we may say that the products of the volumes of such pairs of solutions as contain no common ion must be equal to each other. The solutions were all isohydric; that is, they had the same ionic concentration. The equilibrium condition, therefore, means that the total number of ions in each of the four solutions must be the same. In the chemical equilibrium MA, + M,A, ŽM,, + M,A1, let us call the total masses of the four substances mi, nia, mz and me respectively, and their coefficients of ionization Qı, Az, Az and 04. For equilibrium on mixing, and therefore when equilibrium is reached in any case, our relation becomes maz. Me Q4 = m2,. Mzaz. This result is evidently an expression of the mass law, but it shows that the active mass of one of the substances we are considering is not its total mass, but only the fractional quantity which is dissociated into electrolytic ions. 352 [CH. XII SOLUTION AND ELECTROLYSIS We have seen that the solubility of a salt may be reduced by the addition of an electrolyte containing one of the same ions. On the other hand, under certain conditions, the addition of an electrolyte may increase the solubility of a precipitate or other sparingly soluble.body. For example, the small quantity of calcium tartrate which dissolves in water is highly dis- sociated. If hydrochloric acid be added, tartaric acid is produced, which, in presence of the ions of calcium chloride, etc., is only slightly dissociated. The concentration of the tartrate ions is therefore much reduced, the ionic product falls below the saturation value, and more calcium tartrate is dis- solved. Further applications of this theory of chemical equilibrium in electrolytes will be found in Arrhenius' paper, and in most books on Physical Chemistry. Thermal electrolytes. When two neutral salt solutions are mixed, there is, in general, neither evolution nor absorption of heat. properties of this experimental result has been formulated in what is known as Hess' law of thermo- neutrality. The dissociation theory indicates that, when all four possible salts are fully ionized, and consequently exist in solution in a dissociated condition, no appreciable change can occur on mixing, and no thermal phenomena can appear. If one of the reagents or one of the products of the action is only slightly dissociated, a separation of molecules or a combination of ions will take place when the solutions are mixed, and heat will be developed or absorbed. In the same way, the remarkable conclusion at which Thomsen arrived from his experiments on the heat of neutral- ization of acids and bases may be explained. He found that when a strong acid reacted with an equivalent quantity of a strong base in dilute solution, the heat evolved was always about 13,700 or 13,800 calories per gram-equivalent, whatever the acid and base used. The dissociation theory considers the reaction, for example, between hydrochloric acid and potash to be represented by the equation Å +ci++OH=K+CI+H,0. CH. XII] 353 THE THEORY OF ELECTROLYTIC DISSOCIATION The ions K and Cl suffer no change, but the H of the acid and the OH of the alkali unite to form water, which, being present in a relatively enormous quantity, is only dissociated to an exceedingly small amount. An exactly similar process occurs when any strongly ionized acid acts on any strongly ionized base, and it is thus evident why, in such cases, the heat evolution should remain about constant. The law of thermo-neutrality, and the constancy of the heat of neutralization of strong acids and bases have been explained in ways which do not involve the dissociation hypothesis. Crompton', for example, points out that the experiments of Thomsen prove that, when hydrogen is replaced in a mono- molecular organic compound by any radicle, the heat evolved is independent of the group with which the hydrogen was originally united. Extending this result to inorganic bodies, it might be that the heat of replacement of hydrogen in the acid is equal and of opposite sign to that of the replacement of hydroxyl in the base. The total heat of neutralization would then be zero, except for the thermal change accompanying the alteration in state of the elements of water, which before the action exist as parts of diluted foreign molecules, and after the action are added to the liquid solvent as part of itself. The heat evolution, then, would be a thermal value analogous to the heat of condensation of water from vapour to liquid, and the law of thermo-neutrality of reacting salts would hold good when no water is formed. Such a theory of course expresses the isolated facts to explain which it was framed, but it cannot connect the thermal and electric properties of solutions. In reactions with the weaker acids and bases, the ionization of which is less complete, the heat evolved will diverge from the normal value, for the salts produced are usually more dissociated, and ions will be formed during the process. For instance, in the solutions used by Thomsen, sulphuric acid is only about half dissociated, and shows a heat of neutralization higher than the normal, so that heat must be evolved when it is resolved into its ions. 1 1 Chem. Soc. Journ. Trans. LXXI. 951 (1897). W. S. 354 SOLUTION AND ELECTROLYSIS Since the energy associated with a quantity of substance when ionized is different from that associated ionization. With it when in the normal chemical state, the heat of formation in aqueous solution of the molecule of an electrolyte from its ions will generally be different from that evolved when it is produced from its non-ionized elements. The heat of ionization of an electrolytic substance can be calculated by an application of the principles of thermodynamics. In the deduction of the mass law of chemical equilibrium on p. 339, it was shown that the change of available energy of a system per molecule of isothermal reaction could be expressed in the form dy=ny&i + Noz Az + ... + RT (log 6,26,92 ... Cm. C, N, ...). Thus Oy = 840+ RT log K', where Sfo is a standard of reference, and K' is 6,99 6,102 ... K. As the condition of equilibrium at each temperature, dy must vanish, so that She-RT 100 R By partial differentiation, for unaltered materials, ) ( )=- Rag log K' =- Ralog K .......... (70), a result which is independent of the unknown term fo. In the free energy equation (p. 29) y=e+T nou - да H and e refer to changes in the free and internal energy respectively, so that X is equivalent to dy above. Now the heat à absorbed by the system is math ma chi 1=e=p=- =-T707 ). Hence from (70) we get 1= RT Y log K.....................(71) as the heat absorbed by the system per molecule of isothermal reaction. This expression, due to Van 't Hoff, is a more general form of equation (17) on p. 115, which gives the heat of • CH. XII] THE THEORY OF ELECTROLYTIC DISSOCIATION 355 solution of a substance in terms of the temperature coefficient of solubility. Equation (17) can of course be obtained from (71). If we make the assumption that the heat of reaction is independent of the temperature, which will restrict our result to somewhat small temperature ranges, we may integrate this new equation and obtain log i = a - .....................(72). These results apply to chemical changes in any dilute system, and may therefore be used to calculate the heat of ionization per gram-molecule when the constants K, and K, are known for two neighbouring temperatures. The coefficient of dissociation of aqueous solutions is generally found to decrease as the temperature rises; and by experiment- ally determining its value for different temperatures and calculating the rate of variation, Arrhenius? has measured the heats of formation of various molecules from their ions by means of this equation. It is important to observe that his results only apply to solutions in water, and that, for the strongly dissociated bodies, for which Ostwald's dilution law fails, it is not to be expected that this theory, depending on similar principles, should lead to true results for the heats of ionization. The numbers for strongly dissociated bodies in the following table are calculated from observations on decinormal solutions. Substance 1 at 21°.5 at 35° + 28 - 183 - 427 - 2103 - 3200 Acetic acid CH2COOH Propionic acid C,H,COOH Butyric acid C HCOOH Phosphoric acid H PO, Hydrofluoric acid HF Hydrochloric acid HCI Nitric acid HNO, Soda NaOů Potassium chloride KC1 Barium chloride BaCl, Sodium butyrate C,H,COONa - 386 - 557 - 935 – 2458 - 3549 - 1080 - 1362 - 1292 - 362 - 307 547 + 1 Zeits. phys. Chem. IV. 96 (1889); 1X. 339 (1892). 23–2 356 [CH. XII * SOLUTION AND ELECTROLYSIS From this table, by adding to the heat of formation of water from its ions that evolved by the completion of the dissociation Substance Calculated Observed Hydrochloric acid HCI Hydrobromic, HBr Nitric Acetic CH,COOH Phosphoric , H2PO4 Hydrofluoric HF » HNO, 13447 13525 13550 13263 14959 16320 13740 13750 13680 13400 14830 16270 » In the case of strongly dissociated substances, the number of molecules undissociated is so small that the variation from the normal value of the heat of neutralization is too slight to test the equation by experiment. For the weak acids, phosphoric, acetic, and hydrofluoric, which conform to the dilution law, the concordance is seen by the table to be satisfactory. From equation (71) on p. 354, it follows that, if the heat of formation is negative, that is, the heat of dissociation positive, the value of a (log K)/OT is also negative, and the dissociation must become less with increasing temperature. The con- ductivity is dependent on two factors, (1) the dissociation, and (2) the frictional resistance offered by the solution to the passage of the ions through it. If we call the reciprocal of this resistance the ionic fluidity of the solution, the mole- cular conductivity will be proportional to the dissociation and to the ionic fluidity. At great dilution the dissociation is complete, and the ions are so far apart that no change in temperature can affect the state of dissociation. Any alter- ation in conductivity with change of temperature must then be due to an alteration in fluidity, and the temperature coefficient of fluidity can be determined by measuring the temperature coefficient of conductivity at a dilution so great that the molecular conductivity. has reached its limiting value. Now the table on p. 355 shows that the heats of formation from their ions of the substances examined have a greater negative CH. XII] 357 THE THEORY OF ELECTROLYTIC DISSOCIATION value at the higher temperature. From equation (71) it follows that the rate of decrease of dissociation with increase of tem- perature must therefore increase as the temperature rises. If the temperature coefficient of fluidity either decreases with rise of temperature, keeps constant, or increases more slowly than the negative coefficient of dissociation, it is clear that a maximum conductivity must be reached at a certain tem- perature, beyond which any further heating will decrease the dissociation more than it increases the fluidity, and so, on the whole, diminish the conductivity Arrhenius calculated, by deductions from the equation, that and phosphoric acids, should have maximum values for the con- ductivity at 57º and 78° respectively. He then experimentally determined their conductivities at different temperatures, and actually found maxima at 55° and 75º. Sack", by measuring the conductivity of copper sulphate solutions in closed vessels, found a maximum at 96° for a 0:64 per cent. solution ; calcu- lation by Arrhenius' method gives 999 for a solution of this concentration. The heat of ionization hitherto considered is the heat evolved when the molecule of a salt or acid is dissociated into its ions in aqueous solution. The determination of the heat change associated with the formation of an equivalent weight of ions during the process of solution of a metal is a different problem, and Ostwaldº has attacked it on the assumptions that the single potential difference at the interface between a metal and a solution is known, and that the Gibbs-Helmholtz equation E=2+0000 is applicable not only to the whole cell, but also to each potential difference, and 1 the total heat effect at the electrode, which measures the heat of ionization generated by the passage of the metal into the ionic state. From this point of view, i Wied. Ann. XLIII. 212 (1891). 2 Lehrbuch, p. 955. 358 [CH. XII SOLUTION AND ELECTROLYSIS such thermo-chemical data as the heat of precipitation of copper from its solution by zinc, are always the sums or differences of two heats of ionization, and if one heat of ionization is known, others may be calculated from thermo- chemical values. The following are some of the heats of ionization given by Ostwald : Per gram- equivalent Per gram- atom Potassium +612 Zinc +331 Cadmium +165 Thallium + 8 Iron (ferrous) +202 Per gram- equivalent +612 +166 + 83 + 8 +101 Per gram- atom Iron (change from ferrous to ferric ions) – 121 Lead - 14 Copper - 177 Silver - 264 Mercury -- 207 - 7 – 264 - 207 The thermal unit is 100 calories. The results depend on the presumed correct determination of single potential dif- ferences by the use of capillary electrometers and dropping electrodes. The conductivity of carefully distilled water is very small, and it can therefore only be dissociated to a Dissociation of water. very slight extent. The best water which can very sigare be prepared by distillation in presence of air has a conductivity of about 0.7 x 10-6 measured in reciprocal ohms across a centimetre cube. Kohlrausch and Heydweiler? have distilled water in a vacuum and collected it directly in a resistance cell, which had been kept for ten years full of distilled water in order to dissolve all the soluble constituents of the glass; in this manner they obtained water with a conductivity of 0.015 x 10-6 at 0°, and 0:043 x 10-6 at 18°. From the experimental results alone it is impossible to tell whether the slight trace of conductivity which remains is due to residual impurities or to ionization of the water itself, but an examination of the question may be made from the thermo- dynamic standpoint. The constant heat of neutralization of i Wied. Ann. LIII. 209 (1894). In the paper the conductivity is expressed in terms of that of mercury; the numbers have here been reduced to reciprocal ohms across a centimetre cube. CH. XII] 359 THE THEORY OF ELECTROLYTIC DISSOCIATION strong acids and alkalies is due on the dissociation theory to the combination of the ions of water, and therefore gives for the heat of ionization per gram-molecule a value of 13,700 calories at 18°. Van 't Hoff's equation (71) än log K = RT2 in combination with the dilution law for weak binary electro- lytes which shows, as on p. 341, that K is Q/V, leads to the result 1 θα λ a ƏT-2RT2 from which the temperature coefficient of the dissociation can : соод theory, depends on the product of the dissociation and the sum of the ionic mobilities, which varies with the ionic fluidity. The ionic mobilities of the hydrogen and hydroxyl were found by experiments on 0:001 normal solutions of potash, hydrochloric acid, and potassium chloride, to vary with temperature in accordance with the equation 104 (u + v) = 352 +8:35, t being the temperature on the Centigrade scale. At this great dilution the ionization of the solutes may be taken as complete, so that the influence of temperature on conductivity is due to its effect on fluidity alone. The total temperature coefficient of conductivity of pure water calculated from these data is 0.0581. The experiments showed that, as con- tinual purification of the water lowered its conductivity from 0.29 x 10-6 to 0.043 x 10-6, the temperature coefficient of its conductivity increased from 0.027 to 0:0532. It was hence estimated that the temperature coefficient would rise to the thermodynamic value when the conductivity had sunk to 0:0386 x 10-6 at 18°. This result, then, was taken to be the conductivity of pure water. It will be seen that about ten per cent. of the conducting power of Kohlrausch's best water is due to impurities. From the conductivity of pure water, its dis- sociation can be calculated ; and Kohlrausch's values indicate that the number of gram-equivalents dissociated per litre is 360 SOLUTION AND ELECTROLYSIS (CH. XII 0.35 x 10–7 at 0°, 0.80 x 10-7 at 18°, 1.09 x 10-7 at 26°, and 2:48 x 10-7 at 50°. Thus a cubic metre of water at 18° contains about 1.4 milligrams of dissociated molecules, or 0:08 milligrams of hydrogen ions. It may be observed that the ionic mobilities assumed in this investigation are the maximum values. Now at extreme dilution the equivalent conductivity of acids and alkalies diminishes, and it is possible that this phenomenon may somewhat affect the result of the calculation. Another value for the dissociation of water has been obtained by examining its influence on chemical reaction velocities. Methyl acetate and water form methyl alcohol and acetic acid at a rate proportional to the number of hydroxyl ions present in the solution. Wijst used this reaction to measure the dissociation of water; he prepared an aqueous solution of methyl acetate carefully freed from acid or other impurity, and titrated it at intervals with standard alkali to measure the amount of acetic acid produced. The acid, as it is formed, retards the action, so that it is necessary to estimate the rate of transformation at the beginning of the process. The concentration of the dissociated ions appeared to be about 1.2 x 10-7 gram-equivalents per litre at 25°. . A third method of estimating the dissociation of pure water has been used by Ostwald? A plate of spongy platinum in contact with hydrogen and an electrolyte acts as a hydrogen electrode, and if two such electrodes are arranged, one in an acid and the other in an alkali, the system may be treated as a concentration cell with regard to the hydrogen ions. In a normal acid solution, owing to the incomplete ionization, the concentration of the hydrogen ions is about 0:8, so that the concentration of the same ions round the alkali electrode can be calculated from the logarithmic formula [(48) p. 248] EriRT qy with the notation there indicated. The electromotive force of the cell is complicated by the potential difference of contact i Zeits. phys. Chem. xi. 492 ; XII. 514 (1893). 2 Zeits. phys. Chem. XI. 521 (1893). CH. XII] 361 THE THEORY OF ELECTROLYTIC DISSOCIATION between the two solutions, as was pointed out by Nernst?; and at 18° the corrected value is given as 0·81 volt. Putting in this number, we may consider the effect of the liquid contact to be eliminated and assume the transport ratio r to be 0.5, and Van 't Hoff's factor i to be 2. The gram ionic charge q is 9644 C.G.S. units, and y the valency of the ions is 1. Transforming to common logarithms, the equation then gives 0-81 = 0·0575 logo =1014. Since P, is 0:8, P, the concentration of the hydrogen ions in the alk ali solution is 0:8 x 10–14. By the mass law we know that the product of the two ionic concentrations divided by the concentration of the undissociated water should be a constant. The water is present in large excess and its quantity may be taken as unalterable, so that the ionic product itself is constant, and will have the same value in pure water as in the solution of the hydrogen and hydroxyl ions must be equal, and the dissociated fraction is therefore 0:8 x 10-7 gram-equivalents per litre. This exact agreement with Kohlrausch's result may not be justified by the approximate nature of the calculations, but it shows that values of the same order are obtained in the two ways. The function The differences which exist between the conductivities of the same substance when dissolved in different of the solvent. solvents show that the power solvents show that the power of conducting a current depends on the nature of the solvent as well as on that of the solute. The conductivity depends on two factors, the ionization and the ionic fluidity of the liquid, and, to secure ready conduction, both these properties must have high values. A suggestion made independently by J. J. Thomsonand Nernst3 may possibly explain the property possessed by certain i Zeits. phys. Chem. xiv. 155 (1894). 2 Phil. Mag. [5] XXXVI. 320 (1893). 3 Zeits. phys. Chem. XI. 220 (1893). 362 [CH. XII SOLUTION AND ELECTROLYSIS solvents of ionizing substances dissolved in them. If the forces holding the ions together in a molecule are electrical in their nature, they will be much weakened by immersing the molecule in a medium of high specific inductive capacity.. The effect can be illustrated by considering the influence of a mass of conducting material placed near two little particles charged with opposite kinds of electricity. The result of the presence of the conductor can be represented by imagining that electrical images of opposite sign are formed near the charges just inside the conductor. The external forces due to the charged particles are led may be so much diminished that separation may Fig. 65. occur. The effect of an insulator of high dielectric constant is similar in kind, though rather less in magnitude; and, other things being equal, the relative ionization powers of solvents should be proportional to their specific inductive capacities. Some results, which, as far as they go, support this con- clusion for solutions in water, methyl alcohol, and ethyl alcohol, have been given by the present writer? The specific inductive capacities of the three solvents are, according to Tereschin : water, 83:7: methyl alcohol, 32:65 : ethyl alcohol, 258. If we suppose provisionally that the resistances offered by these solvents to the motion of the ions are in about the same ratios as their viscosities, we must divide these numbers by 100, 63 and 120, respectively. We then get for the theoretical ratio of the conductivities, An investigation by Völlmer showed that, for many salts, the ratio of the conductivities in the three solvents was Water 100 Methyl Alcohol 73 Ethyl Alcohol 34. It seems probable, then, that the specific inductive capacity and the viscosity are important factors in determining the relative ionization powers of solvents. More recently an at- tempt was made to ionize water by dissolving it in different 1 Phil. Mag. xxxvIII. 392 (1894). CH. XII] 363 THE THEORY OF ELECTROLYTIC DISSOCIATION solvents. The object of the work was not attained, but it was shown by Novak and by the writer that, for mixtures of water with excess of formic acid, of which the dielectric constant is about 62, the conductivity curve is more like that of an electrolyte in water than it is when substances of lower dielectric constant, such as acetic acid, are used as solvent? Slight dissociation of water dissolved in methyl alcohol has been found by Carrara, who shows that extremely dilute solu- tions conform to the mass law?. On the other hand there seem to be many exceptions to this rule of concordance between ionizing power and dielectric constant. Liquefied ammonia and sulphur dioxide dissolve salts to form solutions which conduct well, but both solvents have low specific inductive capacities. Other exceptions have been given by Kahlenberg and Schlundt. In view of the well- known fact that many aqueous solutions, such as those of ammonia and acetic acid, are only ionized to a very small extent, it is evident that no such rule as that under discussion can be universally true. Influences due to the specific nature both of solvent and solute must prevent any complete generali- zation. The fundamental idea of the Thomson-Nernst theory is, however, a valuable advance towards the explanation of the ionizing power of solvents. It is worthy of remark that, as well as reducing the forces between ions, the conducting body in Figure 65 will attract each ion to itself. The same thing would occur in a solvent of high specific inductive capacity. When the forces between two ions have been loosened, a slight collision with other mole- cules, or with molecules of the solvent, may suffice to cause dissociation; the liberated ions may be annexed by the solvent, and loose compounds formed. The ions, being dissociated from each other and readily passed on from one particle of the solvent to the next, would then be able to work their way through the liquid under the action of the external electric forces. 1 Phil. Mag. [5] XLIV. 1 and 9 (1897). 3 Gazz. Chim. Ital. xxvII. 1. 422 (1897). 3 Journ. Phys. Chem. v. 382 and 503 (1901). 364 Il SOLUTION AND ELECTROLYSIS [CH. XII Brühl has pointed out that since oxygen can act as a quadrivalent as well as a divalent element, water and other substances containing it must be looked on as unsaturated compounds. Hence arise their high dielectric constants, great powers of ionization and readiness of combination. The ions in such substances may be supposed to be loosely and distantly connected, so that the electric moment of a molecule is great. Such a molecule when in solution will come under a powerful influence from any ion it encounters, and is therefore easily dissociated. Alcohols, ketones, ethereal salts, and acids also contain oxygen, and their dissociating power decreases as their molecular weight rises and their content of oxygen diminishes. The valency of nitrogen, like that of oxygen, can vary, and nitrogen compounds, nitriles, etc., give conducting solutions. dissociating power. Dutoit and Aston? have further remarked that the liquid solvents considered above, when examined by the capillary methods of Ramsay and Shields and otherwise, are found to consist of polymerized molecules. It is probable that all these properties are connected, though again excep- tions to any law of exact correlation have been indicated by Kahlenberg dissociation. Solutions of salts which are strong electrolytes give a neutral reaction; but a salt such as chloride Hydrolytic or nitrate of copper or zinc, containing a strong acid and a weak base, is found to give an acid solution, or if the base is strong and the acid weak, as in sodium carbonate or potassium cyanide, the reaction of the solution is alkaline. These results are explicable if we remember that water is to a slight extent dissociated, and may thus act either as a weak acid in virtue of its hydrogen ions or as a weak base because it contains hydroxyl. When a salt MA is dissolved in water, the reversible decomposition known as hydrolysis MA + HOH= MOH + HA i Ber. XXVIII. 2866 (1895); Zeits. phys. Chem. XVIII. 514 (1895); XXVII. 319 (1898). 2 Compt. rend. cxxv. 240 (1897). CH. XII] 365 THE THEORY OF ELECTROLYTIC DISSOCIATION may produce a non-electrolytic dissociation of the salt. This process is always possible, and must therefore occur to some degree in every case. The condition of equilibrium, equation (69) on p. 351, shows that the product of the ionic concentrations must be the same on each side of the equation. The ionic concentra- tion of water is excessively small, so that when both the acid and base are strongly dissociated, they must be present in very small quantities, and there is practically no hydrolysis. On the other hand, if the salt contains a weak acid or base, having an ionic concentration comparable with that of water, the conditions of equilibrium will require an appreciable amount of acid or alkali, and a considerable fraction of the salt will be found to be hydrolytically dissociated. If the acid is strong and the base weak, there will now be an excess of hydrogen ions, and the solution will have an acid reaction, while if the base is strong and the acid weak, that reaction will be alkaline. In determining experimentally the amount of hydrolysis in any given case, it is impossible to estimate the acid or base produced by the usual chemical methods, for, by them, the equilibrium would be disturbed, and progressive hydrolysis would eventually decompose all the original salt. Measurements of optical or other physical properties of the solutions can, however, be employed, and the accelerating influence on certain reactions of the free hydrogen or hydroxyl ions has also been used to investigate the subject. The velocity constant for the catalysis of methyl acetate, or the inversion of cane sugar (p. 337), is approximately proportional to the number of free hydrogen ions present in the solution, while the hydroxyl can be estimated by observing the initial rate of saponification of ethyl acetate. The numbers in the first table which follows are given by Walker' as the percentage hydrolysis of the hydrochlo- rides of weak bases, at a temperature of 25°, and a dilution of 32 litres per gram-molecule. Aniline 2.6 Orthotoluidine 3.1 Paratoluidine 1.5 Urea 76 i Physical Chemistry, p. 281. 366 [CH. XII SOLUTION AND ELECTROLYSIS The next table is due to Shields, and expresses the per- centage hydrolysis of salts of weak acids and strong bases at 24°, and at the given dilutions per gram-molecule. Dilution in litres Potassium cyanide Sodium carbonate Hydrolysis 0:31 0.72 1.12 2:34 2.12 3:17 4.87 7.10 3:05 6.65 Potassium phenate 0.92 Borax Sodium acetate 0.008 The amount of hydrolytic dissociation being small in all these cases, the mass law simplifies to a proportionality between the percentage ionic concentration and the square root of the dilution (see p. 341), and this result is borne out by the values for the more dilute solutions given above. In all these cases the hydrolysis is slight; but Shields found that trisodium phosphate was about 98 per cent. dissociated into free caustic soda and phosphoric acid at a dilution of 50 litres, and Walker states that salts of the very weak base diphenylamine are almost completely hydrolysed by water. Another case of considerable hydrolytic dissociation is found in salts of the weak base ferric oxide; in fact, ferric hydrate can be obtained in a soluble form by placing ferric chloride in a vessel separated from a large volume of water by a sheet of parchment paper. After some days, owing to progressive hydrolysis, nearly all the hydrochloric acid will be found to have passed into the water, leaving the iron behind as a brown solution of ferric hydrate. Since the equivalent conductivity of hydrochloric acid is much greater than that of a normal salt, it is possible to roughly estimate the amount of hydrolysis in a solution of ferric chloride 1 Phil. Mag. (5) xxxv. 365 (1893). CH. XII] 367 THE THEORY OF ELECTROLYTIC DISSOCIATION LI from the conductivity data. Taking the figures for the acid and for the ferric chloride given in the Appendix, and assuming that the equivalent conductivity of a normal salt is about 100 in reciprocal ohms, it is easy to calculate that a solution of ferric chloride at a dilution of 1000 litres is hydrolysed to about 56 per cent. This result neglects the influence of the residual ferric chloride on the dissociation of the acid and is therefore probably too low. Ferric acetate, which has both a weak acid and a weak base, seems to be more completely hydrolysed, the conductivity being of the same order as that of pure acetic acid'. Conclusion. The theory of electrolysis described in this chapter has proved one of the most stimulating hypotheses in the recent history of physical science. At the outset it met with much opposition, chiefly from chemists who held that its fundamental demands were inconsistent with well-established chemical conclusions. At present, criticism comes mainly from another side, and seeks to show that the relations which the theory suggests between the electrical, osmotic, and chemical properties of solutions, aqueous and other, fail when examined experimentally. The reasons for such failure have been pointed out in this chapter; the theory only indicates the relations in question under certain simple con- ditions, which can seldom be secured in practice. As experi- mental arrangements approximate to ideal conditions, the correspondence between theory and observation increases, and the variations in other cases are explicable by causes suggested in the development of the theory itself. We must again em- phasize the complete mutual independence of the theory of ionic dissociation and any particular view of the nature of solution or the mode of action of osmotic pressure. It is quite poss- ible that solution is a process of chemical combination; the dissociation required by the electrolytic theory is a separation of the opposite ions from each other, and would not in the least prevent a connexion of those ions with molecules of the solvent. Some form of dissociation theory seems to be clearly 1 Whetham, Phil. Trans. A. CLXXXVI. 516 (1895). . 368 [CH. XII SOLUTION AND ELECTROLYSIS indicated by the electrical properties of solutions, and, until these properties are otherwise explained, the theory as at present formulated will be a guide in further investigation. The extended study of more concentrated solutions will throw light on the nature of the interactions between the different solute molecules, and between the solute and the solvent; the effects of these interactions on many of the properties of any given solution are eliminated by working at such extreme dilution that the dissolved substance conforms to the laws of dilute matter. The complete theory of electrolysis needs further experimental data upon which to build, but the fundamental conception of ionic dissociation seems to secure a foundation for further development. CHAPTER XIII. DIFFUSION IN SOLUTIONS. Theory of diffusion. Experiments on diffusion. Diffusion and osmotic pressure. Diffusion of electrolytes. Potential differences between electrolytes. Liquid cells. Complete theory of ionic migration. Electrolytic solution pressure. Diffusion through membranes. Theory of diffusion. It is well known that a solution, left to itself, gradually becomes of equal concentration throughout. This process implies an automatic drift of the dissolved substance through the liquid, and has received the name of diffusion. The diffusion of matter is analogous to the conduction of heat, and Fick applied Fourier's treatment of the latter phenomenon to the elucidation of the former. The quantity of substance which diffuses through unit area in one second may be taken as proportional to the difference in concentration between the fluids at that area and at another parallel area indefinitely near it. This difference in concentration is propor- tional to the rate of variation of the concentration c with the distance x, so that the number of gram-molecules of solute which, in a time ot, cross an area A of a long cylinder of constant cross section is &N, =- DA 90 8t ..........(73), where D is called the diffusion constant or the diffusivity. do i Pogg. Ann. xciv. 59 (1855). W. S. 370 [CH. XIII SOLUTION AND ELECTROLYSIS do At another area at a position 8 + 8x near the first, the concentration will be c-40 8x and the transfer across it is &N=- DA (0 - Save) &t. Hence in unit time the element of volume comprised between the two areas will on the whole gain in contents by 8N, – 8N.= DA TO OP. But the volume of this element is Ada, and the rate of increase of concentration is dc/dt. We thus obtain the equation of propagation Da o te de se des d²c de or ºdac2dt **** ...................... (74) This differential equation represents the general nature of diffusion. It can be integrated for definite cases, when the process is simplified by the geometrical and other conditions of the system. on diffusion. A systematic investigation of diffusion without any separat- ing membrane was first made by Graham?, who Experiments immersed in a lonero immersed in a large volume of water a wide- mouthed bottle containing a solution, and after some time measured the quantity of substance in the water. By this method he found that acids diffused about twice as quickly as neutral salts, and that the rate of diffusion of these salts varied much according to their composition. Two dissolved substances diffused independently of each other, so that it was possible to separate the constituents of some double salts, the alums for example, which are decomposed by water. The quantity which diffused was found to be nearly propor- tional to the concentration of the original solution, and to depend largely on the temperature. Substances like tannin, 1 Phil. Trans. 1850, pp. 1, 805; 1851, p. 483. CH. XIII] 371 DIFFUSION IN SOLUTIONS albumen and gums, diffused very much more slowly than the other bodies examined, and only at about one-fiftieth the rate of hydrochloric acid. These less diffusible bodies are non- crystalline, and Graham called them colloids in distinction to the more diffusible crystalloids. Weberl was the first to work out a satisfactory method of determining the absolute value of the diffusion constant in Fick's equation. When two plates of amalgamated zinc are placed in two solutions of zinc sulphate of different concen- trations, the solutions being in contact with each other, a difference of electrical potential is produced between the plates which is proportional to the difference in concentration, pro- vided that difference is small. A concentrated solution of zinc sulphate was placed in the lower part of a cylindrical vessel, the bottom of which was made of an amalgamated zinc plate, and a dilute solution gently poured in on the top of the first. The electromotive force between the lower zinc plate and a similar plate placed in the topmost layer of liquid was measured, and found to decrease as the difference in concen- tration became less. If we apply Fick's law to this case we get an infinite series in the expression for the electromotive force, but when the time is long, the first term only is impor- tant, and we get, if H is the height of the vessel, and t the time, Erbe + 2 Dt...... ............. (75). 2 The following table gives the observed values of HD, which should be constant if Fick's law holds good. Days 4–5 2032 5–6 •2066 6-7 2045 7_8 •2027 8-9 •2027 9-10 2049 10/11 .2049 Mean •2042 i Wied. Ann. VII. 469 and 536 (1879). 24—2 372 [CH. XIII SOLUTION AND ELECTROLYSIS Stefan? showed that in the case of a very long cylinder, in which the concentration at one end remains constant, the quantity diffusing through an area A should be, according to Fick's law, N=cAN DE To apply this to a finite cylinder we must imagine that the amount which would have passed beyond the limiting layer is reflected, and, travelling backwards in accordance with the same laws, is added to the quantity present in the lower layers. Experimentally realizing these conditions, Scheffer2 placed a solution underneath a volume of pure water and measured the quantity of substance which diffused upwards. The following are some of his results, n being the number of molecules of water in which one molecule of substance is dissolved. Substance Temperature 11 7.2 35 Hydrochloric acid Nitric acid Sulphuric acid Acetic acid Potash Ammonia Urea Mannite 426 18.8 84 2.67 1.84 1.78 1.73 1.07 0.77 1.66 1.06 0.81 0:38 13.5 13.6 4.5 75 16 110 220 In general the diffusion constant was found to be independent of the dilution, but, in the case of hydrochloric acid, it appeared to increase somewhat with the concentration. Grahams and Voigtländer4 found that the rate of diffusion in solid agar-agar jelly solutions was nearly the same as in i Wien. Akad. Ber. LXXIX. 161 (1879). 2 Ber. xv. 788, xvi. 1903 (1882-3), and Zeits. phys. Chem. 390 (1888). 3 Phil. Trans. 1861, p. 183. 4 Zeits. phys. Chemie, III. 316 (1889). CH. XIII] 373 DIFFUSION IN SOLUTIONS water, and, as these jellies obviate all disturbing effects due to shaking or convection currents, they have been extensively employed. For a 0.72 per cent. solution of sulphuric acid, diffusing into a cylinder of agar jelly, Voigtländer gives the following numbers; N represents the number of milligrams of sulphuric acid diffusing through a given area. The results confirm Stefan's formula. Time in minutes NVO 60 480 2880 0:30 1:08 3:10 7.05 1.04 1:08 1.09 1:02 The distance to which a determinate concentration reaches is proportional to the square root of the time of diffusion. Thus the formula can be tested and the constants determined by tracing the decolorization of a dilute alkaline solution, coloured red by phenolphthallein, as the acid diffuses upward. The following table, due to Voigtländer, gives the value of the diffusivity at 0°, 20° and 40°, and, in the last two columns, the mean temperature coefficients from 0° to 20º and 20° to 40°. Substance D. D20 D40 a2 Formic acid Acetic , Propionic acid Sulphuric, Hydrochloric acid Nitric acid Potash Soda Potassium chloride Sodium chloride Calcium 12 Barium 2 1.49 1.04 0.882 2:01 ·0306 •0326 0358 •033 0:472 0:318 0.245 0.637 1.07 1:10 1.01 0.764 0.786 0.535 0:394 0·525 0.867 0.64 0:514 1.21 2:06 2:10 1.75 1.26 0228 ·0245 0261 ·0236 ·0246 ·0226 ·0209 ·0195 ·0219 •0243 1:40 2:36 1:35 2:18 1071 1.40 1:58 *026 •024 ·0279 0332 1.04 0.98 ·0232 0306 374 [CH. XIII SOLUTION AND ELECTROLYSIS When the concentration of different parts of a solution is not uniform, the osmotic pressure must also Diffusion and osmotic pressure. . vary. By imagining the parts of the solution valy separated by ideal semi-permeable membranes, we see that the osmotic pressure is the force per unit area, or the partial pressure, which must be applied, by the diaphragm or otherwise, to the dissolved molecules in bulk in order to prevent their diffusion. By the principle of reaction, it follows that, in a solution of varying concentration, the force which causes diffusive translation of the molecules in a thin slice of the liquid is the reversed difference of osmotic pressures on the two faces of the slice? The phenomena of diffusion have been investigated on these lines by W. Nernst? and M. Planck. If we have a vertical cylinder with a solution of some non- electrolyte in its lower part, and pure water at the top, the dissolved substance gradually makes its way upwards through the water, and, neglecting the small disturbing effect of gravity, a uniform solution will finally result. At a height : in the cylinder let the osmotic pressure be P, so that if A be the area of cross section, the substance in the layer whose volume is Adx finds itself under the action of a force equal to – AP, the negative sign being taken because the force acts in the direction in which the pressure decreases. If c be the concentration in gram-molecules per cubic centimetre, the force which in this layer acts on each gram-molecule is A dP 1dP A dx - č dx * Let F denote the force required to drive one gram-molecule through the solution with the velocity of one centimetre per second. Since the velocity of drift is constant, F must also denote the resistance offered by the viscous medium. The velocity attained is 1 dp F dæi i Larmor, Aether and Matter, p. 293. 2 Zeits. phys. Chem. 11. 615 (1888); iv. 129 (1889). 3 Wied. Ann. XL. 561 (1890). CH. XIII] DIFFUSION IN SOLUTIONS 375 and if &N be the number of gram-molecules which cross each layer in a time 8t, since the number crossing unit area per second is proportional to the concentration and to the average velocity of the individual molecules, we get 1 dP 1 dP Ac&t=- FA die &N=- La Coc When the solution is dilute, and there is no polymerization or dissociation of molecules with change of concentration, we may apply the gas equation for the osmotic pressure, and write P=cRT, the value of the constant R corresponding to one gram-molecule of any substance being taken as usual. This gives &N=-114 90 St .................. (76). By comparison with Fick's equation (73) &N=- Da Le ot, D, the diffusion constant, is seen to correspond to the factor RT/F. The slow rate of diffusion has led to the adoption of the day instead of the second as the unit of time for experimental work, so that the observed diffusivity D is given by the expression D dc st. &N=- 86400 A daº From equation (76) we see that the force required to drive one gram-molecule through the solution with a velocity of one centimetre per second is RT A do st F=- Ñ A da 86400 RT CD . Thus if we know the diffusion constant, we can calculate the force required to produce unit velocity. Voigtländer gives 0:472 as the diffusivity of formic acid at 0° C., and from this we can calculate that the force required to drive one 376 [CH, XIII SOLUTION AND ELECTROLYSIS gram-molecule (46 grams) of formic acid through water with a velocity of one centimetre per second is equal to the weight of 4340 million kilograms. The necessity for such an enormous force is at once realized if we remember the minute size of the molecules and the consequent great influence of the resistance of the medium. A solution of uniform temperature will in the end become homogeneous; but if the upper layers be kept hotter, the con- centration in the lower layers must be greater, in order that the osmotic pressure should be the same throughout. This result was experimentally established by Soretand explained as above by Van 't Hoff? The experiments supply a method of determining the influence of temperature on osmotic pressure, and the results are in accordance with the gas law for dilute solutions. If the osmotic pressure-gradient were the only driving force, the different mobility of the two ions of an Diffusion of electrolytes. electrolyte, such as hydrochloric acid, would cause separation between them. In a solution of bydrochloric acid at the bottom of a tall glass cylinder, with pure water lying above it, the hydrogen ions travel faster than the chlorine, and carry their positive charges with them, leaving the lower layers negatively charged. An electrostatic force thus arises, which opposes the process of separation, and keeps the number of opposite ions in each part of the system very nearly the same. Nevertheless some separation does occur, and this explains the fact that water, in contact with an aqueous solution of an electrolyte, takes, with regard to it, a positive or negative potential as the positive or negative ion travels the faster. When solutions of two different electrolytes are placed in contact, a similar state arises. Let us suppose that we have a solution of hydrochloric acid in contact with one of lithium bromide. On the one hand more hydrogen ions than chlorine ions will diffuse out of the acid solution, and therefore the - 1 Ann. Chim. Phys. XXII. 293 (1881). 2 Zeits. phys. Chem. I. 487 (1887). CH. XIII] 377 DIFFUSION IN SOLUTIONS salt solution will receive a positive charge. On the other hand, more bromine ions than lithium ions will diffuse from the salt solution into the acid, and thus the potential difference will be increased. Let us return to the consideration of the solution of a single electrolyte containing two monovalent ions, placed beneath pure water. From the velocities of the two ions under unit potential gradient, as found by Kohlrausch's theory, it is easy to deduce the velocity with which they will travel when unit force acts on them. Let us call these velocities U aud V for the cation and anion respectively. The actual [ U dᏢ , Ꮴ dᏢ velocities in our case will therefore be - and -- so that the amounts passing any cross section of the cylinder in a time st are dp -UA St and - VA - St. dP When U is different from V, a difference of potential is set up; with the effect, on reaching a steady state of electric separation, of making the ions travel together. If the poten- tial gradient is dE/dx the force on a gram-equivalent of an ion carrying a charge q is qd E da, and numbers of the two ions which would cross, under the action of this force alone, are DE dE – UAcq 8t and + V Acq Under the influence of both the osmotic and the electric forces the number of gram-equivalents which diffuse in a given time must be equal, so that we get &N=- UA8t (ale + og det -- VAS (adre - ca este; or eliminating dE/dx, 2UV DP SN = MTI V da For dilute solutions we may assume that the gaseous laws hold good, so that P=cRT, 378 SOLUTION AND ELECTROLYSIS [CH. XIII C, the concentration, being the reciprocal of the volume in which one gram-molecule is dissolved. Therefore SN=-20% Bir A WC st =*U + VRTA MC St. dic We shall need the intermediate steps of this investigation when we consider Nernst's account of contact differences of potential; this last equation merely states that the resistance offered by the liquid to the passage of an electrolyte is the sum of the resistances offered to the passage of its ions, and can be directly deduced on that assumption without further electric hypotheses. Thus the osmotic pressure of a binary electrolyte has double the normal value, so that the number of gram- molecules of hydrochloric acid diffusing across any section of the vessel in a time dt is, by equation (76), 2RT , dc FA Trot. velocity are 1/U and 1/V respectively, so that the resistance to hydrochloric acid is 1 1 U+ V p=71+ = UV , and we recover Nernst's equation 2UV dc 8N=- 21V RTA SN=- U + V From the general theory of diffusion we have already deduced equation (73) &N =-DA CC St. By comparing this with Nernst's equation, we see that, for electrolytes, the diffusion constant is given by the expression dic D=219, RT. T is the absolute temperature, R the gas constant corresponding to one gram-equivalent of substance, 1.980 calories per degree or 8.284 x 107 ergs per degree, so that it only remains to calculate U and V, the velocities with which the ions move CH. XIII] 379 DIFFUSION IN SOLUTIONS under the action of unit force. The quantity of electricity associated with one gram-equivalent of any ion is † 9644 electromagnetic units. If the potential gradient is one volt (108 C.G.S. units) per centimetre, the force acting on this gram- equivalent will be 9644 x 108 dynes. This, in dilute solution, gives the ion its specific velocity, say u. Thus the force Pw required to give the ion unit velocity is 9:644 x 100/u dynes or 9.83 x 105/u kilograms weight. If the ion have an equivalent weight W, the force P, producing unit velocity when acting on one gram is 9.83 x 105/Wu kilograms weight. Thus, in order to drive one gram of potassium ions with a velocity of one centimetre per second through a very dilute water solution, a force is required equal to the weight of 38,000,000 kilograms. The table gives other examples?. Kilograms weight Kilograms weight Prir P, Phy P, 15 x 108 14 x 108 X 40 x 106 Na 38 x 106 95 390 , 22 14 15 » 27 27 » Li NH! 83 » 5.4 15 3:1 H NO, OH C,H,02 C HOZ » 310 , Ag 16 39 30 1 Since the ions move with uniform velocity, the frictional forces brought into play must be equal and opposite to the driving forces acting, and therefore these numbers also represent the ionic friction coefficients in very dilute solution at 18° C. Let us now return to the consideration of the velocity. We have seen that the force acting on one gram-equivalent of an ion, when the potential gradient is one volt per centimetre, is 9644 x 108 dynes, and that, in dilute solution, this gives to the ion its specific velocity u. The velocity it would attain under unit force will therefore be IT_ U er x 10-8 cms. per second. 1 Kohlrausch, Wied. Ann. L. 385 (1893). 380 SOLUTION AND ELECTROLYSIS (CH. XIII In the case of hydrochloric acid, for example, the specific mobility of the hydrogen is 0.0032, and that of the chlorine 0:00069; thus U= 3:32 x 10-15, and V = 7.15 x 10-16 and, for the diffusion coefficient, we have 2UV D= DEU+ V TRT= 2:49, the velocities, for convenience, being reckoned in centimetres per day. The agreement between theory and Scheffer's observations on diffusion is shown by the table. Substance D observed | D calculated 2:49 2.27 2.10 1:45 Hydrochloric acid, HCI Nitric acid, HNO, Potash, KOH Soda, NaOH Sodium chloride, Naci Sodium nitrate, NaNO, Sodium formate, NaCỘOH Sodium acetate, NaCO,CH, Ammonium chloride, NH ČI Potassium nitrate, KNO, 2:30 2.22 1.85 1:40 1.11 1:03 0.95 0•78 1.12 1.06 0.95 0.79 1.44 1:38 1:33 1:30 The theoretical numbers are slightly increased by the assumption that the ionization of the solutions is complete, which is not accurately the case. This correction, then, would improve the agreement. The possibility of thus correctly calculating the diffusion constant must be regarded as very strong evidence in favour of the methods of the investigation. Further developments for the cases of other solvents and of mixed electrolytes have been traced by Arrhenius?, who shows, for example, that the rate at which hydrochloric acid diffuses will be increased by the presence of one of its salts. This is confirmed experimentally; when 1:04 normal HCl diffuses into 0:1 NaCl, D is calculated as 2:43 and observed as 250, and when the NaCl solution is 0:67 normal, calculation gives 3.58 and observation 3:51. i Zeits. phys. Chem. x. 51 (1892). CH. XIII] DIFFUSION IN SOLUTIONS 381 As we have seen above, when a solution is placed in contact with water, the water, which becomes a dilute solution, will take a positive or negative potential with regard to the stronger solution, in accord- ance with the greater specific mobility of the cation or the anion. Taking the equation which expresses the relation that, when a steady state is reached, the ions migrate at equal rates, viz. Potential differ- ences between electrolytes. UA8t (ale + c d e = V 48 (ale - cq d. we get de 1 V-U DP da cq V + U da' or, since for dilute solutions P=cRT, DE RT V - U IP då – Pq V + U di which gives on integration RT V - U. E = - 9 V to loge y + where P, and P, denote the osmotic pressures of the ions in the dilute and concentrated solutions respectively, and E denotes the difference of potential, i.e. the electromotive force between the two liquids. Now U and V, the ionic velocities under unit forces can, by multiplying by 9, the quantity of electricity asso- ciated with one gram-equivalent of an electrolyte, be transformed into u and v, the velocities under unit potential gradient. We have already restricted the investigation to the case of dilute solutions, so that we can also replace the ratio between the two osmotic pressures by the corresponding ratio between the two concentrations. The equation now becomes E - RTV-U logº? .................(77). q 2 + Thus the potential difference between two solutions with different concentrations of the same electrolyte, containing only univalent ions, is proportional to v — U, the difference between the mobilities of the anion and the cation. 382 [CH. XIII SOLUTION AND ELECTROLYSIS If the valency of the cation be yı and that of the anion ya, a similar investigation shows that v U E-RT ya Yulog .................(78). 9 v tu In order to compare these equations with observation, Nernst? devised a form of concentration cell in which Liquid cells. the electromotive force depends only on the two solutions. Such arrangements are sometimes known as liquid cells. We may take as an example, the following series : Hg/HgCl/0.1 normal KC1/0:01 KC1/0:01 HC1/0•1 HC1/0:1 KCl/HgCl/Hg. Two things are here to be observed; the first, that the ends of the chain are identical, and the potential differences there neutralize each other; the second, that, in dilute solutions, it is only the ratio and not the absolute values of the osmotic pressures or the concentrations that are involved. Thus the effect at the junction 0:01 KC1/0:01 HCl is equal and opposite to that at the junction 0:1 HC1/0:1 KCl, and the only effective junctions are those between 0:1 KC1/0:01 KCl and between 0:01 HC1/0·1 HCl. From the ionic mobilities of potassium, chlorine and hydrogen, the difference of potential at each of these junctions can be calculated, and the sum of the two results compared with the experimental value of the electro- motive force of the arrangement. The following table gives the results of Nernst's comparison of the calculated and observed values for this and other similar liquid cells. Electrolytes E.M. F. calculated E.M.F. observed KCI, NaCl KCI, LiCl KCl, NH,Cl NH CI, NaCl KCI, ÁCI KCI, HNO, KCI, C,H,,ŠOH 0·0132 0·0203 0.0010 0-0122 -0.0383 -0.0400 --0.0502 0:0111 0.0183 0.0004 0.0098 -0.0357 -0.0469 i Zeits. phys. Chem. IV. 129 (1889). CH. XIII] DIFFUSION IN SOLUTIONS. 383 The more general case of any two electrolytes in contact with each other has been considered by Planck?. The equations are somewhat complicated, but, when the total concentration of the ions in the two solutions is the same, and all the ions have the same valency y, the expressions reduce to the simple form, RT, Uy + E = log is t vi' Nernst has determined the electromotive force of cells which can be used to verify this equation; the following are the results of the comparison. Electrolytes E (calculated) | E (observed) HCI, KCI HCI, NaCl HCI, Lici KCI, NaCl KCI, Lici Nači, Lici 0.0282 0.0334 0.0358 0.0052 0.0077 0.0024 0.0285 0.0350 0.0400 0.0040 0.0069 0.0027 lete theory Hittorf's account of the phenomena of ionic migration deals only with the initial changes of concentration n. which appear at the two electrodes on the of ionic migration. passage of a current, before the diffusion that supervenes produces a sensible effect? As long as the middle part of the solution retains its original concentration, Hittorf's investigation holds good, and this condition must be maintained in experimental measurements of transport numbers. When the current flows for a long time, the electrode regions of densities modified by the current extend and meet each other, and the results of backward diffusion become im- portant. The general problem of electrolytic conduction which then arises has been investigated by the use of Fourier's i Wied. ann. XXXIX. 161; XL. 561 (1890); account in Ostwald's Lehrbuch, II. 848. 2 See above, pp. 208–212. 384 [CH. XIII ŞOLUTION AND ELECTROLYSIS diffusion analysis by Planck, Larmor?, and others, on the assumptions that the ions both migrate and diffuse indepen- dently of each other and that the ionization is complete. Ultimately a steady state will be reached; with a constant current and a non-dissolvable anode, the concentration dimi- nishes uniformly with the time as the electrolysis proceeds, and its gradient has a definite value irrespective of the value of the concentration itself, changing uniformly from 1/2RTqu at the anode to – I/2RTqv at the cathode, where I denotes the current, R the usual gas constant per gram-molecule, T the absolute temperature, q the electric charge on one gram- equivalent of a monovalent ion, u the mobility of the cation, and v the mobility of the anion. The difference in the concentrations at the anode and cathode in the steady state is found to be Il u-u 29D u tv? which is equal to Hittorf's difference produced initially per unit time divided by D11, D being the diffusion constant and I the length between the electrodes. As the ions diffuse at different speeds, whether electrolysis is going on or not, any changes of concentration at once give rise to internal electro- motive forces. Even when the steady state is reached, the gradient of electromotive force is of complex character. When the applied electromotive force is kept constant, and the current allowed to change, the quantities will vary exponentially with the time. A special case of Larmor's equations, in which the circuit is imagined to be broken, so that the current is zero, gives Nernst's expressions for the potential differences at the interface of two solutions of an electrolyte of different concentrations. Here the state of concentration is not steady, the only possible steady state being one of uniform density. Another application of the principles of the investigation enables the effect of a transverse magnetic field to be examined, and the coefficient of the resultant Hall effect to be calculated; for, by the laws of electrodynamics, a transverse magnetic field 1 Aether and Matter, p. 291. CH. XIII] 385 DIFFUSION IN SOLUTIONS must produce a sideways force on the moving ions which con- stitute the current. Larmor shows that a magnetic field H is equivalent to a transverse uniform electric force F which, if c denotes the concentration of the solution, has the value v-uIH v +u 2cq An investigation of the more general case which arises when the electrolyte is only partially ionized, has been given by F. G. Donnan? F = Electrolytic sure. Nernst's hypothesis of a solution pressure of metals in contact with electrolytic solvents may also be approached from the point of view of ionic dif- solution pres- fusion. To each metal is ascribed a definite solution pressure, depending only on the nature of the solvent and the temperature; this pressure tends to carry the metal into solution in the form of positively charged ions. The process will electrify the solution positively, and leave the metal with a negative charge. In this manner, according to Nernst, is set up the potential difference at the surface of the metal, the phenomena of which we have pre- viously studied. The electric forces will oppose the further solution of the metal, tending to drive back again the ions already in the liquid. The electrostatic charges on the ions are very great, and the potential difference of equilibrium may be reached long before a weighable quantity of metal has been dissolved. . On any view, the process of solution can only continue if negative ions can simultaneously dissolve, or other positive ions be removed from solution. The latter condition is illustrated by the replacement of hydrogen in acids, or the precipitation of one metal by another. When hydrogen is evolved, it is probable that it is first dissolved by the metal, from which it separates when its vapour pressure exceeds that of the atmo- sphere. The action can be stopped by a sufficient external i Phil. Trans. CLXXXV. A. 815 (1894), or loc. cit. W. S. 25 386 [CH. XIII SOLUTION AND ELECTROLYSIS pressure, the value of which can be determined by thermo- dynamic considerations, and, on Nernst's ideas, depends on the solution pressure of the metal. Thus Beketoff? and Brunner? have shown that hydrogen at a high pressure can precipitate silver, platinum and palladium ; Cailletet arrested its evolution from zinc and sulphuric acid; while Nernsts and Tammann* have examined the action of other metals. From Nernst's standpoint, this process of metallic solution is analogous to the diffusion of ions across the interface between a concentrated and a dilute solution of the same electrolyte. Such a metal as zinc is looked on as a solvent in which the concentration and the osmotic pressure of its own positive ions are very high. Some of these ions diffuse into a liquid in contact with the metal, till the characteristic ionic potential difference is set up. The electric forces then prevent further change, and, since the metal maintains the constancy of its ionic concentration, the osmotic pressures on the two sides of the interface are never equalized, unless the metal and solvent happen to show no difference of potential. We have seen that on Nernst's theory of electrolytic diffu- sion, the potential difference between two solutions of an electrolyte of different concentrations can be expressed as RTV-U, qv+ UP If, ignoring the essential difference in the two cases, we extend this equation to the interface between a metal m and a solution, we are concerned with the cation only, for no anion is trans- ferred across the boundary. Thus v is zero and we get E- E-RT, P. E=-* q P1 where Pm now denotes the osmotic pressure of the cations in the substance of the metal itself, that is, its solution pressure. We thus regain the equation which was deduced in a former i Compt. Rend. XLVIII. 422 (1889). 2 Pojg. Ann. CXXII. 153 (1864). 3 Compt. Rend. LXVIII. 395 (1869). 4 Zeits. Phys. Chem. IX. 1 (1892). CH. XIII] 387 DIFFUSION IN SOLUTIONS chapter (p. 257) from a consideration of the osmotic work equivalent to unit electric transfer. We have already con- sidered the limitations of this equation and pointed out that, following Helmholtz, the term involving Pm may be treated as an affinity constant, characteristic of the metal and the solvent. In applying these considerations to common chemical gal- vanic cells, such as Daniell's, we neglected the electromotive force at the junction of the liquids; as will now be clear, the theory of ionic diffusion enables us, in simple cases, to supply the term previously missing from the equation. In concentration cells the metal is the same at each elec- trode, so that Pm can be eliminated; it is therefore possible to develop the theory of such cells from the study of ionic diffusion. For a monovalent metal, such as silver, we have E = RI (log - po I y 10g - logo RT 20_logo qu+ Since v/(u + v) is for dilute solutions equal to r, the transport ratio for the anion, and n, the number of ions given by a molecule of the electrolyte, is here 2, this result is identical with equation (50) on p. 248. By similar methods we can regain the equations already given in Chapter X. for other kinds of concentration cell. The exact significance of the physical constant named 'solu- tion pressure' is uncertain. Following Nernst, Ostwald considers that, in a given solvent, it is a function of the metal and temperature only, and consequently that the single potential difference at the interface is independent of the nature of the negative ion. Measurements, in part described in Chapter XI., of the potential differences at single reversible junctions, when the cation is of the same metal as the electrode, have often been made from this point of view. We may here again refer to those of Le Blancl and Neumann? These observers measured the electromotive forces of cells made up i Zeits. phys. Chem. xII. 345 (1893). . . 2 Zeits. Phys. Chem. xiv. 225 (1894). . . 25—2 388 · [CH. XIII SOLUTION AND ELECTROLYSIS with the junction in question at one electrode, and mercury in the usual normal potassium chloride solution with an excess of calomel at the other. Assuming the potential difference be- tween the electrolytes to be small, Neumann found that at great dilution the electromotive force of the cell was in general independent of the anion; but Paschen, Bancroft, and other ;- observers, working with metals in solutions not of their own salts (arrangements which possibly form limiting cases of reversible electrodes and are subject to the same laws), have found that the potential difference does depend on the anion when the metal is copper, platinum, or mercury. Many ex- periments on cells containing non-reversible electrodes have been made to determine the influence of the nature of the ions and of concentration. Among these experiments we may mention those of Paschen?, Ostwald?, Oberbeck and Edlers, Bancroft4, and A. E. Taylor. Taylor suggests that the differ- ences found by some of the observers on changing the anion may be due to large potential differences of non-osmotic type at the surface of contact of the two liquids in the cells, for he finds that such large differences often arise in cases where there is a tendency to form complex salts. branes. Before Graham's experiments on free diffusion through water, many observations had been made on Diffusion through mem the passage of dissolved matter through various animal and vegetable membranes. Such mem- branes, made of bladder, parchment paper, and similar materials, are of the nature of colloids, and appear to be quite imperme- able to other colloidal substances. Solutions of colloids may be freed from crystalloids by placing the mixture in a vessel closed by a membrane, which, on its other side, is in contact with a large volume of the pure solvent. The crystalloids pass through, and, after a considerable time, are completely separated from the dissolved colloids. The process is known as dialysis. 1 Wied. Ann. XLIII. 590 (1891). 2 Zeits. phys. Chem. I. 583 (1887). 3 Wied. Ann. XLII. 209 (1891). 4 Zeits. phys. Chem. XII. 289 (1893); Physical Review, III. 250 (1896). 5 Jour. Phys. Chem. I. 1 and 81 (1896). CH. XIII] 389 DIFFUSION IN SOLUTIONS The rate at which crystalloids pass through one of these membranes depends on the nature both of the diffusing sub- stance and of the membrane. Water will usually pass more freely than salts dissolved in it, and thus a temporary osmotic pressure can be obtained by using a membrane of bladder or parchment paper. The septum is not a perfect semi-permeable wall, however, and the limiting value of the osmotic pressure is never reached; gradually the salt diffuses outwards, and the concentration of the liquid becomes identical on both sides. 1 The relative rates of passage of solute and solvent were shown by Eckard1 to depend on the nature of the membrane, which must therefore also control the temporary pressure observed. The true maximum value of the osmotic pressure, which we have studied in Chapter V., can only be obtained by aid of a perfect semi-permeable wall, and must clearly be independent of the nature of the partition; for if not, a perpetual motion arrangement could at once be devised. With the membranes we are now considering, irreversible processes are involved, and the conditions are entirely different from those which theoretically hold when an ideal perfect semi-permeable wall is used. Such ideal partitions are theoretically possible, and, by making use of this idea, we can simplify the application of the principles of thermodynamics to the elucidation of the phenomena of solution. It is however very difficult to construct perfect semipermeable membranes, and a considerable number of those prepared in accordance with the directions given on p. 96 will always be found to show some leakage of salt. The greatest pressure actually reached will then vary with different mem- branes, but this variation is a consequence of the imperfection of the partition, which allows some of the available energy of mixture to pass directly into heat, and, in accordance with theory, vanishes if membranes are obtained which show no leakage. The theories which we have developed cannot be applied to the phenomena shown by leaking membranes, whether natural or artificial, for such leakage must render the system essentially irreversible. Nevertheless, the study i Pogg. Ann. CXXVIII. 61 (1866). 390 [CH. XIII SOLUTION AND ELECTROLYSIS of the temporary pressures which can be obtained by the help of organic membranes, the rate of diffusion of different substances through them, and their thermodynamic or osmotic efficiency, are problems of fundamental importance for the physiologist. The mode of action of the membrane is at present little understood. The various possible views are described on p. 97, under the head of inorganic semi-permeable membranes, and it is as yet impossible to say if the separating process depends (1) on a mechanical sieve-like action, (2) on the satura- tion of the membrane or the formation of loose chemical compounds with it on one side and their decomposition on the other, or (3) on the filtering action of capillarity explained on p. 98. As there suggested, it is possible that the three modes of explanation may run into each other, different aspects being more prominent in different cases. CHAPTER XIV. The colloidal state. Process of gelation and structure of gels. Coagulative power of electrolytes. The nature of colloidal solutions. state. THERE is a marked difference in physical and chemical The colloidal properties between bodies of definite crystalline form, such as most inorganic salts and minerals, and soft or amorphous substances, such as albumen and the various kinds of jelly. Graham distinguished the two groups as crystalloids and colloids respectively, and particularly ex- amined them with regard to their relative diffusive powers. Many different kinds of chemical compounds show colloidal properties. Besides a vast number of animal and vegetable substances, some of which seem to play a great part in the phenomena distinctive of living matter, many of the precipitates which are formed in the course of inorganic chemical reactions appear in an amorphous or colloidal state. The sulphides of slightly oxidizable metals such as antimony and arsenic are good examples. Thus if a solution of arsenious acid is allowed to flow into water saturated with sulphuretted hydrogen by means of a continuous current of the gas, a colloidal hydrosulphide is formed, which can be freed from excess of sulphuretted hydro- gen by passing a current of hydrogen, and from salts by dialysis. Many hydrates, too, are colloids, ferric hydrate, for instance, which can readily be prepared from the corresponding salts of iron. By treating dilute solutions of gold chloride with 392 [CH. XIV SOLUTION AND ELECTROLYSIS reducing agents, such as a few drops of a solution of phosphorus in ether, the gold is set free in the colloidal condition, forming a ruby-coloured solution which can be purified by dialysis. Silver, bismuth and mercury can also be obtained in colloidal solution. Colloid solutions seem to be non-conductors of electricity, the dissolved colloids moving as a whole up or down the potential gradient in the same way as non-conducting solid particles. The classification of substances into colloids and crystalloids again brings us to the study of that part of our subject which is concerned with the phenomena of allotropy, amorphous modifications, and crystallization, and has been referred to on pp. 45 to 47 in the chapter on the Phase Rule. If, as there indicated, a true solid is always crystalline, colloids which possess some of the properties of solids must really be under- cooled liquids; in fact, such a view of their nature was sug- gested by Graham! Fluid colloids seem to be capable of existing in a coagulated or insoluble condition, which they readily assume under a slight disturbing influence. The solu- tion of hydrated silica, for instance, may remain liquid for days or weeks in a sealed tube, but is sure to coagulate at last. The existence in nature of mineral and crystalline forms of silica, which have been deposited from water, suggests that, even in its coagulated condition, the colloidal substance is unstable, passing eventually into a crystalline variety. Glass, too, usually a typical colloid, may become crystalline with lapse Tof time. We may conclude, then, that colloids are essentially unstable bodies, never in true equilibrium, though the forces, viscouis or other, opposing a change of state, may be so large that the condition will persist for a very long time. When examined chemically, colloids show very little activity, and chemical changes are produced in them slowly and with difficulty. They freely form addition products, however, with such bodies as water and alcohol, such combined water or alcohol being readily interchangeable with other similar sub- stances. The process of absorption of water is often accompanied i Phil. Trans. CLI. 183 (1861); Collected Papers, p. 553. CH. XIV] 393 SOLUTIONS OF COLLOIDS with considerable increase of volume. The corresponding con- traction when the water is removed by evaporation sometimes gives rise to considerable forces; a solution of isinglass, drying in a glass vessel over sulphuric acid in vacuo, may tear away strips from the surface of the glass owing to its strength of adhesion. Many solid colloids, and solid solutions of colloids and water, can be used as solvents for mineral salts and acids ; as we have stated (pp. 217, 372), the ionic mobility and the diffusivity are then very little less than in liquid aqueous solu- tions of equivalent strength. On the other hand, the power of separating colloids and crystalloids by dialysis shows that colloidal membranes are almost impermeable to other colloids. Solutions of colloids in crystalloid solvents, such as water or alcohol, seem to be divisible into two classes. Both classes appear to mix with warm water in all proportions, and the mixture will solidify under certain conditions to form a mass which may be called a gel ; but one class, represented by gelatine and agar jelly, will, when solidified, redissolve on warming or dilution, while the other class, containing such substances as hydrated silica, albumen, and metallic hydro- sulphides, will, under the influence of heat or on the addition of electrolytes, form gels which cannot be redissolved. The solidification of members of the first class into redissolvable substances is termed setting, that of substances in the second class, which form insoluble precipitates, is ternied coagulation?. Liquid solutions of colloids in water have been called by Graham hydrosols, and the solids, formed by setting or coagu- lation, hydrogels. Hardy has distinguished the two kinds of systems forming soluble and insoluble precipitates as reversible and non-reversible". The names are convenient, but as there appears to be a considerable difference between the melting and solidifying points of jellies, etc., it must be understood that such systems are not necessarily reversible in the thermody- namic sense of the word. 1 W. B. Hardy, Proc. R. S. LXVI. 95 (1900). 2 loc. cit. 394 [CH. XIV SOLUTION AND ELECTROLYSIS Process of structure of The mechanism of gelation in reversible colloidal systems has been studied experimentally by van Bemmelen? and by Hardy. gelation and Van Bemmelen measured the vapour pres- gels. sures of gels which had been formed by the coagulation of hydrated silica and contained varying proportions of absorbed water. When water is removed slowly, a regular con- tinuous curve is obtained; when the removal is rapid, the diagram shows changes of curvature. Van Bemmelen considers that the system does not consist of two definite phases in the sense of the Phase Rule, for the two parts into which it separates on coagulation are not divided by a definite interface. Still, two parts can be distinguished, one of which is colloidal, viscous, and possesses a net-like structure in which the other more fluid liquid is partly absorbed and partly retained mechanically. The colloidal liquid passes into the solid state by the lapse of time or by the influence of foreign bodies. The emission and absorption of water vapour by colloidal matter has been investigated theoretically by Duhem”, who deduces the results observed by van Bemmelen from the ther- modynamic properties of a system of which two of the controlling variables are subject to hysteresis. Hardy examined mixtures of agar and water, agar water and alcohol, and gelatine water and alcohol. The last-named ternary system gives a homogeneous liquid when warm, but divides on cooling into two phases possessing different refractive indices, and is therefore suitable for microscopic investigation. When the proportion of gelatine is small, from 6 to 14 per cent., fluid droplets are seen to form as the liquid cools; they solidify and eventually join together into a loose framework. The mass has then become a more or less solid gel. With a higher proportion of gelatine, 365 per cent., this arrangement was inverted, and the drops formed contained less gelatine than the residual substance, which now forms a solid solution, interrupted by spherical spaces filled with liquid. The temperature at which the separation into two phases occurs is raised by an i Zeits. anorgan. Chem. XIII. 233 (1896) ; XVIII. 14 (1898). 2 Jour. Phys. Chem. IV. 65 (1900). CH. XIV] 395 SOLUTIONS OF COLLOIDS increase in the proportions of gelatine or alcohol, and lowered by the addition of the common solvent water. No binary system was found in which the changes could be followed by the microscope; but with a mixture of agar and water, the gel could be separated into two phases consisting of a solid and a liquid solution respectively, by expressing the latter through canvas. The constitution is therefore probably similar to that investigated for the three-component system described above. Coagulative lytes. Graham observed that the addition of salts, sometimes in minute quantities, often caused colloidal solu- power of electro- tions to coagulate? Hydrated alumina, for instance, prepared by dialysing a solution of the chloride containing excess of the hydrate, was so unstable that a few drops of well-water at once produced coagulation, and the same change was brought about by pouring the solution into a new glass vessel, unless the vessel had repeatedly been washed with distilled water. This action of salts was further investigated by Schulze, who found that hydrosols of sulphide of arsenic were coagulated by salts at a rate depending largely on the valency of the metal. Defining the coagulative power as the reciprocal of the concentration in gram-molecules per litre necessary to coagulate a given solution, Schulze found that the relative coagulative powers of univalent, divalent, and trivalent metals were in the ratios 1:30:1650. These results were verified by Prosts, who used sulphide of cadmium as the colloid, and by Linder and Picton", working with sulphide of antimony. Linder and Picton found that a slight trace of the metal is entangled in the coagulum, the salt apparently being decomposed to a corresponding extent. Their measurements showed that, for different salts of a given metal, the coagulative powers are proportional to the equivalent electrical conductiv- ities, and that the relative coagulative powers of various i Collected Papers, p. 580. 2 Jour. prakt. Chem. XXV. 431 (1882). 3 Bull. Acad. Roy. Sci. de Belg. [3] xiv. 312 (1887). 4 Jour. Chem. Soc. Trans. LXVII. 63 (1895). 396 [CH. XIV ; SOLUTION AND ELECTROLYSIS sulphates of univalent, divalent, and trivalent metals ranged round the mean values 1:35:1023. The effect of adding a small quantity of the salt of one metal was to reduce the amount of the salt of another metal with the same valency which was required for coagulation ; but if the metal of the second salt had a different valency, the amount of salt needed was actually increased by the presence of the first salt: more strontium chloride, for instance, was necessary when a little potassium chloride was previously dissolved. It is probable that the molecular changes which accompany coagulation are not sudden discontinuous processes, for Linder and Picton? found that, as the point of coagulation is approached, the size of the colloid particles increases even though actual coagulation does not occur, and, under similar conditions, Grahamº observed a gradual increase in the viscosity of the solution. An explanation of some of these remarkable valency rela- tions has been offered by the present writers. The connexion with electrical conductivity discovered by Linder and Picton shows that the coagulative power of a salt depends on its electrical properties. Let us suppose that, in order to produce the aggregation of colloidal particles which constitutes coagula- tion, a certain minimum electrostatic charge has to be brought within reach of a colloidal group, and that such conjunctions must occur with a certain minimum frequency throughout the solution. Since the electrical charge on an ion is proportional to its valency, we shall get equal charges by the conjunction of 2n triads, 3n diads, or 6n monads, where n is any whole number. In a solution where ions are moving freely, the probability that an ion is at any instant within reach of a fixed point is, putting certainty equal to unity, approximately represented by a fraction proportional to the ratio between the volume occupied by the spheres of influence of the ions and the whole volume of the solution, and may be written as Ac, where A is a constant 1 Jour. Chem. Soc. Trans. LXVIII. 73 (1895). 2 Collected Papers, p. 619. 3 Phil. Mag. [5] XLVIII. 474 (1899); also Hardy and Whetham, Jour. Physio- logy, xxIv. 288 (1899). CH. XIV] 397 SOLUTIONS OF COLLOIDS and c represents the concentration of the solution. The chance that two such ions should be present together is the product of their separate chances, that is, (Ac)? Similarly, the chance for the conjunction of three ions is (Ac), and for the conjunction of n ions is (Ac)” In order that three solutions, containing trivalent, divalent, and univalent ions respectively, should have equal coagulative powers, the frequency with which the necessary conjunctions should occur must be the same in each solution. We should then have, the constant being assumed equal in each case, A2C22n = A3nc,3n = Aonc, on = a constant=B. Therefore - Bin Bin D Ca A Ca 4 0 4 C1, C2, C3 representing the concentrations of monads, diads, and triads in their respective solutions. Thus we get for the ratios of the concentrations of equi-coagulative solutions 1 1 C2:02:03 = 36: B3n : B2n =1: Bon : B3n. 1 1 Let us put Ben ; the ratios can then be written 1 1 x 220 The reciprocals of the numbers expressing the relative concen- trations of equi-coagulative solutions give values proportional to the coagulative powers of solutions of equal concentration ; so that, calling the coagulative powers of equivalent solutions containing monovalent, divalent, and trivalent ions respectively P1, P2, P3, we get P1:22:23=1:2:. Let us now take some numerical examples. Putting x= 32, we get the series 1:32:1024, which agrees very well with Linder and Picton's results for colloidal solutions of antimony sulphide, 1:35:1023; 398 [CH. XIV SOLUTION AND ELECTROLYSIS and putting x = 40, we get 1:40:1600, numbers comparable to Schulze's values for sulphide of arsenic, 1:30:1650. When we consider the difficulty of the experiments, and remember that the coagulative powers of solutions containing different ions of equal valency are not equal, but vary as the equivalent conductivities, these results show a better agree- ment between the calculated and observed values than might have been expected. The particles in solutions of colloids in water generally move when in an electric field, the direction of motion depending on the nature of the colloid and of the solvent. Thus Hardy1 found that proteid, modified by heating to the boiling point when dissolved in water, reverses the direction of its motion under the influence of electric forces, when the reaction of the fluid holding it is changed from slightly acid to slightly alkaline. A minute quantity of free alkali causes the proteid particles to move against the current, while the addition of an equally minute quantity of acid is followed by movement in the same direction as the current. Movement in an electric field shows that the particles must be charged electrically, a double layer probably being formed at their surfaces, in accordance with Quincke's theory of electric endosinose. The reversal of direction implies a reversal of sign in the charges on the particles, and therefore, by slowly adding acid or alkali to the liquid, it is possible to obtain an iso-electric point at which there is no potential difference between the liquid and the particles. Hardy finds! that as this point is approached, the stability of the system diminishes, and at the iso-electric point it is probable that coagulation spontaneously occurs. The same observer has also discovered that, in the case of colloids travelling with the electric current, it is the anion which is active in causing coagulation, and not the metallic ion as in the experiments of 1 Jour. Physiol. XXIV. 288 (1899); Proc. R. S. LXVI. 110 (1900). CH. XIV] 399 SOLUTIONS OF COLLOIDS Schulze, Prost, and Linder and Picton, who all used colloids which move against the current. Thus it is always the ion) possessing a charge of opposite kind to that on the colloid particles that is effective in producing coagulation. These observations suggest that the coagulative power of electrolytes may depend on a modification, under the electro- static influence of the ionic charges, of the surface energy of the interface between the two phases of the colloidal system. As shown in the Chapter on contact electricity, the natural surface energy of such an interface is diminished by the presence of certain kinds of electric double layers. The tendency of the surface tension to condense many small particles into a few larger ones (p. 43) is thus reduced, and the system of small particles may become stable. Approach to the iso-electric point will, by decreasing the intensity of the double layer, increase the surface tension, and diminish the stability of the system, while the absorption of ions possessing charges of opposite sign to those on the particles will reduce the charges on the particles, and again act in a similar manner. The average size of the particles will be increased, and, if the influence at work is sufficient, the particles may be precipitated, or if enough colloid matter is present, the whole solution may coagulate into a more or less solid mass. As another mode of stating the explanation, we may say that a high potential difference implies a great mutual affinity between the two phases, tending to expand the interface. As the opposite charges of the electric double layer are annulled, the affinity diminishes; it vanishes at the iso-electric point, and the solution becomes unstable. A different explanation of the coagulative properties of certain substances has been offered by Quincket, on the basis of changes of surface tension only. These changes are sup- posed to be produced by the spreading of the electrolytic solutions over the surfaces of the particles, forming a new inter- face with the surrounding liquid. This hypothesis makes no attempt to explain the relations of coagulative power with electrical conductivity and valency. 1 B. A. Report, 1901, p. 60. 400 [CH. XIV SOLUTION AND ELECTROLYSIS Nature of tions. Liquid solutions of colloids may be regarded either as ordinary solutions, of which the solutes possess enor- colloidal solu- mously high molecular weights, or as systems of two phases, composed of suspensions of par- ticles in the liquid, different from it and of greater than molecular dimensions. Much discussion has taken place on the relative merits of these two hypotheses. It is certain that some colloid solutions may be kept almost indefinitely without precipitation ; but, if the foreign particles are small enough, the viscosity of the water is enough to make the settling process almost inde- finitely slow. The properties of hydrosols differ considerably from those of true solutions; the rate of diffusion is very much less, the heat of solution is usually inappreciable or at all events very small, while no certain indications have been obtained of measurable osmotic pressures or depressions of the freezing point of the solvent. In some colloid solutions, the presence of suspended particles can readily be detected. Picton and Lindert, who have made extensive investigations on this subject, have observed a con- tinuous gradation in size from particles large enough to be visible under a microscope. Such particles exist in solutions of mercuric sulphide and of arsenious sulphide prepared from the tartrate; under a magnification of 1000 diameters they appear as minute solid particles in rapid Brownian movement, crowded together so closely that very little free space is left. Other solutions of colloidal sulphides, together with those of ferric bydrate, chromic hydrate, aluminium hydrate, silicic acid, cellulose, starch, and acid and neutral Congo-red, while non- resolvable under the microscope, contain particles large enough to scatter and polarize a beam of lime-light. These optical methods fail to show the presence of particles in the colloidal solutions of molybdic acid, and of silicic acid in presence of hydrochloric acid. On the other hand, certain crystalloids possessing very complicated molecules, oxyhaemoglobin, car- bonic oxide haemoglobin, and a compound of ferric hydrate with ferric chloride, which is said to crystallize as 9Fe,03. FeCl2, yield solutions which contain particles large enough to scatter 1 Jour. Chem. Soc. Trans. LXI. 148 (1892). 1 CH. XIV] 401 SOLUTIONS OF COLLOIDS and polarize light? A colloidal solution of arsenic sulphide, prepared from the aqueous solution of pure arsenious acid, showed a diffusive power comparable with that of crystalloids, though the same solution polarized light. Picton and Linder conclude that there is no distinction in kind between colloid and crystalloid solution, but that a continuous gradation exists between solutions containing colloid particles visible under a microscope and electrolytic solutions of common crystalloid salts and acids. The absence of measurable osmotic-pressure pro- perties appears to be merely an affair of arithmetic. Particles of a size to scatter light in accordance with the observations to which we have referred, must be comparable in size with the wave-length of light, about 5 x 10-6 centimetre. If the parti- cles are close together we may conclude there are about 104 in a linear centimetre, or 1012 in a cubic centimetre. In a normal solution of a crystalloid which gives an osmotic pressure of about 22 atmospheres, the number of solute molecules is approximately 5 x 1020. The osmotic pressure of the colloid solution in question will therefore be about 2 x 10-9 of that of a normal solution of a crystalloid, a value much too small to be measurable. It is worthy of note that turbid suspensions of clay, kaoline, etc., in water are rapidly cleared by the addition of small quantities of metallic salts? This action, which is almost certainly of the same nature as the coagulation studied above, probably helps in the formation of sand-banks at the mouths of rivers, the salts of the sea water clearing the suspensions of clay brought down by the fresh water; precipitation then occurs owing to the diminished velocity. The conditions which determine the colloid or crystalloid nature of a substance are at present little understood. The persistence of the colloid properties when a substance passes from the dissolved to the non-dissolved state, shows that the i Gamgee has shown in other ways that oxyhaemoglobin has a mixture of colloidal and crystalloidal properties. Proc. R. S. LXX. 79 (1902). 2 Schulze, Pogg. Ann. cxxix. 366 (1866); Schloesing, Compt. Rend. Lxx. 1345 (1870); Bodlander, Gött. Nachr. 1893, p. 267; Spring, Rec. Trav. Chim. Poys. Bas, 1900, pp. 222, 294. W. s. 26 402 [CH. XIV . SOLUTION AND ELECTROLYSIS determining conditions must be of fundamental importance. The molecular forces seem to be much less active in colloids, but the freedom with which some of them disintegrate and dissolve in presence of water and other liquids indicates that some interaction between them and their solvent must occur. On these lines, making certain assumptions as to the nature of the forces at work and their variation with the distance, Donnani has offered an investigation of the conditions which would secure the disintegration and solution of a colloid. It seems likely that the forces and interactions which are involved in crystalloid solution are of the nature of those which 1 solve, the actions between solvent and solute are conditioned also by the phenomena which are studied under the names of surface tension and capillarity. As the size of the dissolved aggregates or particles increases, the importance of the chemical forces diminishes and that of the capillary forces grows. In studying the properties of colloidal solutions by the light of the Phase Rule, we must remember that the surface of separation between the phases is enormously extended owing to the minute size of the particles, and the surface energy therefore becomes of great, perhaps of preponderating, importance. An investiga- tion of the influence of capillarity on the theory of equilibrium will be found in Gibbs' work?; he shows that an interfacial transition layer provides in a sense a new phase coexistent with those on each side of it and having its own characteristic equa- tion. Again, colloids may be regarded as undercooled liquids, and in a condition of unstable equilibrium. Their condition may therefore depend on the time, which introduces a new variable beyond those contemplated by the ordinary application of the Phase Rule 3. In conclusion we may point out that, if colloid and crystal- loid solution are but the extreme limits of a continuous series of phenomena, the study of dissolved colloids of varying degrees of aggregation promises to throw light on the general problem of the fundamental nature of solution. 1 Phil. Mag. [6] 1. 647 (1901). ? Trans. Connect. Acad. 111. 380 (1877). 3 Bancroft, The Phase Rule, p. 234. ADDITIONS. Solid solutions. BRUNI and Padoa? have prepared solid solutions by the sublima- tion of a mixture of two crystalline substances, Chapter 11: 8.71. such as mercuric iodide and bromide. The mixture was placed at the bottom of a glass bulb, which was then partially exhausted and kept in a bath of alloy at a temperature a few degrees below the fusing point of the mixture. After a day or so, homogeneous crystals of a solid solution were found in the upper part of the bulb. mixtures. Lord Rayleigh? has measured the compositions of liquid and vapour in the distillation of mixtures, Chapter III. p. 75. Distillation of drawing curves with the two compositions as axes. With 96 per cent. alcohol the compo- sitions were identical, in agreement with the minimum boiling point found by Noyes and Warfel? By proper arrangements, separation of the mixture can be effected by a single continuous operation. Solubility of mixtures. with Since the year 1897 a series of researches has been carried out by Van't Hoff and his pupils on the solu- Chapter IV. p. 93. Solubility of bility of simple salts, double salts, and mixtures, with the immediate object of elucidating the geological process involved in the formation of oceanic salt deposits, such as those of Stassfurt*. 1 Atti Accad. dei Lincei, Roma, XI. 565 (1902). 2 Phil. Mag. [6] 1v. 521 (Nov. 1902). 3 Amer. Chem. Soc. Jour. XXIII. 463 (1901). 4 A report on the work was communicated by E. F. Armstrong to the British Association (1901, p. 262); the original papers will be found in the Abland. Kön. Akad. JVissensch., Berlin, 1897—1902. 26_2 404 SOLUTION AND ELECTROLYSIS 10011 When several salts are simultaneously present, the possible number of solids in equilibrium with the solution may be predicted by the Phase Rule, but the nature of any double salts, the possibility of their co-existence, and the order in which the various solids appear, must be determined by experi- ment. As an example we may take a solution containing potassium chloride KCl and magnesium chloride MgCl2.6H20, substances which form a double salt of composition KCl. MgCl,.6H,0 called Carnallite. Here we have three components, namely, water and the two simple salts; the double salt, not 11010 being an independent vari- able, is merely a possible solid phase. To obtain a monovariant system, which is in equilibrium at one given temperature when the pressure is fixed, we must assemble four phases, two being solids. Working at the constant pressure of the atmosphere, and at a con- stant temperature of 25°, the conditions of such a system are completely determined, and the liquid phase can have only one composition. When, at the beginning of the deposition, the only solid phase is composed of the crystals of the less soluble 10 20 30 40 50 salt, the system is not de- Molecules K, Cl, termined, and the composi- Fig. 66. tion of the liquid will vary as evaporation proceeds till a new solid phase appears. The composition of the liquid phase then remains constant as long as both solids are deposited. The phenomena may be repre- Molecules MgCl, ADDITIONS 405 sented on a diagram (Fig. 66), for which the necessary data are given in the following table, the amount of potassium chloride being reckoned in double molecules as K,Cl2, for the sake of comparison with MgCl2. Number of molecules per Substances saturating Points on thousand molecules the solution the diagram of water K,C1, MgCl, 44 or 5.5 ΚΟΙ KCl and Carnallite Carnallite and MgCl,.6H,0 MgCl,.6H,0 toto hand 72.5 105 108 : O Points lying inside the lines ABCD represent the composition of unsaturated solutions; points on the line AB indicate the number of double molecules of potassium chloride which saturate the liquid as the amount of magnesium chloride is increased ; similarly the lines. BC and CD represent the conditions of saturation with Carnallite and magnesium chloride respectively. The points B and C, representing the composition of solutions simultaneously saturated with two solid phases, are determined by the experimental results given in the table. In more complicated systems the number of variables can often be reduced by remembering that in what are known as reciprocal salt pairs, for example, MgCl,+K2SO4= K,Cl2 + MgSO4, the amount of the second pair can be expressed in terms of the amount of the first. This consideration makes it often possible to represent on a solid model the phenomena observed when several salts are present. By studying the evaporation of sea water on these lines, it has been found that the order in which salts should be depo- sited is probably as follows. (1) Sodium Chloride; (2) Sodium Chloride and Magnesium Sulphate; (3) Sodium Chloride and Leonite; (4) Sodium Chloride, Leonite, and Potassium Chloride, or Sodium Chloride and Kainite; (5) Sodium Chloride, Kiese- rite and Carnallite; (6) Sodium Chloride, Kieserite, Carnallite, 406 SOLUTION AND ELECTROLYSIS and Magnesium Chloride, the solution then drying up without further change of composition. This succession agrees with that found on actually evapo- rating sea water at 25°, and approximately conforms to that observed in the geological deposits at Stassfurt. Chapter V. p. 96. membranes. Morse and Horni precipitated a membrane of copper ferrocyanide in the walls of a porous cell by Semi-permeable placing solutions of copper sulphate and * potassium ferrocyanide on each side of the wall, and passing an electric current till the resistance became 1500 to 3000 ohms. Membranes tbus obtained easily with- stood pressures of four or five atmospheres. It has been shown by Lyle and Hosking? that, when plotted with the temperature, the equivalent conduc- Chapter IX. p. 224. Ionic Viscosity. · tivity and the fluidity of solutions of sodium chloride give similar but not identical curves, which indicate that both conductivity and fluidity would vanish at a temperature of - 35°.5 Centigrade. Effect on con- ductivity of the nature of the solvent. The conductivity of solutions of salts etc. dissolved in liquid hydrocyanic acid has been investigated by Chapter XII. pp. 332 and 363. Kahlenberg and Schlundt? The potassium salts have conductivities about three times those of the corresponding aqueous solutions. These aqueous solutions are themselves highly ionized, so that the increased conductivity in hydrocyanic acid : must be due to the smaller ionic viscosity of that solvent. In light of the high dielectric constant (about 95) of the liquid, it is interesting to observe that some other salts showed less con- ductivity than in water, and that both water and alcohol were found to dissolve to form non-conducting solutions. (See p. 362.) 1 Amer. Chem. Jour. XXVI. 80 (1901). 2 Phil. Mag. [6] III. 487 (1902). 3 Jour. Phys. Chem. vi. 447 (1902). TABLE OF ELECTRO-CHEMICAL PROPERTIES OF AQUEOUS SOLUTIONS, COMPILED BY THE Rev. T. C. FITZPATRICK, M.A., FELLOW OF CHRIST'S COLLEGE, CAMBRIDGE, and Reprinted, by permission, from the Report of the British Association for the Advancement of Science, 1893. The comparison of the numerical results of electrolytic observa- tions is rendered difficult by the fact that the data are scattered in various periodicals and expressed by different observers in units that are not comparable without considerable labour. The following table has been compiled with the object of facilitating the com- parison. piler, with the exception that a selection only is made in the case of organic bodies. Observations for a number of additional substances will be found in Ostwald's papers in the Journal für Chemie, vols. xxxi., xxxii., and xxxiii., and in the Zeitschrift für physikalische Chemie, vol. i. With this restriction it is hoped that no important observations published before the year 1893 have been omitted, and table is sufficiently free from mistakes for it to be of service. The data included refer to the strength and specific gravity of solutions, with the corresponding conductivities, migration constants, and fluidities. The several columns are as follows: I. Percentage composition, i.e. the number of parts by weight of the salt (as represented by the chemical formula) in 100 parts of the solution. 408 SOLUTION AND ELECTROLYSIS II. The number of gramme equivalents per litre, i.e. the number of grammes of the salt per litre divided by the chemical equivalent in grammes, as given for each salt. III. The specific gravities of the solutions : in most cases the specific gravities of the solutions are not given by the observers, and the numbers given have been deduced from Gerlach's tables in the Zeitschrift für analytische Chemie, vol. viii. p. 243, &c. IV. The temperatures at which the solutions have the specific gravities given in the previous column for the given strength of solution. V. The conductivity, as expressed by the observer. In the cases in which the observer has expressed his results for specific equivalent conductivity no numbers are given in this column. VI. The temperature at which the conductivities of the solu- tions have been determined. VII. The temperature coefficient referred to the conductivity at 18°, i.e. VIII. The specific equivalent conductivity of the solutions at 18° in terms of the conductivity of mercury at 0°; the specific equivalent conductivity is the conductivity of a column of the liquid 1 centi- metre long and 1 square centimetre in section, divided by the number of gramme equivalents per litre. In some few cases, in which no temperature coefficients have been determined, the results have been given for the temperature at which the observations were made. The numbers given in the column are the values for the specific equivalent conductivity 109. IX. This column contains the values for specific equivalent conductivity at 18° in C.G.S. units: they are obtained from those in the previous column by being multiplied by the value of the conduc- tivity of mercury at 0° in C.G.S. units. The factor is 1.063 x 10-5. The values in Kohlrausch's units, reciprocal ohms per centimetre cube per gram equivalent of salt per cubic centimetre, can be obtained by dividing by 10 the numbers actually given in the column (i.e. 1293 becomes 129.3 for the first solution of potassium chloride, &c.). The results may in some cases differ by a few parts in a thousand from Kohlrausch's latest values given in his book das Leitvermögen der Elektrolyte (Leipzig, 1898). ELECTRO-CHEMICAL PROPERTIES OF AQUEOUS SOLUTIONS 409 X. The migration constant for the anion; for instance, in the case of copper sulphate (CuSOs), for (SO4). Some more recent results are given on p. 212. XI. The temperatures at which the migration constants have been determined. XII. The number of gramme equivalents per litre, as defined for column II., for which the fluidity data are given in the following columns. XIII. The fluidity of the solutions of the strength given in the previous column. Most of the results given for the fluidity of solutions are expressed in terms of the fluidity of water at the same temperature; to obtain the absolute values for the solutions they have been multiplied by the value for the fluidity of water at the given teni perature. The values used for this purpose have been taken from Sprung's observations for the viscosity of water given in Poggendorff's Annalen, vol. clix. p. 1. • To obtain the values for fluidity in C.G.S. units, the numbers in this column must be multiplied by the factor ·1019. XIV. The temperature at which the solutions have the fluidity given in the previous column. XV. The temperature coefficient of fluidity at 18°, that is 1 18f18 Fix (). XVI. In the last column are given the references to the various papers from which the data are taken : against each refer- ence will be found a number, which appears also against the first of the data which have been taken froin the paper in question. 410 TO SOLUTION AND ELECTROLYSIS. HYDROCHLORIC ACID. Equivalent Gramme Molecule, HCI, 36.46. 1333 2186 ||||| 11111 |||| 1 Kohlrausch, Wied. Annal. vol. xxvi. p. 196. 3155 10000. 20000. 90000. JOOO. 2000. 9000. 100. 200. 900. IO. |||||||||| 3340 3440 3455 వర్యం 3672 3672 collo 1 60 50 60 50 50 c 50 Co co 3438 3416 3054 3631 2 Ostwald, Journal für Chemie, vol. xxxi. p. 437. is Hittorf, Pogg. An- nal. vol. cvi. p. 395. ·0214 "Grotian, Pogg. An- nal. vol. clx. p. 262. O128 2000. I 3330 3540 |||||||||1ooo 0 ||||||||||| 912. L'0016 I'O012 3244 ILI. 191. 3207 *744 891. |||||| |||||||||| oll|||||||||||||||||||||||||||||||||!! |||||||||||||||||||||| J'0062 10086 | I'or 39 | 7:6 l'0179 | 15.5 [ *0472 I°0501 ! 1°0832 | 155 |||||||||| IO 2.64 7.4 5.5 50 160 Co 2010 1420 1.1552 15.5 o ·000244 100 *000061 '000122 *000488 *000975 ·00195 ·0078 |||||||||||| |||||||||||| Sition design |||||||||llll II|||||||||| ||||||||||| centenari *0312 •0625 •125 0000364 *000073 *000219 *000364 *00073 *00219 *00364 •0073 *0219 '0364 *047 •109 •182 IE. *364 704 12 1.807 2.68 3.58 9:20 10:41 16.8 25.59 31.5 3.0 *000225 *00045 *00089 ·00178 ·00355 ·0071 *0142 *0285 *057 •14 .228 *456 TABLE OF ELECTRO-CHEMICAL PROPERTIES. 411 TABLE OF ELECTRO-CHEMICAL PROPERTIES OF SOLUTIONS IN WATER. Composition Conductivity Data Migration Data Fluidity Data Notes Percentage Composition Equivalent Granıme Molecules per Litre Specific Gravity Temperature Conductivity in Observer's Units Temperature Temperature Coefficient Specific Equivalent Conduc- tivity at 18° in terms of Mercury x 108 Specific Equivalent Conduc- tivity at 18° in C.G.S. Units x 1013 Temperature Equivalent Gramme Molecules per Litre Fluidity x 102 Temperature Temperature Coefficient 26 '907 *25 I'0045 1'0086 15-5 15.5 | 80.9 1251 77.9 | 3268 3166 15 Lenz, Irvinevuru 10 .807 | l'Acad. de St Pé- | tersbourg, vol. xxvi. 3609 3581 ·0286 *057 •114 .228 *456 910 1.813 2.665 5:28 10°4 20.6 *00784 0157 *0314 *0627 •1255 -251 •502 3532 il |||||| III|||| ||||||| 40.5 IIII 1'0018 1'0046 | 10090 3289 | 3496 3234 3438 3138 | 3336 3014 | 3204 15.5 15-5 15.5 1513 |||| || 1!!!! "OOOOT 00002 *00006 0001 *0002 *0006 001 *002 *006 OI !!!!!!!!! 1111111 - *0000746 '000149 *000448 | *000746 *00149 *00448 *00746 *0149 *0448 •0746 .224 •372 743 3.04 5.15 7.13 13:1 1701 1997 11 Kohlrausch, Wied. Annal. vol. xxvi. p. 195. | 2 Hittorf, Poyg. An- nal. vol. xcviii. 1). 27. POTASSIUM CHLORIDE. Equivalent Gramme Molecule, KCI, 74.59. - | 12161 1293 1217 | 1294 1212 1209 1285 1209 1199 1193 1268 1185 1260 1162 1235 1147 1219 1107 | 1178 1083 1047 III3 958 ప|| 2 | విపరపపపపపప ||||||||||| 03 | 1151 ano e chemical || ||||||||||||||||||| |||||||| learn |||||||| 1'0019 1'0046 I'0228 1 '0342 I '0457 1°1034 I'1155 I'1359 714 l'o 194 |||||||:8888888888I||||||| 18 45 12:4 15 3 Wagner, Zeitschrift für physik. Chemie, vol. v. 1. 36. oí + Sprung, Pogg. An- nal. vol. clix. p. 1. 6 Mutzel, Wied. An- nal. vol. xliii. p. 25. 6 Bouty, Journal de Physique, vol. vi. p. 10. 7 Arrhenius, Zeit- schrift für physik. Chemie, vol. i. p. 295. 2:55 30 1250 'OI 'OI 1206 *00746 0746 *743 1.48 3º74 7.13 1307 1'0046 1'0096 1'0228 1°0457 1°0912 | 1•1359 | 15 1'206 12:1 113'0 220.0 508.0 9910 188860 ciereneren 1130 1100 1016 991 944 914 II IIIlllll 907 27420 412 SOLUTION AND ELECTROLYSIS. POTASSIUM CALORIDE-continued. Equivalent Gramme Molecule, KC1, 74.59. *O221 134. 81 1310 1276 1241 1207 1174 1143 II|Il öll || | 0 !!!!!! 131'I 127.6 124.2 I 'OOO8 !!!!!!!!!!! 011111111111 18 Ostwald, Zeitschrift | für physik.Chemie, vol. i. p. 85. 9 Vicentini, Atti dell' Accad. di Torino, vol. xx. P. 688. !!!!!!!!!!! ol|||ll||||| IlIllIIllll 111 '0236 1180° 1254 *0231 | 1140 | 1211 '0222 | 1110 | 1180 *0220 1080 | 1148 0218 1060 | 1127 !!!!! 1285 Ooool 00002 '00006 *0001 *0002 *0006 .001 ·002 *006 !!!!!!! ZIIIIIIIIII II||| 1 !!!!!!!!!!! IIII!!! AMMONIUM CHLORIDE. Equivalent Gramme Molecule, NH_CI, 53.5. - 12051 1281 I 209 1215 1292 1209 1285 1204 1280 1197 1273 1190 1265 1180 1255 1157 1230 1142 1214 IIOI 1171 1078 1146 1035 I100 11 Kohlrausch, Wied. Annal. vol. xxvi. p. 195. 2 Sprung, Pogg. An- nal. vol. clix. p. 1. 8 Grotian, Pogg. An- nal. vol. clx. p. 262. 14 Arrhenius, Zeit- *0229 schrift für physik. 0212 Chemie, vol. i. p. *0198 295. . 15 Hittorf, Pogg. An- nal. vol. xcviii. p. 'OI ☺ III|II||||||||||||||| co 1 0 1 0 1 0 1 60 60 50 0 50 50 50 60 60 60 111111lllllll|||||| *03 150 15.0 I'0002 1'0013 I '0019 1'0084 1'0113 go 1152 818181111 10° SITTI 33. I'45 30 *000976 *00195 *00725 *0145 *029 *058 •116 •232 *0039 *0078 *0156 *0312 *00097 *0019 *0038 'O100 •0184 *0072 *0142 *0283 *0746 •137 '0000535 *000107 *000321 *000535 *00107 00321 00535 *0107 *0321 *0535 1605 •267 *534 :57 2.65 3:44 56263 7.59 15.92 3:12 1 '0461 15.0 1 '0483 11.8 | 10730 1501 | 540 .0625 65'96 18 V •125 1'0005 | 1560 OI I'0042 12705 2440 0 0 0 0 1054 1020 976 1120 1084 1037 991 •25 466.0 •00152 23,3 I 276 16 Lenz, Mémoire de l'Acad. de St Pén tersbourg, vol. xxvi. No. 3. 7 Vicentini, Atti dell' Accad. di Torino, vol. xx. p. 688. 111111 1111 Illlllllllll IIIIIII!!! IIIIII !!!!!!!!!! 0226 0 0 0 0 0 0151 0309 IIIlllo !!!! 12007 1150 II 20 '0224 Iogo *O221 | 1060 18 | 0221 1030 *00282 *00578 'oo99 *0176 *0342 ·0224 053 I 222 1190 1159 1127 1095 *0942 183 : 00001 | - *000058 *000117 *000351 *000585 *00117 *00351 11 Kohlrausch, Wied. 1 Annal. vol. xxvi. 1). 195. IIiiii II!!!! SODIUM CALORIDE. Equivalent Gramme Molecule, NaCl, 58.5. | 1024; 1088 1028 1093 1027 1092 1094 1018 1082 IIIIII ya 1 1 1 1 1029 '00006 '0001 *0002 0006 *001 *002 '006 01 '03 IoI4 1008 Uibo NIC . N OK man *O117 *0351 0585 •1755 292 31 *0245 2 Sprung, Pogg. An- ral. vol. clix. p. 13. *0252 8 Arrhenius, Zeit- schrift für physik. Chemie, voi. i. p. 295. 1 1 1 aloo oo la 10 10 To co o o o 4 Mutzel, Wied. An- nal. vol. xliii. 1). 25. il ||||1888 8 8 118 118881111 -583 I0006 15'0 I'O015 | 15.0 1'0023 5.6 1'0038 15.0 1'0068 1704 1 .0207 I'0334 1 '0406 1'1159 o o coriando -945 10 G con open o dono Il 111!!!!!!! 6 Hittorf, Pogg. An- nal. vol. cvi. p. 374. 6 Lenz, Mémoire de l'Acad. de St Pé- tersbourg,vol. xxvi. 2.865 4.61 5.62 15.03 15071 22:34 24:6 3'0 4.477 50 1 1 1 1 1:1716 | 130 1.1890 1590 '0625 •125 1.0021 | 15'0 1.0050 | 150 | 54.26 18 104°2 | 18 | 413 414 SOLUTION AND ELECTROLYSIS. SODIUM CHLORIDE-continued. Equivalent Gramme Molecule, Naçi, 58.5. . . . 18 . 1'0105 1 '0207 || || - 18 - + Il II - 197.6 369.0 119.57 116-3 112-1 H10:1 107.0 104.0 111 111111 11 111 111111 110 |||| 17 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 80. 8 Vicentini, Atti dell' Accad. di Torino, vol. xx. p. 688. oll ||ll||| III IIIII! | ||||| I'oooo *0236 *0232 .0232 9708 1031 950 | 1010 920 | 978 ||| 11! 18 LITHIUM CHLORIDE. Equivalent Gramme Molecule, LiCl, 42.5, 1026 1015 1004 1002 1116 - 11 Kohlrausch, Wied.. Annal. vol. xxvi. I!!!!! ||||| p. 195. *0252 •0248 Tálalla oll|||||||||| IIIII||||||||||lllll 160 161 160 160 0 0 0 0 0 0 0 0 0 IIIIlIIlllllllllllll || 2 Sprung, Pogg. A1- nal. vol. clix. p. 17. 8 Wagner, Zeitschrift für physik. Chemie, vol. v. p. 38. 4 Arrhenius, Zeit- schrift für physik. Chemie, vol. i. p. 295. I 1'0006 I'0021 •I • II *235 111011öcimiento || I'O126 • 25 144 2.86 *5 ·0058 *0115 *023 046 *092 *183 *000976 *00195 '0039 .0078 *0156 *0312 *00643 00936 ·0287 'OOIT *0016 *0049 '00004251 '00001 *o0o085 '00002 .000255 *00006 '000425 '0001 '00085 *0002 '00255 *0006 *00425 *001 '0085 '002 *0255 *0425 'OI *1275 '006 '03 *04 '05 212 424 2.985 4.146 70757 IllIIIIII 5 Kuschel, Wied. An- nal, vol. xiii. p. 295. og I'0249 | 10784 ||| ? TABLE OF ELECTRO-CHEMICAL PROPERTIES. 415 1a | 3:0 3.213 50 6.895 1000 ΙΙΙΙο ||||| 303 |||ll 16 Fitzpatrick, Phil. Mag. (5th series), pol. xxiv. p. 377. III|| ||||| I'2173 ão 1 106 *0083 *00195 0165 •0039 11111 11111111 *0331 •0662 11111 11111111 *0078 Troll!!! | 50 50 0 0 0 zo zo zo |||||||| *0156 *0312 .0625 •125 25 •1325 |||||||| |||||||| |||||||| -265 '53 I '056 1.0028 10063 15 6941 969 *o0506 .0069 *0111 *0229 772 STRONTIUM CHLORIDE. Equivalent Gramme Molecule, ] SrCl2, 79'02. 18 | 0244 | 10701 1137 1040 1105 I'41 0240 1000 *0237 880 5508 *00064 *00087 *0014 *0029 III. 1063 331 bei 353 •0217 706 9543 |||||llllllll 640 ·0212 1 1 1 1 IIIIIIIIIIIII II|||||1 | | పాపపపప పప 882 8672 20 i 0244 11 Vicentini, Atti dell' | '0235 | Accad. di Torino, 61 | vol. xx. p. 688. 400 2 Sprung, Pogg. An- nal. vol. clix. p. 18. 8 Mutzel, Wied. An- 923 nal. vol. xliii. p. 25. 752 4 Wagner, Zeitschrift für physik. Chemie, 9604 vol. v. p. 40. 6 Kohlrausch, Wied. 941 | 20 911 Annal. vol. vi. p. 853 | 20 | 148. 360 *O208 *0204 ||||||||| 15 2.0 2.5 30 3'5 II!!!! 1082 1250 1387 1499 I||||||| I'O 8982 120 1391 19:12 26.93 34.91 *000104 *000208 *000624 *00104 *00208 '00001 '00002 '00006 *0001 '0002 ||||| II!! BARIUM CHLORIDE. Equivalent Gramme Molecule, į BaCl2, 104. | 1142 | 1214 1144 | 1216 1133 | 1204 1126 1197 1118 | 1189 II!!! .715 807) - 11 Kohlrausch, Wied. '0240 | Annal. vol. xxvi. | *0226 p. 195. 20 0222 | 2 Sprung, Pogg. An- - | nal. vol. clix. p. 18. 2955 683 416 SOLUTION AND ELECTROLYSIS. BARIUM CHLORIDE-continued. Equivalent Gramme Molecule, BaCl2, 104. 0006 *001 *002 *006 11 1102 1092 1074 1031 *O234 1 1006 oli lisinin 1172 1161 1142 1000 8 Arrhenius, Zeit. schrift für physik. Chemie, vol. i. p. 295. N OL *03 OOX got 11111|||||||||| 1.0001 1'0022 I*0044 I'0070 1'0094 I'0112 I'0457 | 15.0 L'0905 15.0 J'1028 | 1900 1'2277 14:4 I 2546 73 | 1.2655 | 15.0 co II 10 la 160 o Co o o o o o III||||||||||llo 1111öci si in ga ocije na 3 0919989 19881111 II|||||||||||||| 1907 4 Wagner, Zeitschrift für physik. Chemie, vol. v. p. 35. 5 Mutzel, Wied. An- nal. vol. xliii. p. 25. 6 Hittorf, Pogg. An- nal. vol. cvi. p. 379. *0214 0207 | 18 | 0193 487 CALCIUM CHLORIDE. Equivalent Gramme Molecule, CaCl2, 55.46. 434 2001 718 1400361 90 15.0 20'0 11 | 11 11 Kohlrausch, Wied. Annal. vol. vi. p. 148. 348.0 *O218 2.71 456 5-307 150 *O213 ·0207 *0235 | ? Hittorf, Pogg. An- ·0300 ral. vol. cvi. p. 381. 633.0 1083.0 1389.0 15830 20 3'0 4'0 4'3 *O203 *O201 o o Ovieron o dos o o 8 Sprung, Pogy. An- nal. vol. clix. p. 19. wolde ó ou o o o os 1.2119 150 1666'0 1644'0 TIMI T *O202 *O206 5 | 6 | 6 | 6 II 18:18:1811 11 oci moj ovisi 6 + Wagner, Zeitschrift für physik. Chemie, vol. v. p. 36. 5 Mutzel, Wied. An- nal. vol. xliii. p. 25. 15.0 1204 80 15410 I'3267| 150 137000 | 1'3633 | 15.0 1177.0 1 1'3637 | 20:01 *00624 *0104 *0208 *0624 *104 *311 *518 •784 1'03 1.24 4:97 9:54 10.65 *12 ΙΟ l'13 21.6° 23.5 ,30 33-37 36.6 37.08 *0231 *O244 90 9°14 | TABLE OF ELECTRO-CHEMICAL PROPERTIES. 417 00099 o os 990 1052 970 |||| 1031 !!! ||| ||| - 989 30 - - III lii 16 Vicentini, Atti dell' Accad. di Torino, vol. xx. p. 688. 7 Fitzpatrick, Phil. Mag. (5th series), vol. xxvi. p. 377. - *00312 *00025 1109 1071 1111111 111 0125 32:67 63'0 120.2 228.0 I'0017 | 15'0 430°5 1'0043 sog'o | 1.0093 15'0 | 1442.0 - z oo O CO o II|II|||| 969 II||||| 1033 I !!!!! ||||||| ||||||| 861 IIII 915 809 860 721 766 1 *000975 *00195 MAGNESIUM CHLORIDE. Equivalent Gramme Molecule, } MgCl.,, 47.46. J19'92, 25 1070 115.8 1043 III.6 1010 107.2 ·0185 *037 .0039 *00781 10719 046 |||||| | 1 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 109. 2 Kohlrausch, Wied. Annal. vol. xxvi. p. 194. *074 1024 999 •0156 *0312 *148 I'0005 | 15.0 97-3 957 | *O241 un To *0475 *142 .237 *412 |||||| ||1815R 11060 o 160 160 loc o co ma che ha •473 •164 •5 *O220 I'0004 | 15.0 1.0013 15'0 1:0035 0 1'0035 | 150 I'0065 | 15.0 I'0197 15.0 I'0366 | 14:4 1.0386 | 15.0 I'IT14 150 I'1792 15:0 I.1934 1.2685 941 I'O |||||||||||||| ||||||||||| s Vicentini, Atti dell Accad. di Torino, vol. xx. p. 689. 4 Hittorf, Pogg. An- nal. vol. cvi. p. 383. 6 Wagner, Zeitschrift für physik. Chemie, vol. V. p. 38. 6 Mutzel, Wied. An- nal. vol. xliii. p. 25. *O222 30 *0224 *0238 425 288 50 541 7.67 isini IO'O 0340 0016 *0027 W. S. •277 *552 I'I 773 2-327 4:31 4.57 12.81 20:12 21°53 28071 ·0073 *0001 ‘0153 *00154 *00192 '00322 11 ||| Ill !! | : 418 SOLUTION AND ELECTROLYSIS. ZINC CALORIDE. Equivalent Gramme Molecule, 1 ZnCla, 67.82. olli '000068 *000136 *000407 *000678 *001356 *00407 *01356 '00001 '00002 *00006 *0001 0002 *0006 '001 002 •006 II!!!! |||||||| 1094 103611 IIOI 10351 1100 1031 1096 1029 1020 1004 1067 1057 979 1040 *00678 1 Kohlrausch, Wied. Annal. vol. xxvi. p. 195. 2 Vicentini, Atti dell' Accad. di Torino, vol. xx. p. 689. 8 Hittorf, Pogg. An- nal. vol. cvi. p. 397. 994 *0678 ·0407 |||||||||||||||||||lo TI .!!!!!!! ||||||||||||||| 0|||||||||||||||||| L L !!!!!! SOM TILL II l | •2034 973 905 . I'0007 *03 I 1995 25'0 ||||||||||||||||| *05 250 3.28 1'0023 T.0062 I'0312 I '0570 I•1600 1995 19.5 1985 195 19.5 4 Arrhenius, Zeit- schrift für physik. Chemie, vol. i. p. 295. I'O 6.4 1745 30 26.52 26.88 45.35 50 IO'O 1°2587 | 1905 I°4921 | 195 6 Wagner, Zeitschrift für physik. Chemie, vol. v. p. 40. 6 Long, Wied. Annal. vol. xi. p. 37. *0117 '023 *00173 il || .0034 !! || II || •774 25 500 IO'O 20'0 30'0 40.0 •378 1.617 3-517 Gronor 1560 15.0 1560 150 15.0 ON I '024 1'048 1'094 I.190 I°299 I'423 10570 110746 5.76 |||||||| |||||||| !!!!!!!! |||||||| IIII!!!! |||||||| | 15'0 94 100 II.6 15:48 15'0 | 15:01 TABLE OF ELECTRO-CHEMICAL PROPERTIES. 419 '0503 *0999 8.34 701 20 | 1 Wershoven, Zeit- schrift für physik. Chemie, vol. v. p. 492. ||||| చర్చ CADMIUM CHLORIDE. Equivalent Gramme Molecule, CaCl2, 9137. 4.61 | 18 | 0231 / 835 | 887 '0226 14:5 *0231 660 2407 '0227 512 41.6 450 49'2 '0222 51°1 '0222 439 *0055 l '9991 | 18.0 '01095 | 9996 | 18:01 '02194 | 1'0004 | 18:0 1'0022 | 18'0 I'0045 | 105 I'0039 | 18.0 *0849 1'0057 / 18.0 •1102 10075 180 *1105 I'0076 | 18.0 •1100 *399 :518 •769 1 1 1 1 1 1 1 *599 0526 1 0 0 0 0 1 0 0 0 0 33.8 2 Grotian, Wied. An- nal. vol. xviii. p. 194. ·0224 *997 447 L'O I '002 849 45:52 *0937 *574 I'203 5.01 10.04 I'0062 I ‘0437 1°0923 0224 0218 180 180 155.0 18:01 225'0 1 1 1479 IIllIIIIIIIIIIIlll ||!!!!!!! 8 Hittorf, Pogg. An- nal. vol. cvi. p. 547. 4 Wagner, Zeitschrift für physik. Chemie, vol. V. p. 36. 5 Vicentini, Atti dell' Accad. di Torino, vol. xx. p. 689. llllllllllllllllllllllllllll 14.94 18.0 *O218 140 262.0 27700 18:01 Іоб I'1436 1•1984 I2415 I.2891 1.874 2.603 3:12 3.75 4°373 510 6.558 o 1 1 3 1 0 1 1 0 0 1 0 0 0 29.97 2620 0252 6 95 985 18.0 700 18.0 6.8 9.8 180 1 33:53 40'13 IIIllIIIIIII!!!!! 11 ||||||||||||| 204'0 19:8 22.96 26.60 43.76 44'06 7.50 7.56 49.51 9:067 131'0 14 .00649 '01097 '0193 *0471 *00071 *0012 00211 *00515 E *0241 96051 *0244 920 18 0236 870 18 / 0237 | 780 | 829 1 1 ||| 27-2 CUPRIC CHLORIDE. Equivalent Gramme Molecule, CuCla, 67.07. 9301 989 957 925 *125 *0063 *0107 *0201 •0396 0885 '00094 *0016 *003 *0059 '0132 T!!!! IIIII I!!!! 10644 1044 | 996 | 907 II!!! 11 Vicentini, Atti dell Accad. di Torino, vol. xx. p. 689. 2 Wagner, Zeitschrift für physik. Chemie, vol. v. p. 37. 420 SOLUTION AND ELECTROLYSIS. FERROUS CHLORIDE. Equivalent Gramme Molecule, 3 FeCl2, 63:32. Olli 7101 754 ) 700 744 680 | 723 | COO Olli 111 11 Vicentini, Atti dell' Accad. di Torino, vol. xx. p. 690. NICKEL CALORIDE. Equivalent Gramme Molecule, į Nici,, 64:67. 7761 730% 181 02451 *O240 11111 ||||| ||||| | దీపపప IIIII 11111 10702 1046 996 11111 1 1 Vicentini, Atti dell' Į Accad. di Torino, vol. xx. p. 690. 2 Wagner, Zeitschrift I für physik. Chemie, vol. v. p. 39. 0245 907 *522 1'0045 4924 MANGANESE CHLORIDE. Equivalent Gramme Molecule, j MnCl,, 62-87. | - | .6822 — •0216 *O206 '0202 ·0206 0683 083 831 1°733 2-715 30785 4524 4.960 50710 JO'O 15'0 20'0 23:22 1.0895 I'1378 naererererlo dio o o ö 0 60 120 60 60 col I!!!!!!! 1043 Ilm All II!!!!!! I lovil 1 Long, Wied. Annal. | vol. xi. 2. 37. 1 2 Hittorf, Pogg. An- nal. vol. cvi. p. 383. 8 Wagner, Zeitschrift für physik. Chemie, vol. v. p. 37. ІобI I•2275 1•1900 1•2472 150 1•2828 | 15.0 995 904 250 *0203 TO20 950 | 18 | .0208 ALUMINIUM CHLORIDE. Equivalent Gramme Molecule, * Al,Clo, 4437. 83011 8001 1111 III 111! 160 os I!! III 1111 11 Vicentini, Atti dell' Accad. di Torino, vol. xx. p. 689. 2 Hittorf, Pogg. An- nal. vol. cvi. p. 391. *0064 *01583 '02406 OO10I '0025 0038 *00789 *o0963 'O1196 01875 *00122 *00149 ·00185 '0029 5'0 28.0 *00697 *00887 •03642 '00157 *002 *0037 4'22 TABLE OF ELECTRO-CHEMICAL PROPERTIES. 421 *0010 *0020 *0024 FERRIC CHLORIDE. Equivalent Gramme Molecule, FeClo, 54. | 2360 | 25091 1660 1765 1510 1605 1460 1552 1 290 1371 |||||| ·0034 11 Vicentini, Atti dell' Accad. di Torino, vol. xx. 2 Fitzpatrick, Phil. Mag. vol. xxiv. p. 377. *0053 *0060 *0324 1382 0168 *00312 IIIIIIIllIIllll 1111 111111 IIllllllllllll | | అపుడపపపపపపపడు IIIIIIIIIIIII!! 16172 1496 1356 1211 •00625 ||||||||| IIIIIIIIIIIIIII IIIlll ||||||||| . II|II|II||||||| IIIlll. 111111111 Till IIIlllll 8 Hittorf, Pogg. An- nal. vol. cvi. p. 389. ‘0125 *025 OS 1053 908 741 3.81 32:51 V HYDROBROMIO ACID. Equivalent Gramme Molecule, HBr, 80-75. 3559 3612 1 000244 *000488 , 1 Ostwald, Journ. Für Chemie, vol. xxxi. p. 438. ვნg6 *000976 *00195 •0039 *0078 3644 mi dico o Ao contro co IIIllll oron ororerororo I!!! 2 Hittorf, Pogg. An- nal. vol. cvi. p. 399. •125 3640 3632 3612 3571 TI!!!!!!!!!!! ||||||||||||| IIlllllllllll IIIIIIIIIIIII 250 502 3519 *0625 •125 *25 1'004 1'007 1'014 1'027 14 20 14 14 11!!! 3267 A 3.92 10:36 422 SOLUTION AND ELECTROLYSIS. POTASSIUM BROMIDE. Equivalent Gramme Molecule, KBr, 118.79. *072 I 0063 5144 o low O - 11 Kohlrausch, Wied. | Annal. vol. vi. p. I'O 497 960 1 404 1832 1057 J020 995 974 321 | 1028 Iº5 2'0 2.5 OS TO IL !!!!!!!! 11111888110 '0203 *0179 2 Hittorf, Pogg. An- nal. vol. xcviii. p. 27. 2243 30 2623 929 3:15 I!!! 850 2977 3294 4'0 181 "OIGO | 18 0156 18 Sprung, Pogg. An- 1 nal. vol. clix. p. 11. •0324 0748 CADMIUM BROMIDE. Equivalent Gramme Molecule, CdBr2, 135*75. 2:15' | 18 | '0235 | 899 956 4:37 18 '0237 | 792 842 18.0239 691 735 11.6 002386/ 9990 | 18, *005517 99935 'O1134 1'00002|| •01867 1'0010 *03743 1'0031 *07517 1.0075 || Wershoven, Zeit- schrift für physik. Chemie, vol. v. p. 493. 154 |||||| .253 623 662 023 506 1'013 *O233 ఎవరు ఎప్పుడు II|||| IIllll||||ll |||||| III!!!!!!!! Illllllllll 2 Grotian, Wied. An- nal. vol. xviii. p. 194. •0751 33:42 473 *390 IOI'O 275 .813 I'OJ 5807 10:10 20ʻII 29.95 42-99 10073 1.0437 10916 1.2004 1•3288 *0232 *0225 *0232 0239 10781 2.936 152.0 219.0 253'0 18 ! 242.0 TOO 131 91'4 52 II||| | 4'904 l 18 .0288 49 HYDRIODIC ACID. o co 3567 *000976 *00195 '0039 ||||| I!!!! jnici Iiiii crorore 11111 11 Ostwald, Journ. für Chemie, vol. xxxi. p. 438. 3616 3628 3644 3644 Illll 11111 III!! II!!! 11111 2907 *0031 ‘0062 0123 '0495 1 TABLE OF ELECTRO-CHEMICAL PROPERTIES. 423 ·099 3632 198 !!!! *0312 *0625 3608 3559 3511 2 Hittorf, Pogg. An- nal. vol. cvi. p. 401. I'0058 135 •397 792 1.576 3:11 6•1 17.17 IIIlllllll IIIII!!!! IIIIII!!! IIIIIIIII IIIII!!!! III!!!!! •125 25 I'0117 135 1°0230 13.5 | 1°0453 1395 80-4 1319 1282 11 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 85. POTASSIUM IODIDE. Equivalent Gramme Molecule, KI, 1659. 143-1? 139-1 13601 1254 1329 1225 12903 1192 1156 ñ chcem Illlll I!!!!! |||||| Illll 2 Kohlrausch, Wied. Annal. vol. xxvi. p. 195. * *0009761 .00195 *0039 *0156 '0312 '0078 -269 *518 125.4 IlIllll 111111 *000166 *000332 | IIIlIIlIlll ||||ll 8 Hittorf, Pogg. An- nal. vol. xcviii. p. .000995 29. *O016 1293 *00001 *00002 *00006 *0001 0002 *0006 'OOI 002 •006 *00332 00 *541 I'17) IlIllllllllllllllll||||ll *O242 * Sprung, Pogg. An- ·0219 nal. vol. clix. p. 1. 10094 1057 1082 1 12072 1283 1216 1293 1216 1293 1216 1214 1291 1209 1285 1203 1279 1197 1273 1176 1250 1161 1234 123 1194 | 1102 1172 1069 997 2.610 0096 I040 •OI •03 To be 150 160 60 60 60 60 60 0 60 60 60 60 60 60 !!!!!!!!!!!!!!!!! ·0190 5 Arrhenius, Zeit- schrift für physik. Chemie, vol. i. p. 295. 11:23:11 |||||| 8255 9 •495 1•640 7.823 10:57 14.84 26•86 36.8 5263 19:5 onos 1'0048 1'0112 19:5 I'0603 1995 I'1081 | 12'0 ['1180 1905 I'2414 II°O 1°3530 1945 1.5860 19.51 968 1020 I'O 2:01 3'0 5'0 II!!! 18 | 0156 | 900 18.0142 770 E 424 AND ELECTROLYSIS. SOLUTION TYY AMMONIUM IODIDE. Equivalent Gramme Molecule, NH,I, 144:84. To'o 7221 18 20'0 735 1°574 2.54 3.663 1494 30.0 1°0652 3.1397 I.2260 | 1*3260 T 1.4415 OOO OO OO OOO 2318 982 1044 949 1009 912 1969 867 1 922 786 835 | 18 III 110 II!!! 1 Kohlrausch, Wied. Annal. vol. vi. p. 149. I!!!! ol!!!! I!!!! 40'0 18 4.98 3166 3917 18.0154 50, *346 857 1 10'0 20'0 *721 1.567 2:57 | 1'0374 1'0803 1•1735 పపపపప SODIUM IODIDE. Equivalent Gramme Molecule, NaI, 149:84. 2792 | 18 *02221 806 543 *0216 753 801 1069 *0204 682 1545 1972 | 18 0199 523 | 11111 I!!!! I!!!! !!!!! 1 Kohlrausch, Wied. Annal. vol. vi. p. 149. I!!!! 300 *0198 600 E 400 1:2830 3.77 ' 1'4127 | 18 | 27 LITHIUM IODIDE. Equivalent Gramme Molecule, Lil, 133.82. | 18 | '02191 761 18 :0216 783 18.0212 18 .0207 588 625 1258 181 .0203' 555 | 590 536 708 665 625 11 Kohlrausch, Wied. Annal. vol. vi. p. 149. 50.0 IOʻo .804 | 1'0361 | 181 1*07561 18 1•1180 18 1•1643 1421381 15.0 20'0 25.0 I 253 1°740 2.267 I!!!! III! 11111 : 11111 J023 *0429 I .204 *0112 6.6 589 *00235 , '9991 ( 18.01 *0055 '9996 18.0 1.0005 18.0 *O220 I'0021 *0330 1'0038 | 18.0 *0441 I'0056 18.0 *0552 1.0072 | 18.0 399 Til!!! CADMIUM IODIDE. Equivalent Gramme Molecule, jCNIZ, 182.53. 1.95 | 18 829 / 881 3.83 18 1740 626 107 517 454 17.0 1907 ||||||| 14'I Il IIIIIII III Il !!!!!!! 11 Wershoven, Zeit- schrift für physik. Chenie, vol. v. polo 493. 2 Grotian, Wied. A12- nal. vol. xviii. p. 194. 8 Hittorf, Pogg. An- nal. vol. cyi. p. 543. 410 I'O 378 ·0562 1'0073 18.0 | 1972 0286 Ιο17 I'41 Il || Il TABLE OF ELECTRO-CHEMICAL PROPERTIES. 425 1 16r 144 0242 ||||||||| To Colo Colo Do It *O240 13 140 T||||||||||| I||||||||||| |||||||||||| |||||||||||| 0244 107 U . 2900 | 18 | 293'0 18 | 0263 1 *0328 ·0596 ·0864 •10 పప 00094 | 99895) *00171 | 99921 *00231 / 99938] *00287 *99945 *007.19 I'0007 'O1441 10027 *02923 ( 1 '0067 1869 POTASSIUM CADMIUM IODIDE. Equivalent Gramme Molecule, 4K,C014, 347*43. 1997 | 18 | .0226 | 2016 | 2143 3*32 *0231 1935 2057 4:32 | 18 | 0228 1987 5.26 1831 1946 31.8 21.6 1498 1592 · 38.5 | ·0234 / 1317 1400 11 Wershoven, Zeit- schrift für physik. Chemie, vol. v. p. 493. ||||||| |||||||| •0229 *O233 •25 |||||||| 0231 •50 T'003 1•674 o 1 60 0 0 0 0 0 0 2 Grotian, Wied. An- nal. vol. xviii. p. 194. Mill Till IIlllllllllllll IIIII|II|||||||| 38.32 1 301 8 Hittorf, Pogg. A1- ral. vol. cvi. p. 527. 104 1'0387 o ogg o Son cu 148.0 278.0 *0224 408.0 0218 6890 0214 9860 *0207 1319'0. ! 18 | 0198 113l||| |||||||| |||||||| 709 18 724 674 | ! 216 — - 4.87 18.0 55.5 II.2 5623 10.03 14:07 ထ = ထ ထ = ၁ 18.0 -278 *3 *599 913 I'230 1°274 1•700 2.138 18.0 I'1354 1•1854 1•1890 J'2551 Il'o I'3171 180 24.75 29•6 234'0 35-32 3.254 3.770 2810 40'03 44:13 47.5 1.4821 | 18.0 1.5576 18.0 18.0 I'0065 ఈ | పడిపప | ప 1'0821 I '006 5:04 10-14 15.11 25.25 30°33 34.96 *0291 •151 *315 -490 .896 J'1280 1°2338 I.3552 45.12 1°362 1.957 *000488 | *o0o976 *00195 1 *00391 '000244 | *000488 000976 00195 HYDROFLUORIC ACID. Equivalent Gramme Molecule, HF, 20`1. 69.421| 25 | 313421 59.56 25 2689 49.49 25 2235 39:11 | 25 | 1765 1 1111 Till I!! ||| I!!! | 1 Ostwald, Journ. für Chemie, vol. xxxii. p. 303. 12 At 25º. 426 SOLUTION AND ELECTROLYSIS. 1368 .0078 •0156 *0312 *0625 25 1043 IIIIII! !!!!!!! IIIIII olli III HYDROFLUORIC ACID-continued. Equivalent Gramme Molecule, HF, 20ʻl. lo 30-30 25 23:11 17038 786 13:14 594 10.00 451 7.89 6:54 | 25 ||||||| IIIIIII |||||llo IIIIIII 356 | 296 POTASSIUN FLUORIDE. Equivalent Gramme Molecule, KF, 58.14. 734 780 18 *0214 718 11 Kohlrausch, Wied. Annal. vol. vi. p. 149. 1196 1609 I!!!!!!!!!! oooooooooovi ||||||||||| IIIIIIII!!! *O217 '0219 *O220 '0222 60 60 0 0 0 0 ||||||||| III|||||||| ||||||| IIIIIIIIIII ||||||||||| 2338 2416 2422 2385 2303 I|||||||||| 345 303 265 230 | 322 282 244 | 18 | 0260 1 Kohlrausch, Wied. Annal. vol. xxvi. p. 196. *000063 *000126 *00038 *00063 *00126 *00378 *0063 *O126 *0378 ·063 *00001 *00002 '00006 *0001 '0002 *0006 001 *002 *006 |||||||||| IIIIIIIIII 1111111111 పప పపపపపపపప IIII!!! |||||||||| |||||||||| NITRIC ACID. Equivalent Gramme Molecule, HNO3, 63·04. | 11449 1213 1904 2024 | 3043 3282 3492 3622 |||||||||| IIIIIIIIII IIIIIII||| IIIIIIIIII 3643 | 3665 3421 3636 0162 | 3395 | 3609 TABLE OF ELECTRO-CHEMICAL PROPERTIES. 427 •189 I'O2 •315 2.IL övi nici III!! 3.28 15 I '0034 I '0185 1'0354 I'1010 1.1660 1•3061 *0227 | 2 Grotian, Pogg. An- *0211 nal. vol. clx. p. 262. *O200 •0184 8 Ostwald, Journ. für Chemie, vol. xxxi. p. 439. !!!!!!!! |||||||| 2944 D1 11 11 2991 2770 2070 1470 30 O O OO OOO o 2200 1562 648 4 Lenz, Mémoire de l'Acad. de St Pé- tersbourg, vol. xxvi. 3234 3432 000121 *000243 *000487 *000975 Gora ||||II|II c G GG GTI *00195 •0039 ܩܪܢ GG G Gܫܶܛ ܟ݁ܪܶܬ݂ ܩܶܪܢܪܬ 111111111111111111111 1111 I!!!!!!!!! *0078 0156 nenororerorororonor unore !!!!!!!!!!!! ||||||||||||| *0312 3500 I!!! IIIIIIIIIIIll. 0625 23 •125 - 1'0017 1°0044 I'oogo I'0185 erererer 25 77.9 3159 M 2005 ·063 *126 .252 *504 1'0019 1.0046 1'0094 T10188 403 78.3 15 32543459 3200 3401 3103 3298 | 2953 ! 3139 !!!! |||| 150'0 3:09 6.09 17.17 22'0 48.26 10:0 *00075 *0015 *0030 *0061 'OI22 *0245 .049 098 197 •393 •784 1:56 3.09 *396 •785 1:57 3:12 *000101 *000202 *000607 *00101 *00202 *00007 101 *0202 •0607 '00001 *00002 *00006 0001 *0002 *0006 OOI *002 ·006 II||||||| IIIIIIIII IIIllllll IIIIIIlll II||||| 111111111 POTASSIUM NITRATE. Equivalent Gramme Molecule, KNO3, 101.17. 12154| 1292) 1198 1274 1220 | 1297 1207 1199 1190 943 5255 1173 | 1247 1140 | 1212 11 Kohlrausch, Wied. | Annal. vol. xxvi. p. 195. . •0246 2 Sprung, Pogg. An- *0225 | nal. vol. clix. p. 12. *0214 8 Arrhenius, Zeit- - schrift für physik. Chemie, vol. i. p. 295. I'3 1265 1180 11 428 SOLUTION AND ELECTROLYSIS. POTASSIUM NITRATE“continued. Equivalent Gramme Molecule, KNO3, 101•17. 'OI 1.99988 10013 | 0216 | 1122 | 1193 1134 1102 05 1.0028 o inininindo i • III!!!!! la l 1 oo oo oo ooo 1045 1°0064 1'0068 I'0201 I '0314 I '0620 I'0621 I'1290 ||||||||||| 14 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 85. 6 Hittorf, Pogg. An- nal. vol. ciii. p. 41. 6 Wagner, Zeitschrift für physik. Chemie, vol. v. p. 37. 7 Mutzel, Tied. A1- nal. vol. xliii. p. 26. 15'0 11.4 500 2'0 2 ol|||||||||| |||||| lopp mo! !!!!!!!! |||| 3:0 'oo99 *0197 132.6 *0395 *079 .0039 Londrororo 1255 1224 1193 ΙΙ6Ι II23 Lenz, Mémoire de l'Acad. de St Pé- tersbourg, vol. xxvi. '000976 *00195 .0078 *0156 '0312 *0625 1.0037 | 150 '125 1.0080 | 150 1'0159 | 15'0 | 1'0314 15'0 |||||| 135*9* 129. 21 125º7 121.6 117.2 61.98 117.8 22101 4080 | 18 1086 'IOI *303 *504 1.005 1.06 3 '08 4:9 94 9:52 19.8 •158 *316 .63 10254 2.49 409 1053 IOOI 937 867 •25 |||| IIII!!!!! IIIIII!! IIIIIII! 0167 intino inco 11|||||| !!!!!!!! AMMONIUM NITRATE. Equivalent Gramme Molecule, NH, NO3, 79*9. 442.01 | 18 884 1 831•0 118 7672 1011 15070 1.606 1018 20820 3.8 1000 25610 927 2929'0 | 18 3190.o 18 3351°0 18.0158 3419'0 | 18 0157 427 – 11 Kohlrausch, Wied. ·0236Annal. vol. vi. p. *0223 149. •0169 2 Sprung, Pogg. An- *0173 nal. vol. clix. p. 10. 5:46 7.11 743 TABLE OF ELECTRO-CHEMICAL PROPERTIES. 429 - 18 Lenz, Mémoire de / *0625 •125 I!!! |||| 62.93.18 I 20'I 2270 | 18 43207 118 | 1006 | 1069 1 961 | 1021 908 / 965 865 | 9191 E Till 1111 I!!! Till •25 tersbourg, vol. xxvi. '000085 *00017 *00051 SODIUM NITRATE. Equivalent Gramme Molecule, NaNO3, 85.08. 1036 1033 1031 II|11 11111111 !!!!! 1036 00001 *00002 *00006 '0001 *0002 *0006 'OOI 002 *006 *OI : 1027 2.422 *0017 *0051 1016 1 Kohlrausch, Tied. | Annal. vol. xxvi. p. 195. *0241 •0234 / 2 Lenz, Mémoire de *0245 l'Acad. de St Pé- tersbourg, vol. xxvi. 8 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 80. •0085 1013 942 1001 017 IIII|||||||||||||| 979 er *125 964 932 03 *424 05 1'0004 I '0018 1'0052 20'2 20'2 13:0 *091 4 Hittorf, Pogg. An- nal. vol. cvi. p. 377. 1'0053 I '057 I 2 •125 *204 *335 2.8 |||||||| IIIIIIIIIIIIIIIIIIIIIIIIIIII!!! 8 |||| |||||| 10074 Io'o L'oi18 I20 1'0195 I20 1'0273 2002 1 '0542 2002 1.1581 20'2 1.1904 | 9'2 | 18:1811 III III III III!!! I'O 5 Sprung, Pogg. An- nal. vol. clix. p. 14. 6 Arrhenius, Zeit- schrift für physik. Chemie, vol. i. p. 295. 22.04 25.0 ||||||||||| 3.0 3.5 |||lllllllllllllllllll *53. 14056 52:12 98.4 .0625 •125 25 *5 L'0026 202 I'0067 20'2 | 10137 20*2 1'0273 2002 7 Mutzel, Wied. A1- nal. vol. xliii. p. 25. 21 184.8 3400 414 725 *0083 ‘0166 *0331 *0662 7325 .265 000976 *00195 .0039 1020 113•7 III.2 108.5 1056 1024 990 |||||| *0156 '0312 1'0004 | 20'2 / 430 SOLUTION AND ELECTROLYSIS. LITHIUM NITRATE. Equivalent Gramme Molecule, LiNO3, 68.9. •0134 *0067 ·0268 •107 '000976 *00195 *0039 102'0 |||||lo |||||| *0535 *0078 96.1 1 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 83. 2 Fitzpatrick, Phil. Mag. (5th series), vol. xxiv. p. 377. 92-6 •214 89:6 •0134 *0268 *0535 *107 214 .428 *0156 *0312 *00195 *0039 *0078 *0156 *o$25 •125 IIIIllllll|||||| 1||||||||| zo||||| III!!! !!!1111111 |||||||||| IITTUTTI! |||||| IIIIIIIIIIIIlll. IIIlIIlIllIIllll 1111llllll||||llº isosto *0312 III|II|||| לסן 5320 *00017 *00034 QO102 '0017 '0034 ‘O102 11 Kohlrausch, Wied. Annal. vol. xxvi. p. 195. ||||| *00001 '00002 *00006 *0001 *0002 *0006 .001 *002 '006 *OI 1077 IIIIIIII 1660 3030 645 550 SILVER NITRATE. Equivalent Gramme Molecule, AgNO3, 169.9. | 1080| 1148 1073 1141 1145 1146 1145 1069 1136 1068 1135 1057 1033 1098 1081 1077 III|II |||||||||| *017 *034 •102 ||||||||||||||||| 1124 11 0 1 0 1 0 0 0 0 0 0 0 0 ||||||||||||||||| 2 Hittorf, Pogg. An- nal. vol. lxxxix. p. 203. 8 Wagner, Zeitschrift für physik. Chemie, vol. v. p. 40. *O221 T!!!! Ingill !!!!! 1017 •17 •403 I'0044 .507 1027 842 947 1 °0070 1.0076 180 18.6 ton ILI 185 18:4 TABLE OF ELECTRO-CHEMICAL PROPERTIES. 431 0218 6°45 7.927 8.772 ထ ထ ထ III!! I'o 1.0558 | 1962 1°0693 1'0774 J'1395 1°1534 1•2788 13079 1'4120 1•6843 *O216 o 1 1 0 1.601 14 Loeb and Nernst, Zeitschrift für physik. Chenie, vol. ii. p. 956. 6 Vicentini, Atti dell Accad. di Torino, vol. XX. p. 688. II'I 18.0 O 0207 5.0 *O2 *0008 *0136 *0255 *051 '119 ထ ထ IIII '0015 *003 *007 *0105 '015 12324 1221 I 206 1188 1134 1124 1110 1094 *O222 Till ||||lllllllllllllllllll III PLIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIII|||||||| тобі 1153 1126 025 TO Os -842 1086 1000 *052 I'O 31 IO22 50 50 como la loma : 104 '00763 *o0915 *0166 *0410 *00045 *00054 .00097 *00242 1111 '0228 10405 1105 '0229 1030 1095 18 | 0227 | 1010 | 1074 181 - 1 990 1052 108031.25 1067 *0227 042 *494 I '029 1.608 2-240 2.929 4.490 1°0418 1•0857 1.1318 1•1815 | 1.2363 I'3542 STRONTIUM NITRATE. Equivalent Gramme Molecule, 2 Sr(NO3)2, 105.54. 18 | 02251 585 '0225 479 401 335 ·0226 179 *o0918 *01076 '01604 *03747 14.91 16:18 26.81 28.73 36'11 50:44 *178 -255 .42 1.657 5'0 To'o 15.0 20'0 25'0 35.0 0228 277 *0241 III1 |||||| 111111 |||| III IIIlll | Long, Wied. Annal. | vol. xi. p. 37. 2 Vicentini, Atti dell' Accad. di Torino, vol. xx. p. 688. 8 Wagner, Zeitschrift für physik.Chemie, vol. V. p. 40. 4 Mutzel, Wied. An- nal. vol. xliii. p. 21. '00087 *00102 '00152 00355 9802 1042 990 1052 950 | 1010 920 1 978 432 SOLUTION AND ELECTROLYSIS. BARIUM NITRATE. Equivalent Gramme Molecule, Ba(NO3)2, 130-54. ! 114 1185 1114 | 1185 | 1 Kohlrausch, Wied. Anal. vol. xxvi. p. 195. I100 סלנו 1165 1152 1133 1121 1111111111111 1098 2 Vicentini, Atti dell' Accad. di Torino, vol. XX. p. 688. 3 Hittorf, Pogg. An- nal. vol. cvi. p. 381. 1044 JOII III||||| 111 111111111111111110 025 111 111|||||||||||||| 4 Wagner, Zeitschrift 111 111111let loire III ||||| vol. v. p. 35. 5 Mutzel, Tied. An- nal. vol. xliii. p. 25. '0241 10102 1073 | 1000 1063 - | 980 | 1042 | - II! : 541'0 CALCIUM NITRATE. Equivalent Gramme Molecule, 1 Ca(NO3)2, 82.04. 1.0307 | 18.0 | 314'01 | 18 | 02191 628 / 668 J'0608 | 18.0 541 575 1•1202 '0217 409 435 18.0 1.2352 18.0 11 Kohlrausch, Wied. Annal. vol. vi. p. 149. 18.0 818.0 O '00001 *00002 *00013 *000261 '000783 *0013 00261 *00783 *013 *0261 •0783 *1305 *391 .648 743 1'29 1*74 '0001 *0002 *0006 '001 ·002 006 'OI '03 OOO OOO OOCOOOOOOOOO O224 '057 1.0052 | 195 1'0060 10.6 Ion3 19.5 I'0146 13:6 I'0502 80 1°0520 | 19:5 *135 *466 5.8 6:20 *00665 *0137 *00051 *00105 *00191 1 3.98 7973 14.64 20'9 26:57 1 o ó ó ó ó ó ó oci 0220 intino inco 230 250 οοοοοοο 1 0 0 0 0 0 0 0 0 el 11111 1111111 2 Wagner, Zeitschrift für physik.Chenie, vol. v. p. 36. I!!!!!!!!!!! |||||||||||| I||||||||||| 141 102 1 2 E g'o 1'498 231 IO'O 3550 1111 TABLE OF ELECTRO-CHEMICAL PROPERTIES. 433 •0255 *051 *102 •203 *00312 '00625 *0125 *025 407 .05 - 30 348 57.87 1122 209:6 3955 1'0069 18.0 730'0 1'0070 74 I'0535 18.0 1324'0 1°1707 741 1 1'3919: 7.6! I!!!!!!!!! 11 61 60 60 0 60 .814 1 1111 1ācijoje U1||||||| IIIIIIIII 18 Fitzpatrick, Phil. Mag. (5th series), vol. xxiv. p. 377.“ 4 Hittorf, Pogg. An- nal. vol. cvi. p. 381. 8 Mutzel, Wied. An- nal. vol. xliii. p. 26. . • 2 W. S. 9 1.62 20:16 41°32 2.88 | 7.15 3:612 7052 13:47 19'34 MAGNESIUM NITRATE. Equivalent Gramme Molecule, 1 Mg(NO3)2, 74'04. | 1'0249 | 21 | 309.01 | 18 02181 618 | 657 , 1'0499 21 546'0' 18'0215 546 1°0994 21 8900 18.0211 445 | 1.1482 | 21 | 1096'o 18 .0207 365 I'O 2'0 3.0 di 00 00 '0116 *0232 *0465 *093 •185 *37 12.682 25'O 4807 811 800 ·00156 *00312 00625 *OJ 25 ·025 *05 III!! IIIIIIIIIIIII ||||||||||||| IIIIII! IIIIIIIIIIIII 11 Kohlrausch, Wied. Annal. vol. vi. p. 149. 2 Fitzpatrick, Phil. Mag. (5th series), vol. xxiv. p. 377. 8 Wagner, Zeitschrift fürphysik. Chemie. | vol. v. p. 37. 4 Mutzel, Wied. An- nal. vol. xliii. p. 26. 934 1824 1 l õvi giochi 343-5 I'0051 643-6 l'0099! 21 | 1200'0 465 Nini *0492 I •249 -464 18 18 00418 1 9990 *00849 9994 *02123 | 1'0007 *03951 10025 *08146 | 1.0065 T!!!! 25 పరమ పడవ CADMIUM NITRATE. Equivalent Gramme Molecule, 1 Ca(NO3)2, 117.9. 395| 18 *0234 / 935 994 7.59 | 0233 •125 18.1 0227 32-5 '0230 62.7 *O222 952 11111 111 ||||| Il 11 Wershoven, Zeit- schrift für physik. Chemie, vol. v. p. 493. 2 Grotian, Wied. An- nal.vol. xviii.p.194. 8 Wagner, Zeitschrift | für physik.Chemie, | vol. v. p. 36. I'014 5'02 10'07 0868 444 930 1'0070 1.0416 l 1'0875 00 00 09 65.22 18 *0226 2700 18 *O221 18 | 4800 1181 •02151 516! !! 434 SOLUTION AND ELECTROLYSIS. CADMIUM NITRATE—continued. Equivalent Gramme Molecule, Ca(NO3)2, 117.9. 20.2 377 Ilo 3000 2.047 3*345 4957 r•1926 | 18 1'3124 | 1'4589 18 | 7.6034 18 773'0 | 18 | 0212 8910 18 | 0214 8410 | 18 | .0228 697:0 | 18 | 0253 266 | 169 106 |||lo Till TOO 179 | 113 ! III 48.3 6580 LEAD NITRATE. Equivalent Gramme Molecule, 3 Pb(NO3)2, 165·1. -10231 | 1100 1169 *0081 *0125 *00049 '00076 - 111 Til I 127 '0248 1000 IOIO *0015 1074 50 001 11 Vicentini, Atti dell' Accad. di Torino, vol. xx. p. 689. | 2 Long, Wied. Annal. vol. xi. p. 37. I '0449 1'0937 1•1467 Zo ili 111111 :663 uno || 15 111 111111 083 JO'O 150 20'0 25'0 30.0 565 454 385 409 334 355 292 310 216230 nenorcrorer 111111 I '042 1'460 1°920 2'427 108631 1074 049 993 I'2043 1•2678 | 193358 8 Wagner, Zeitschrift für physik. Chemie, vol. v. p. 36. CHLORIC ACID. Equivalent Gramme Molecule, HC103, 384.87 40902 381-5 | 25 ·0082 *0165 4055 4087 11 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 75. *033 '0009761 ·00195 *0039 *0078 *0156 '0312 066 |||!! |||||| 37700 3710 hellll o 111111 I!!!!! II!!! III!!! II||| 2 At 250. *132 262 : 355.41 3778 POTASSIUM CALORATE. Equivalent Gramme Molecule, KCIO3, 122.59. - | 11414| 1213 | 1135 | 1206 1126 1122 1193 | 1119 1190 000122 *000245 *000735 *OOI 22 *00245 " '00001 *00002 *00006 *0001 *0002 II!!! I!!!! T!!!! III! 11111 11 Kohlrausch, Wied. Annal. vol. xxvi.. p. 195. ! Il TABLE OF ELECTRO-CHEMICAL PROPERTIES. 435. 1179 1171 *00735 'O1226 *0245 0735 '1226 0006 OOI 002 *006 01 TILI III |||||||| 1109 110) IOQI 1068 1053 1006 976 1160 1135 II20 069 • 367 '03 ||||||||||| | 2 Hittorf, Pogg. An- nal. vol. cvi. p. 375. 8 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 85. I!!!!!!!!!! !!!!!!!!!!! 1037 Illlll||||||||lll IT Illillillllllllll 5 | I'O. *000976 ·00195 I 200 1169 *0039 III!!! *0078 ,0156 130-281 1268 1233 I 20'0 | 25 116. 6 25 112-5 ! 25 !!!!! 1136 поб 1075 | 1037 111111 ||||||| !!!!!! 1 Il !!!!!! 0312 - 11332 2.23 III!!!!! IIIIIII SODIUM CHLORATE. Equivalent Gramme Molecule, Nacio3, 106.5. 1•16881 891 106.61 104:11 1106 10105 25 98. 625 1048 1018 9207 | 25 985 | ||||||| IIII!!! 1079 III!!!! Ostwald, Zeitschrift für physik. Chemie, 1 vol. i. p. 81. 12 At 25º. 13 Sprung, Pogg. An- 1 nal. vol. cyi. p. 15. 11111 .609 .86 1.215 3.62 5.903 *012 *O24 *0104 ·0208 *000976 *00195 •0415 ·0825 •0039 .0078 *0156 *0312 •165 *331 95.81 E .00877 1.0009761 '00195 28_2 LITHIUM CHLORATE. Equivalent Gramme Molecule, LiC103, 90°48. 10312 1001 977 •01755 *0351 *0702 *0039 Illlll via vivono 111111 |||||| IIIIII 1111!! IIIII I!!!!! I!!!!! *0078 11 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 83. 2 At 25° III !!! 111111 947 918 *149 *0156 *0312 •281 436 SOLUTION AND ELECTROLYSIS. PERCHLORIC ACID. Equivalent Gramme Molecule, HC104, 100.46. 42042 4156 |||||| IIlIllo wsi odovi 1111 ererererer 111111 Till |||||| IIllll |||||| |||||| III!!! 1 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 76. 2 At 250. li 4090 4018 3928 3840 POTASSIUM PERCHLORATE. Equivalent Gramme Molecule, KCIO4, 138.59. 14862 1450 1412 1373 124.8 1327 1283 139.81 1364 132.8 1111111 HII!!!! 1292 I!!!!!! ||||||| I orororore ||||||| I!!!!!! 11 Ostwald, Zeitschrift für physik.Chemie, vol. i. p. 85. 2 At 250. 8 Hittorf, Pogg. An- nal. vol. cvi. p. 373. 120°7 4633 0119 ·0238 I! *0475 *000976 '00195 *0039 .0078 *0156 *0312 111111 IIIIII SODIUM PERCHLORATE. Equivalent Gramme Molecule, NaClO4, 122.5. 116•1?| 25 , 1234 1133 1204 110.8 25 | 1178 1150 105.2 102'0 | 1084 II!!!! I!!!!! *095 •19 IIIIII 108.2 11 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 85. 2 At 25º. |||||| |||||| III8 *00976 '00195 *039 078 -156 *313 *000976 *00195 *0039 *0078 *OJ 56 0312 •0135 *0009761 *00195 ·054 0039 •108 0078 *216 *0156 '0312 •431 .833 *ooo9761 *00195 '0039 *0078 ·0156 *0312 I|||!! I!!!!! III!!! ܗܿ GGG 111111 LITHIUM PERCHLORATE. Equivalent Gramme Molecule, LiC104, 106.48. 107.4 1142 I1192 1080 1051 1019 987 Illll I!!!!! |||||| III | 1 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 85. 2 At 250. |||||| TABLE OF ELECTRO-CHEMICAL PROPERTIES. 437 SULPHURIC ACID. Equivalent Gramme Molecule, H2SO4, 49°035. | 14139| 1502 11 Kohlrausch, Wied. Annal. vol. xxvi. p. 196. *00001 *00002 '00006 *000 *0002 *0006 'OOI *002 *006 ||||||| IIII!!! 3342 2 Lenz, Mémoire de l'Acad. de St P.é- tersbourg, vol. xxvi. lolll||||llll 2927 3118 3280 3316 3240 3001 2855 2515 2343 3111 3314 3486 3552 3524 3444 3190 3035 2673 2490 2215 O III|II|||||IIIIIIIIII!! 2084 I'0027 3 Hittorf, Pogg. A1- nal. vol. cvi. p. 401. *0249 | 4 Wagner, Zeitschrift ·0237 | für physik. Chemie, ·0258 vol. v. p. 40. 5 Grotian, Wied. An- nal. vol. viii. p. 543. •2063 *212 సరపపు | | మ | ప | 21 | పుపపపపపపపపపు 11111 111 60 60 60 60 60 60 11 160 00 0 0 !!!! llllllllllllllllllllllllllll 1'0155 2018 25 20 I'o 30 I°0304 1 '0941 ro leren ·0423 *0432 *042) 1350 1*1534 5.2804 the heart !! I lo con lo con 5792 2595 1756 *00049 *000049 *000098 *000294 *o0o98 *00294 *0049 *0294 'oog8 ·049 •147 *245 *489 •616 L'OI 2:414 4:1 4.758 13.44 15:59 21.25 38.03 41°0 64.22 '098 •196 *391 .78 1°553 | 2758 2382 2532 2195 | 2333 2043 | 2171 | 1918 | 2038 I!!!! 11111 1.0048 | 1'0100 Grora .000087 | .000o1 1 '000174 | '00002 *000523 1 00006 POTASSIUM SULPHATE. Equivalent Gramme Molecule, 1 K2SO4, 87.16. | 1275 1355 | 1266 1346 - 1254 | 1333 111 I!! - - - 11 Kohlrausch, Wied. 1 Annal. vol. xxvi. 1 p. 196. 438 SOLUTION AND ELECTROLYSIS. POTASSIUM SULPHATE—continued. Equivalent Gramme Molecule, 1K.S04, 84•16. '00087 *00174 ·00523 *0001 *0002 *0006 '001 *002 *006 II||||| 1283 1249 | 1328 1241 | 1319 1220 1291 1207 1181 1256 1130 1201 1167 *OI 5 120 60 0 1 0 0 0 0 0 0 0 0 |||||||| 0223 1098 || || 8 8 8 8 1 8 1 1 8 8 ° *028 *O3 TOOX ET I '0020 I'0015 150 I'0030 | 1500 I'0069 | 15.0 1'0345 | 15.0 1'0639 | 120 1.0677 1560 218 :0|||||||llllllllllllllllllll *0244 2 Lenz, Mémoire de! *0235 | l'Acad. de St Pé i tersbourg, vol. xxvi. 8 Vicentini, Atti dell' Accad. di Torino, vol. xx. p. 688. 4 Hittorf, Pogg. An- nal. vol. xcviii. p. 27. 5 Sprung, Pogg. An- nal. vol. clix. p. 16. 6 Arrhenius, Zeit- schrift für physik. Chemie, vol. i. p. 295. 7 Wagner, Zeitschrift für physik.Chenie, vol. v. p. 37. 0209 G *0625 *0725 •125 *145 1.0040 | 150 1'0047 | 15'0 J.0088 15'0 I 'O102 I '0202 15.0 I'0345 15'0 57'02 65.5 106.0 I2['O 223.0 3610 20 0 0 |||||| •29 722 OO *00064 '00085 *00155 *00325 ‘0099 12503 1329 1210 1286 ·0239 1160 1233 18 | 0231 | 1ogo | 1159 | 18 | 0223 | 1020 | 1084 1 - ||||| l'o | 1'01861 1'0366 1'0708 I'1032 Сллел AMMONIUM SULPHATE. Equivalent Gramme Molecule, 4 (NH4)2S04, 66.075. 351 | 18 | '0221 702 | 746 18 0212 (143 1130 18 '0201 565 | 8530 1535 18 512 745 1856 | 18 | 0193 4.438 600 643 683 601 I'282 2'o 30 40 *0174 '0523 *0871 .241 •261 434 .866 4'212 7.67 8.163 *542 .629 1'080 1.251 2-477 4'212 '00558 *0074 •013. ·0286 ·0862 3.236 6.360 12-312 17-926 1 - 1 Kohlrausch, Wied. Annal. vol. vi. p. 0238 150. 20 | 02291 20 | 0231 1 ·0195 I!! 2037 404 493 TABLE OF ELECTRO-CHEMICAL PROPERTIES. 439 28.336 | 1°1632 15 | 18 | 2087 2233 o o 417 372 15 562 *411 .820 1.632 36236 1.0018 I '0045 I'0095 1°0186 / il || !! 2 Lenz, Mémoire de l'Acad. de St Pé- tersbourg, vol. xxvi. 8 Sprung, Pogg. An- nal. vol. clix. p. 16. I!!11 125 1111 11 !!!! 103 190 347 | || T *000071 1 *000142 *000426 *00071 *00142 *00426 SODIUM SULPHATE. Equivalent Gramme Molecule, Na2SO4, 71•075. | 1054", 1121 1056 1123 1038 | 1103 1034 1099 1026 ) Jogi '00001 *00002 *00006 '0001 *0002 *0006 OOL *002 *006 'O) *03 IIllllll 0257 j? Kohlrausch, Wicil. Annal. vol. xxvi. p. 196. 255 247 2 Lenz, Mémoire de l'Acad. de St Pere tersbourg,vol. xxvi. 8 Vicentini, Atti dell Accad. di Torino, vol. xx. p. 688. *0142 986 '0426 933 998 | Іобо 1042 906 828 ప | మ | పంపపపపపపపపపప *071 .213 olong! •355 111 Genel aroccio a 11.111111111 •706 1.93 IIIIIIIIIIIIIIIIIIIIIII I'0062 1'0181 1'0317 J'0612 1'0735 | 1'1190 Ill ||ll||||ll|||lllllllll 111 1111 11111 8 8 8 8 1 8 1 8881|| 3.542 6.70 I'O nal. vol. cvi. p. 377. 5 Sprung, Pogg. An- nal. vol. clix. p. 15. 6 Arrhenius, Zeit- 7083 118 12°770 2.0 III 1111 1111111111 Chemie, vol. i. p. *0625 I 25 •25 •5 1•750 3.542 1.0080 I'0958 1'0317 616 544 654 578 పప పపప *00085 •00604 ·00974 01834 ! 7 Wagner, Zeitschrift für physik. Chemie, vol. v. p. 39. 10108 1074 970 | 1031 940 999 *00137 *00258 440 SOLUTION AND ELECTROLYSIS. LITHIUM SULPEATE. Equivalent Gramme Molecule, LigSO4, 55.05. 949 | 1008 950 1009 950 945 1110 '00001 '00002 *00006 *0001 *0002 *0006 *001 *002 006 *OI IIIIIIIIIIIIII ol|||||||||||||| 111111 |||||||||||||||||| పేర | ఆ | ఇరిపడిపపడిపదాం |||||||||||||||||| II|IIIIlIlIlIlllll | 1 Kohlrausch, Wied. Annal. vol. xxvi. p. 196. 2 Kuschel, Wied. An- nal. vol. xiii. p. 300. 8 Arrhenius, Zeit- schrift für physik. Chemie, vol. i. p. 295. 4 Wagner, Zeitschrift für physik. Chemie, vol. v. p. 38. 03 ON •I •159 1111111 I '0445 *0236 474 *O23 386 18 | 0240' 287 1 305 20 III lill SILVER SULPHATE. Equivalent Gramme Molecule, Ag2SO4, 155.9. - 1090/ 1159 rogo 1116 - 1010 1073 1970 1031 II! 3131 TETORE DELEJE EDERE 1 Vicentini, Atti dell' Accad. di Torino, vol. xx. p. 689. *000055 *0001I *00033 *00055 *o011 ·0033 *0055 *OIT *033 *055 •548 207 5:27 *0071 0124 *0263 *0473 '00046 *00080 ·00169 *00344 ) *00006 00012 *00036 *0006 *OOT2 *0036 00001 *00002 '00006 '0001 *0002 0006 IIIIII 111111 111111 11 Kohlrausch, Wied. Annal. vol. xxvi. p. 196. అప్పు III 111111 MAGNESIUM SULPHATE. Equivalent Gramme Molecule, MgSO4, 60°035. | 1056 1123 1052 1119 1036 1101 1034 •8715 1028 1°738 | 554 | 20 1111: 111111 1099 1015 7462 20 969 101% *0258 |2 Sprung, Pogg. An- '0283 val. vol. clix. p. 19. TABLE OF ELECTRO-CHEMICAL PROPERTIES. 441 OOI *002 *006 'OI *03 '006 'OT 2 •036 '06 •18 *299 •475 *597 2'912 5.67 15.43 15.92 I '0025 1'0048 1'0058 1.0300 10587 1•1673 I'1763 ·0306 1 8 Ostwald, Zeitschrift '0332 | für physik. Chemie, vol. i. p. 109. 4 Hittorf, Pogg. An- nal. vol. cvi. p. 382. 6 Arrhenius, Zeit- schrift für physik. Chemie, vol. i. p. 295. crerer for o o do o ||||||||| TO TIIT |||||||||||| THE 11|||| |||||| *0222 0229 0254 LE 150 18:38 ||||||||| 3:0. 312 *00575 *0117 6 Wagner, Zeitschrift für physik. Chemie, vol. v. p. 38. *0039 *0234 0468 *000976 ·00195 ·0078 *0156 0312 |||||| O03 111 '00001 *00002 00006 *0001 '0002 *0006 *OOI *002 006 *OI ZINC SULPHATE. Equivalent Gramme Molecule, ZnSO4, 80°58. 1060 11271 10471113 1032 1097 1023 1088 *0625 1001 953 1013 919 977 ||||||| III!!!! 1064 llll||||||||| و نر نہ II |||||||||||||||| ·00008 *000161 *000483 *o008 *00161 *00483 008 •0161 •0483 •08 .242 861 915 అంది | పడిపపపపప 11 Kohlrausch, Wied. Annal. vol. xxvi. p. 196. 2 Hittorf, Pogg. An- nal. vol. cvi. p. 385. 8 Wagner, Zeitschrift für physik. Chemie, vol. v. p. 40. | 4 Arrhenius, Zeit- schrift für physik. Chemie, vol. i. p. *0297 | 295. | '0313 5 Grotian, Pogg. An- ||||||||||||||| 111881 18888 03 986 500 1'0041 J'0090 15 | 1°0404! 15 | 431 302 1.537 2:144 – 12993 | 349 ! nal. vol. cl. 7. 262.1 41 442 SOLUTION AND ELECTROLYSIS. ZINC SULPHATE-continued. Equivalent Gramme Molecule, 1 ZnSO4, 80:58. I'08071 I'2310 '0224 '0241 | 1880 llo 1372 38 6 Bouty, Journ. de 84 Physique, vol. vi. p. 13. Vicentini, Atti dell' Accad. di Torino, vol. xx. p. 689. 8 Beetz, Pogg. Annal. vol. cxvii. p. 9. *001 I '026 Till önca Il llevant 5:38 I'00go 1'0179 I '0404 ||||| !!!!! !!!!! 773 152.0 || | *00057 ·00075 *00129 00335 !!! |||| !!!! ఏపంపపపపపపపపపపపపపప పపపు పపప ప | పవర్ ON ON mlo O 0.cz 1'0780 I'1012 I'131 1*1790 I'2063 1·2310 1°2430 1'2710 1.2746 1•2832 I •2901 1°2986 1•3120 3°3370 1°4260 11111 11111 1111111111111111111111 crororonoiorurerontrererer oooooooooooooo 3*539 131 |||||||||||||||||| |||||||||||||||||| II!!!!!!!!!!!!!!!! 130 III!!!!!!!!!!!!!!! 4400 | 440'0 441'0 445.0 4420 439'0 431'0 3740 3590 125 Il lenne como I 20 II3 103 I'o 3.0 7456 19:637 19:8 28.38 29:36 '008 '080 '01 •799 1.583 3.85 virusi *00459 00604 *O104 *0270 7018 •961 1.276 1.668 2•282 2.656 3:148 11.88 9:34 | 15°60 17075 19:01 20:41 22°44 22:59 2.996 = ထံ 3.913 4:116 4:448 5.752 ထံ 33071 35'04 37.81 TABLE OF ELECTRO-CHEMICAL PROPERTIES. 443 1. '00008 '00016 *00048 .0008 I!!!! 11 Kohlrausch, Wied. Annal. vol. xx.vi. p. 196. I!!!! 0016 III!!!!! 1039 0000 *00002 *00006 060I '0002 *0006 *OOL '002 *006 *OI . 11111111 6754 COPPER SULPHATE. Equivalent Gramme Molecule, CuSO4, 79*78. 1086, 1154 1084 | 1152 1074 | 1142 1062 | 1129 1104 987 1049 950 1009 873 740 675 537 479 17.6 1 0 0 0 0 0 0 0 0 0 0 0 zo 0625 928 2 Vicentini, Atti dell' Accad. di Torino, vol. xx. p. 689. 8 Hittorf, Pogg. An- nal. vol. xcviii. p. 196. 10735 250 1052 25'0 2012 25.0! 942 ກ. 587 805 000 000 0846 424 11111111 I'0015 I'C034 | 140071 1.0078 10135 1°0386 1•0758 1.1521 Illll||||||||||||||||| *163 '315 | G G G G dܞ GG G II|||!1111111111111111111111 I'0253 1 ao 1.o 1 1 !!!!!!!!!! A 000 000 ||||||||||| 4 Arrhenius, Zeit- schrift für physik. Chemie, vol. i. p. 295. 6 Wagner, Zeitschrift für physil. Chemie, vol. v. p. 38. I'd •692 10 1:31 1.962 ir in III!!!11111 111111 1•1036 ·0048 .008 '016 *048 '08 239 *397 •791 1.282 2-457 3.847 9:47 13.6 o 30 1501 10202 070 IIIlll lor *00486 *00622 *o0989 *0156 *0251 *0411 1084 1031 1010 *00061 '00078 *00124 *00196 *00315 *0064 950 Do o o o o I!!! 840 893 |||||| 111111 !!!!!! |||||| 850 rool 744 . CADMIUM SULPHATE. Equivalent Gramme Molecule, J Cašos, 104'03. 00278 1 99893 181 23 | 18 | 0230 1 827 | 879 *00482 | 99915 | 18 | 3.62 | 18 | 0230 1. 750 797 | 0289 1 - 1 - 0489 1 Wershoven, Zeit- schrift für physik. Chemie, vol. v. P. 494. 444 SOLUTION AND ELECTROLYSIS. CADMIUM SULPHATE—continued. Equivalent Gramme Molecule, CaSO4, 104'03. 0 *0999 'oog61 *99961 6.43 0222 668 1 2 Grotian, Wied. An- nal. vol. xviii. p. 193. 495 I 0034 0 0 1 22'24 *0479 *0954 981 37.82 0211 *O207 14:32 '0272 *0983 *514 1'076 3*127 *0221 *O210 *O206 0 0 0 0 1'0015 1.0085 I '0495 I'1039 I'2955 I'4756 •282 1ΟΙΙ 5'08 10:11 -25'03 36:07 .00655 ‘00936 137.0 2320 IIllIIlllllll II! |||lll lll lo 111 111111 ocijeni 1111 111111111 8 Vicentini, Atti dell' Accad. di Torino, vol. xx. p. 689. 4 Wagner, Zeitschrift für physik. Chemie, vol, v. p. 36. 0206 0222 400.0 216 128 3920 *0255 *00063 *0009 *00157 Il 11 Il 890946 820 8711 . FERROUS SULPHATE. Equivalent Gramme Molecule, FeSO4, 76•03. '000g '00128 *00684 00973 01193 *02417 III I!!! 1111 18 | 0230 18 | 0270 | 18 — 1.111 700 808 730 776 670 | 712 | I!!! III 00318 1 1 Vicentini, Atti dell' Accad. di Torino, vol. xx. p. 690. .00157 NICKEL SULPHATE. Equivalent Gramme Molecule, 4 NiSO4, 77.33. ·00572 *00727 *00074 *00094 0018" I!!! I!!! 60 600 l 1111 1111 | Vicentini, Atti dell' Accad. di Torino, vol. xx. p. 690. | 2 Wagner, Zeitschrift für physik. Chemie, vol. v. p. 39. TABLE OF ELECTRO-CHEMICAL PROPERTIES. 445 Till IIIl I!!! 1909 og COBALT SULPHATE. Equivalent Gramme Molecule, CoS04, 77'53. •125 | 10502 81011 861 780 700 744 II! illi 829 11 Vicentini, Atti dell' Accad. di Torino, vol. xx. p. 690. 12 Wagner, Zeitschrift für physik. Chemie, vol. v. p. 39. III I!!! 1 60 60 60 ALUMINIUM SULPHATE. Equivalent Gramme Molecule, 1 A12(SO4)3, 41°02. 8101 861 125 | 10532, 25 | 1010 25 | 927 | 25 | 777 / 25 I!!! *** Orolorun .1.111 11 Vicentini, Atti dell' Accad. di Torino, vol. xx. p. 690.. 2 Wagner, Zeitschrift | für physik. Chemie, vol. v. p. 39. *0109 *0218 '0435 •087 | | '000976 i 00195 0039 ·0078 *0156 *0312 !!!!!! II!!!! Illll 1111 METHYL SULPHURIC ACD. Equivalent Gramme Molecule, HCH2SO4, 112.07. 368•11 | | 39132 365.2 3882 362:8 3857 3803 career II!!! 12 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 76. 357.8 3514 ||||ll . !!!!!! : 111111 •174 3735 2 At 250. *349 345'0 125 3667 9722 948 '00729 '01046 *02054 *00094 *00135 *00265 *00266 *00640 '00865 '00065 '00156 *00211 *0130 *026J *0522 •1045 •209 *418 '000976 : *00195 1 *0039 '0078 *0156 0312 11 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 81. TI!!!! III!!! SODIUM METHYL SULPHATE. Equivalent Gramme Molecule, NaCH3SO4, 134'I. 91.41 | 25 89.2 25 8609 | 25 924 II!!!! SIIT!! |||||| ***ܗܞܞ dinos II!!!! ||||| E |||||| I!!!!! | 2 At 250. 446 SOLUTION AND ELECTROLYSIS. ETHYL SULPHURIC ACID. Equivalent Gramme Molecule, HC,H.S04, 126•07. '000976 *00195 'O122 '0245 *049 *098 •196 -392 *0039 *0078 *0156 *0312 3593 |||||| olill!!! Garanciccio I!!!! IIIlllo 353-4 II!!!! 1 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 76. 12 At 250. III!!! 34706 367-41 39052 - 363.9 3868 3819 3757 3695 3409 | 3624 ) SODIUM ETHYL SULPHATE. Equivalent Gramme Molecule, NaC,H.S04, 148.1. 9302 907 886 873 *0144 0289 *0578 '0009761 ·00195 *0039 ·0078 *0156 '0312 125 III!!! 000 og 111111 - Noor Ace III!!! !!!!!! "IIlll | Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 81. 2 At 25° '1155 *231 848 821 | *000498 *000976 ·00195 80*4 25 11 Ostwald, Journ. für | Chemie, vol. xxxii. p. 314. 2 At 25º. *0039 '002 *004 '008 •016 *032 ·064 •128 -256 *512 22.5 *0078 *0156 IIIllllllll ||||||||||| 58.9 IIIIIIIIIII Tillillllll II||||||| IIIIIllllll IIIIIIII! IIIIIIIIIIl. *0312 SULPHUROUS ACID. Equivalent Gramme Molecule, 3H2SO3, 4103. 83.62 | 251 18882 | 1815 7701 | 25 1741 1637 1501 1330 50°1 1132 41.6 939 32.8 741 574 1992 | 25 434 SELENIC ACID. Equivalent Gramme Molecule, 1 H,Se04, 724. 1734 - | 391521 174'4 | 25 | 3937 1734 | 25 169•7 | 25 11111111111 !!!!!!!!!!!! *0625 •125 25 25.4 25 *00176 1 .000244 | *003521 000488 *00705 1 .ooo976 *0141 100195 1111 I!!! 11 Ostwald, Journ. für Chemie, vol. xxxii. I!!! Ili 1. P. 313. I! 1 3%a22 2 At 250. TABLE OF ELECTRO-CHEMICAL PROPERTIES. 447 1647 111111111 III!!!!!! 157-9 1487 13863 12700 11707 10999 103:2 97*3 ||||II|II IIIII!!!! 111111111.. IIIIII!!! IIIIIIIII II||||||| IIIIII!!! IIlIIIII! 0078 ·0282 *0565 •113 .226 •452 *0039 *0156 ·0312 •0625 *125 .00022 "O18 SODIUM SELENATE. Equivalent Gramme Molecule, 1 Na Se04, 94:44. . 115.21 --- 122521 III.6 1186 107.4 1126 1099 '000976 *00195 .0039 *0078 0156 *0368 |||||| I!!!!! III!!! IIIIII 111111 IIIlll 111111 111111 II!!!! 111111 11 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 106. 2 At 250 0735 •147 *294 1043 *0312 086 78.81 79.8 PHOSPHORIC ACID. Equivalent Gramme Molecule, f H3PO4, 32:67. 11861 1201 790 1189 '000368 | *000735 *00147 *00295 *0059 '0118 1111 '0012 *0024 ·0048 .0096 *0192 *0385 *077 •154 •307 III! | IIII!!! II 111.111!!!! ||||||||||||| 1111111111111 III|||||||||| 111111111 11 Ostwald, Journ. für Chemie, vol. xxxi. p. 460. 2 Reyher, Zeitschrift für physik.Chemie, vol. ii. p. 750. Illllllllllll 598 *375 •75 1°215 2:41 344 27.1 213 1700 142 I'0020 10076 15 I 0136 15 1•0263! 15 10572 25 | 1026 964 1 849 25 4076 I 887 SOLUTION AND ELECTROLYSIS. - POTASSIUM CARBONATE. Equivalent -Gramme Molecule, 3 K.C03, 69:13. 865 1 Kohlrausch, Wied. Annal. vol. xxvi. 915 p. 196. 995 '000069 *000138 *000697 *00138 *00415 *00697 *0138 *0415 0691 I!!!!!! 1058 '00001 *00002 *00006 *0001 *0002 *0006 *OOI *002 *006 'OI *029 1128 1222 1221 1199 1299 1199 1298 1274 2 Kuschel, Wied. An- nal. vol. xiii. p. 289. 3 Arrhenius, Zeit- schrift für physik. Chemie, vol. i. p. 295. *O240 1083 J151 |||||||||||||||||| •207 989 105) *344 I'o026 Coco 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 TOOI llllllllllllllllllllllllº 4 Lenz, Mémoire del l'Acad. de St Pél tersbourg, vol. xxvi. !!!!!!!!!!!!!!!!!!!!!!!!!!! o!!!!!!!!!!!!!!!!!!!!!!!!!! T||||||||||||||lllllllllllllll !! .687 I'oof 441 I'O 0227 3 354 6°522 | I.06oc 021 TI•1162 O2II *O210 27021 12 *0216 46°14 I'4959 |llllllll 059 407 810 1.608 •118 273 | 15 I'0032 15 I'0073 | 1'0147 | 1'0289 | 15 •236 -472 entreren Illl !!!! 3:171 TABLE OF ELECTRO-CHEMICAL PROPERTIES. 449 LITHIUM CARBONATE. · Equivalent Gramme Molecule, Li,C03, 37°02, 882 W. S. '00648 . | 'Onn '01 481 *503 1 .00175 0030 *0040 '136 •232 !!!!! ||||| TI! ||||| !!!!! 11111 ||||| 11111 1 Vicentini, Atti dell' Accad. di Torino, vol. xx. p. 688. 2 Kuschel, Fied. An- nal. vol. xiii. p. 289. SODIUM CARBONATE. Equivalent Gramme Molecule, 2 Na2CO3, 53'04. '000053 '000106 740 | Kohlrausch, Wied. Annal. vol. xxvi. p. 196. *000318 I!!!!! III!!! 3 00001 *00002 *00006 *0001 *0002 *0006 001 *002 840 929 1050 *00053 "OOJO6 *00318 *0053 0106 '0318 053 *159 U12 U02 1037 IOIO IIII||||||||||||| ||||||||||| 1073 పనులు 1 2 1 6 1 2 1 ప పపపపపపపు '006 2 Lenz, Mémoire de l'Acad. de St Pé- tersbourg, vol. xxvi. 3 Kuschel, Wied. An- nal. vol. xüi. p. 289. 1016 ||||||||||| |||||||||||||||||||| III|||||||||||||||| *OI |||||||||||||||||||| 03 •264 1111 11111111111111111111 5 *528 1'0271 *O244 |||||||| 985 I'0529 O2 2.592 50 5'038 13.86 *659 I'307 2.592 5'038 1•1479 15 •125 I'0060 15 I'0137 | 15 I '0271 15 1'0529 | 15 792 142 248 433 పపపప |||| |||| |||| II|| II|| 450 SOLUTION AND ELECTROLYSIS. POTASSIUM CHROMATE. Equivalent Gramme Molecule, 4K,Cr04, 97•33. II111 So III 111 III11 1 Lenz, Mémoire de l'Acad. de St Pé- tersbourg, vol. xxvi. 2 Hittorf, Pogg. 41- nal. vol. cvi. p. 371. 8 Sprung, Pogg. An- nal. vol. clix. p. 1. 521 *0634 •1268 •2536 *517 1 – AMMONIUM CHROMATE, Equivalent Gramme Molecule, }(NH2),CrO4, 76*24. 1 820 871 - 7651 177 698 742 318 615 653 FI!! 97 813 III! IIII 11 Lenz, Mémoire de l'Acad. de St Pé- tersbourg, vol. xxvi. POTASSIUM BICHROMATE. Equivalent Gramme Molecule, K,Cr,0m, 147.52. 621 | 18 117 T!!!! I!!! ||||| 11 Lenz, Mémoire de l'Acad. de St Pé- tersbourg, vol. xxvi. | 2 Hittorf, Pogg. dn- nal. vol. cvi. p. 371. .638 1270 2515 4932 I '0044 | 1995 | 60:11 ΠΟΙΟΙ | 113.0 I '0203 2120 1 '0402 19'5 396'o OOO ODOS 9:50 1'033 2.050 0706 •1413 •2826 1 1'0073 | 19:51 | 1'0153 | 19:51 | 1'0303 | 19:51 4'040 6°390 7.891 •5652 | 1.0553 | 1951 415 874 1 6 AMMONIUM BICHROMATE. Equivalent Gramme Molecule, }(NH4)2Cr2O7, 126:44. . | 72071 823 13390 752 799 252.0 | 18 472.0 | 18 •0883 •1767 *3534 •7068 1111 I!!! 18 T!!! |||| Inil I!!! 1 1 Lenz, Mémoire del. l'Acad. de St Pé-|| tersbourg, vol. xxvi. 757 TABLE OF ELECTRO-CHEMICAL PROPERTIES. 451 4.882 1 !!! !!!! NN on tuor TIIT III. ||| HYDROCYANIC ACID. Equivalent Gramme Molecule, HCN, 26.98. •1081 '101 4:56 'ogo 4*06 *077 3-48 - POTASSIUM CYANIDE. Equivalent Gramme Molecule, KCN, 65'02. 1.47 - •0208 976 1037 *0195 938 | 997- III 11 Ostwald, Journ. für Chemie, vol. xxxii. p. 304. 2 At 250. | 25 iš I '0154 I 0312 local TIT 18 Till Till T111 | 1 Kohlrausch, Wied. Annal. vol. vi. p. 149. 2 Hittorf, Pogg. An- l .nal. vol. cvi. •457 - . *00145 į '000488 *0058 000244 *000976 *00195 *0039 *0078 SULPHOCYANIC ACID. Equivalent Gramme Molecule, HCNS, 58.96. | 3797% 3874 3897 3919 3905 | 1 Ostwald, Journ. für Chemie, vol. xxxii. p. 305. 2 At 25º. •0115 *023 .046 ||||||||| IIII|IIII|| es conscici cowoom |||||||||||| 1||||||||| II|||||||||||| |||||||||| ||||||||||||| |||||||||||| 092 *0156 Illlllllllll •0312 0325 '125 3666 3581 7607 3463 | HYDROFERROCYANIC ACID. Equivalent Gramme Molecule, #H_FeCy6, 5395. 80:41 | 36302 — 7602 3440 72.0 3251 67.1 3030 2831 2646 000362 i Ostwald, Journ. für Chemie, vol. xxxii. p. 307. *0002441 *000488 *000976 *00195 *0039 *0078 *0156 1111111 ||||||| ||||||| II||| II Till II|IIII IIIIII IIIlIIl '084 •168 *337 '0312 '0625 *125 *25 .675 946 3.20 6.30 IT'55 29~2 *00525 •0105 *O210 '0421 0841 IIIIII 2 At 250. 2488 452 SOLUTION AND ELECTROLYSIS. FORMIC ACID. Equivalent Gramme Molecule, HCOOH, 46. I!!! 36.001 29:04 16222 1311 1018 22:54 *00225 *0045 'oogo 0180 0359 •0718 *1435 *287 *574 *000488 *000976 *00195 *0039 •0078 *0156 0312 *0625 17.00 768 1 Ostwald, Journ. für Chemie, vol. xxxi. p. 445. 2 At 250 !!!! 1111111 568 OPIO 414 6.63 ||||||||||| N ||||||||| cuerorororererer •125 4079 3.43 2:46 1•76 I'0015 I '0030 111!! !!!!||||||| ||||||||||||||||| •25 8 Reyher, Zeitschrift für physik. Chemie, vol. ii. p. 749. 4 Berthelot, Annales de Chimie, series 6, vol. xxiii. p. 39. *5 79 1034 *0046 *o092 .046 *115 *001 002 'OI '025 *05 24.9 111/ ||||| |||||| !!! illlll 1709 16 1405 тобі 17 524 340 245 129 170 - POTASSIUM FORMATE. Equivalent Gramme Molecule, HCOOK, 84.13. - | 127731 1173 1247 1147 1123 | 1194 108-8 | 1156 105.8 1124 *0082 120:17 ili *0328 I 219 ·0655 *o00976 *00195 *0039 ·0078 0156 '0312 111111111 |||||| 111111111 *131 *262 |||| |||||| || II 1.111111 111111111 Ill ||||ll | Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 102. 2 Berthelot, Annales de Chimie, vol. xxiii. p. 40. 3 At 250 1341 *0042 *0168 *042 *0005 *002 dici 10 1291 || || ! *005 171 023 | - | 1236 SODIUM FORMATE. Equivalent Gramme Molecule, HCOONa, 68.04. 98.97 25 - | 10512 969 | 25 1030 9407 125 1007 •1258 | 1068 | 25 l - -1 - *0066 0132 ·0265 '000976 *00195 0039 111 11 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 99. TABLE OF ELECTRO-CHEMICAL PROPERTIES. 453 10078 *0156 0312 111 do o o ill Til 111 ܨܶܬ݁ܦܽ 1 Il 912 | 2 At 250. 3 Reyher, Zeitschrift für physik. Chemie, vol. ii. p. 750. I LITHIUM FORMATE. Equivalent Gramme Molecule, HCOOLi, 52°02. 88.11 125 9362 912 - 11 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 103. 886 00505 *O101 *0202 *0405 081 •162 '000976 ·00195 *0039 *0078 *0156 '0312 II|||| ovo oot oo crorerurti IIIIII |||||| 111111 |||||| |||||| 2 At 250. ACETIC ACID. Equivalent Gramme Molecule, CH2COOH, 60. *000244 " *00292 *000488 *00146 ·00585 *0117 11111 314 229 -0234 *000976 *00195 --0039 ·0078 *0156 *0312 ||||||||| *0468 9935 Iho , 1 Ostwald, Journ. für Chemie, vol. xxxi. p. 444. 2 Reyher, Zeitschrift für physik. Chemie, vol. ii. p. 749. 8 Kohlrausch, Wied. Annal. vol. xxvi. p. 197. 2.94 TO ||||||||||||||| 2.123 0625 1:514 •125 I '078 .25 I'0003 I'O014 I'0036 •756 *520 437 30' 2I'I $||||| |||||||| ||||||||||||||||||||||| |||||||||| |||||||||| ||||||||||||||||||||||| ||||||||||||||||||||||| 13049 1386 *00006 00012 *00036 '00001 00002 '00006 *0001 .0002 •053 •106 •212 •187 •374 •748 I'494 2.982 *0006 *0006 II|||||ll 1111111 *OOI *002 *006 *OI ||||||| 454 SOLUTION AND ELECTROLYSIS. Acetic Acid—continued. * Equivalent Gramme Molecule, CH3COOH, 60. . loi Berthelot, Annales de Chimie, vol. xxiii. p. 43. w covridagici Toimihend 118 87 I'0002 I'0036 I'0080 I '0246 I '0389 1*0644 erererererer 20'2 127 505 IIlIIlll 5.2 IlIl cancer de IIIlIIlIlIl./ |||||||| |||| |||||||| IIII IIIlllll.. 2.6 "Ill 11.1.1||ll Till IIIlllllo 900. *O12 '001 *002 '005 1111 20 306 тоб | 141 ||| *018 gooooo. 961000. 889000. 86000. POTASSIUM ACETATE. Equivalent Gramme Molecule, CH2COOK, 98.13. | 939?, 998 943 | 1002 935 994 10000. 20000. 90000. *0001 *0002 *0006 I! 1111111 Till ||||||||||| |||||!|| 8600. 9610. 8990. TOO. 200. 900. TO. 11 Kohlrausch, Wied. | Annal. vol. xxvi. p. 195. 2 Hittorf, Pogg. An- nal. vol. cii. p. 42. 3 Arrhenius, Zeit- schrift für physik. Chemie, vol. i. p. 295. people |||||||||||| 11111111111111111111 6 | విహపర | విపరంపపపపపప lllllllllllllllllll |||||||||||||||||||| *03 *05 •I *114 ['005) er ·0224 I '0467 *0220 0227 |||||||| *0252 860. *294 1'057 9:37 42007 54 1:10: 6€2.1 II '0421 TABLE OF ELECTRO-CHEMICAL PROPERTIES. 455 !!!!!! !!!!! 874 * Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 102. Berthelot, Annales de Chimie, vol. xxiii. p. 43. 851 111111111111 IIIIIIIII!!! IIlIIlIIIIII IIllliii!!!! 019 !!!!!! !!!!!! 772 76.5 | 17 80.5 78.0 951 942 933 754 920 SODIUM ACETATE. Equivalent Gramme Molecule, CH3COONa, 82.04. - 1:4438, - !!! 11 Kohlrausch, Wied. Annal. vol. vi. 1). 150. 424 1 I'066 II||| I'145 2 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 99. Hittorf, Pogg. $12- nal. vol. cvi. p. 379. 415 119 *0340 *0410 || 495 2 IL ||||| |||| diti orico Illlll || ! il 11 illl 1 111 |||||| 4 Reyher, Zeitschrift · für physik. Chemie, vol. ii. p. 750. •0095 105.14 ‘0191 *0382 •0765 *0039 '000976 *00195 ·0078 *0156 '0312 103:1 100'4 98.2 95.4 •153 •306 92.9 *0049 83.66 '0196 *0005 *002 0033 *0294 *049 *059 .098 I'17 •142 *288 2:36 11 5.5 55 L'O125 12.22 H ง ว ววว 26•26 '008 *000976 ·00195 ·0039 '016 *032 .064 •128 • 256 *0078 '0156 '0312 20023 - *0046 63.48 25 *000244 '000488 *000976 *00195 MONOCHLORACETIC ACID. Equivalent Gramme Molecule, CH,CICOOH, 94:46. 68.691 25 | 31022 1 2866 55.64 | 25 2512 46075 11 Ostwald, Journ. für Chemie, vol. xxxi. 1111 ·0092 III III ill 1. p. 446. •0184 2U 2 At 250. 456 SOLUTION AND ELECTROLYSIS. MONOCHLORACETIC ACID-continued. Equivalent Gramme Molecule, CH,CICOOH, 94:46. - 0368 0735 I47 - 1037 20A 11111111 11111111。 的989284 。5%85%%%% 二二二二二二 ​1111111 1797 1337 781 578 430 316 11|||||| 。|||||||| ||||lll ||||||| 。|||||||| llllllll *125 25 179 *00312 || *00625 | O125 000244 OOO488 *000976 OO105 80*94 025 11 Ostwald, Journ. für Chemie, vol. xxxi. p. 446. 2 At 25. 0039 ||||||| ·100 111111111111 111111111111 0078 DICHLORACETIC ACID. Equivalent Gramme Molecule, CHCI,COOH, 128.92. 179-28f | 360og - 3651 3636 360I 3442 3043 2720 2356 4303 1912 3442 I550 | 2575 | 116rl 3277 85%BE%85%%%% ¥288888 S4% |||||||||||| =-|||||||||||| O156 11||llllll llllllllllll. |||||||||||| llllllllllll 0312 “O50 '200 * AM co625 *125. *25 . || | 35152 00795 | 000244 "000488 *000976 co158 3598 |||||||| 00195 11111111 1111||||| 222222 5555555 11111111 3593 TRICHLORACETIC ACID. Equivalent Gramme Molecule, CCl2CO•OH, 163:38. 17784 79 10 3572 79-68 7958 79-12 3572 7900 3567 7855 17095 ·0039 lllllll ||||llll llllllll 11 Ostwald, Journ. für Chemie, vol. xxxii. | p. 322. 12 At 25° llll1111 llllllll 11111||| 254 0078 O156 0312 508. 3547 3475 TABLE OF ELECTRO-CHEMICAL PROPERTIES. 457 *125 llll Till I!!! |||| 3369 3212 2963 25991 11 I!!! I!!! IIII I!!! I!!! MONOBROMACETIC ACID. Equivalent Gramme Molecule, CH,BICOOH, 138.95. 31592 *000488 *00338 •00675 *0135 *027 *054 *0002441 *000976 E , 1 Ostwald, Journ. für Chemie, vol. xxxii. p. 322. 2 At 250. III!!!!!!! |||||||||| |||||||||| *0039 .0078 *0156 *0312 *0625 •125 |||||||||| |||||||||| 1111111111 |||||||||| I!!!!!!!!! 108 |||||||||| 28.52 IIIllll *216 21.62 *432 16:12 11.90 8.65 391 POTASSIUM TRICHLORACETATE. 101.91 10832 II!!!! 111111 1058 1029 1002 975 941 IULUI |||||| I!!!!! 11 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 103. 2 At 25º. IIII!! SODIUM TRICHLORACETATE. Equivalent. Gramme Molecule, CCl2COONa, 185.42. 8562 *000976 *0196 *0392 0785 *157 *0039 *0078 •0156 0312 •018 *036 *072 *144 •576 '000976-1 *00195 *0039 *0078 *0156 0312 I!!!!! |||||| 1 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 100. |||||| o dicocoj TI!! |||||| I!!!!! 111111 IIIIII |||||| |||||| 195 2 At 250. 458 SOLUTION AND ELECTROLYSIS. LITHIUM TRICHLORACETATE, Equivalent Gramme Molecule, CCI,COOLI, 169:4. 000976 .0195 7002 68.1 7462 724 702 IIIlllo 600 IIIIII crorurgi Grou |||||| I!!!!! IIIlllo |11| III!!! III!!! .. |1||lo Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 104. 2 At 25° 62'0 599 - 1 1111 * !!!!! 9:56 1 Ostwald, Journ. für Chemie, vol. xxxii. p. 317. 2 At 250 *000244 *000448 000976 *00195 *0039 .0078 *0356 '0312 *0625 *125 |||||||||||| 111111111111 PROPIONIC ACID. Equivalent Grainme Molecule, C,H,COOH, 74. 18.21 1251 I - i 822?.. 13:19 596 432 6.88 310 4.92 3:50 2:49 IIIIIIllllll !!!!!!!!!!!! III!!!!!!!!! 1•767 8 Reyher, Zeitschrift für physik. Chemie, vol. ii. p. 749. 1.247 0653 •871 044 I'OOIL I'0019 10035 .601 994 | 403 913 | IIIill |||||| III!!! III!!! IIIIII 111111 III!! POTASSIUM PROPIONATE. Equivalent Gramme Molecule, C.H.COOK, 112'13. 103.02 10952 IOI'I 1064 9784 1035 949 1009 979 89.0 946 Tillil III!!! TI!!! ·0039 *0078 '0018 *0036 .0072 *0144 *0289 *0578 *1155 231 *462 924 1.846 3.687 *25 OLIO *0219 *0438 *000976 *00195 *0039 *0078 *0156 *0312 •0875 •175 11 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 102. 2 At 250. 92:1 TABLE OF ELECTRO-CHEMICAL PROPERTIES. 459 SODIUM PROPIONATE. Equivalent Gramme Molecule, C,H,COONa, 96•04. 804 8542 78.8 0368 IIllll 111111 111111 Alvieri |||||| |||||| III!!! 1|||ll 1 Ostwald, Zeitschrift. Į für physik. Chemie, | vol. i. p. 99. 12 At 250. 8 Reyher, Zeitschrift, | für physik. Chemie, 1 vol. ii. p. 750. LITHIUM PROPIONATE. Equivalent Gramme Molecule, C2H5COOLi, 80'02. 7392 655 6951 *0078 0156 •0312 *125 *250 ·00976 '00195 *0078 *0156 *0039 ||||ll I !!!!! 111111 I!!!! Enorerererer 111111 III!!! 111111 ·0625 TI!!!! | Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 104. 2 At 25º. |||||| osisi 0312 A. BROMPROPIONIC ACID. Equivalent Gramne Molecule, C,H,BrCOOH, 152-95. 68.91 31112 2807 2423 447 2020 0094 *0188 *0375 '0009761 *00195 0039 *0078 *0156 *0312 '075 •150 •300 '00372 ·00745 0149 ·0298 *0595 •119 *000244 .000488 *000976 *00195 *0039 *0078 622 5307 11 Ostwald, Journ. für Chemie, vol. xxxii. p. 324. 2 At 25º. 50°1 28.8 II|||||||||| II|IIII||||| 111111111111 |||||||||||| III!!!! II|II|||| |||||||||||| 22:6 IIII|||||||| |||||||||||| IIIIIIIIIIII 17.6 TITIIII||||| 460 SOLUTION AND ELECTROLYSIS. B. IODOPROPIONIC ACID. Equivalent Gramme Molecule, CH,ICH,COOH, 199.8. *000244 '000488 *000976 *00195 16282 1272 *0049 ·0098 ·0195 *078 •156 *312 dico no 1 Ostwald, Journ. für : Chemie, vol. xxxii. p. 325. 2 At 25° .0078 Illllllllll ||||||||||| ||||||||||| ||||||lllll ||||||||||| ||||||||||lo |||IIIIIIII IIIIIIIIIII ||||||||||| IIIIIIIII!! 100 1.53 69 - BUTYRIC ACID. Equivalent Gramme Molecule, C3H,COOH, 88. 18:02 81421 13:4 604 9974 440 7.01 5'04 228 162 125 *000244 *000488 *00214 *00428 ·00855 *0171 ·0685 *137 11 Ostwald, Journ. für Chemie, vol. xxxi. p. 444. I!!! 31 ·0342 |||||||||| 2 At 25º. *ooo976 *00195 *0039 *0156 ·0312 *0625 •125 •25 *0078 |||||||||||| |||||||||||| inition III||||||||| IIIIII|||||| 116 8 Reyher, Zeitschrift für physik.Chemie, vol. ii. p. 749. 25 I '0006 10608 7 I027 25 6 | 25 I 0013 1°0022 25 25 854 •39 | 25 POTASSIUM BUTYRATE. Equivalent Gramme Molecule, C3H,COOK, 126-13. 10662 1035 1008 - IIIlli |||||| IIIIII w oei oot |||||| ·039 .624 •274 *548 1 '099 2:197 4°390 *OI 22 *O245 *049 1.000976 1 *00195 *0039 *0078 *0156 0312 *098 *196 *393 I!!!!! 111111 983 IIIIII 1 Ostwald, Zeitschrift für physik.Chemie, vol. i. p. 102. 2 At 250 III!!! IIIill 917 TABLE OF ELECTRO-CHEMICAL PROPERTIES. 461 SODIUM BUTYRATE. Equivalent Gramme Molecule, C2H,COONa, 110°04. 76.41 | 8122 - 75.0 10253 7394 2 12. 1 '0009761 111111 III!!! |||||| 111111 111111 III!!! I||||| 71'2 | Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 99. 2 At 250. 3 Reyher, Zeitschrift für physik. Chemie, 1 vol. ii. p. 751. 68.9 66•2 LITHIUM BUTYRATE. Equivalent Gramme Molecule, CzH,COOLi, 94'02. 1 2072 •0182 *0365 073 •146 *293 000976 00195 '0039 .0078 *0156 *0312 |||||| I!!!! 670 cincoojeni ilili 111111 I!!!!! |||||| TIT!!! II!!!! Illll II|||| 11 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 104. 2 At 250 590 2 ISOBUTYRIC ACID. Equivalent Gramme Molecule, C3H,COOH, 88. 17.621 12'97 9:50 495 1111 ||| 11111 11 Ostwald, Journ. für Chemie, vol. xxxii. p. 318. 2 At 250 6.86 310 im IIII!!!! I!!!!!!!!!! |||||||||||| 224 161 II I!!!!!!!!!!! |||||||||||| |||||||||||| 3 Reyher, Zeitschrift für physik. Chemie, vol. ii. p. 749. '1258 1059 'o108 ·0215 *043 ·086 '00195 *0039 *0078 0156 *0312 *172 •343 •00215 *0043 *000244 | *000488 *000976 ·00195 *0039 .0078 •0086 0172 *0345 .069 •138 •275 *550 1.100 2.198 4392 I'0004 I'0008 I'a 968 OLA | 859 462 SOLUTION AND ELECTROLYSIS. Equivalent Gramme Molecule, C3H COOK, 126-13. *000976 oll Illlllo III!!! 100-2? 974 94-9 89.6 8607 .0078 *0156 0312 10652 1035 1009 983 952 1922 III!!! 0111111 I!!!!! 1 Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 102. ? At 250 |||||| SODIUM ISOBUTYRATE. Equivalent Gramme Molecule, CgHCOONa, 110.04. 79:01 8402 766 •1258 1021 790 0108 *0215 814 '000976 '00195 0039 *0078 '0156 '0312 I!!!!! 06 IIIlIl odicis II!!!! 11 Ostwald, Zeitschrift für physik.Chenie, vol. i. p. 99. 2 At 25º. 3 Reyher, Zeitschrift für physik.Chemie, IIIIII I onorur •172 *343 732 701 III LITHIUM ISOBUTYRATE. 02. 6652 Il 689 670 63.0 I!!!!! 111111 ! !! 111111 Illlll |||| |||||| Ostwald, Zeitschrift für physik. Chemie, vol. i. p. 104. 2 At 250. 6007 645 584 55.6 621 591 11 Ostwald, Journ. für Chemie, vol. xxxii. p. 328. | 1174 ) ‘0122 *0245 *049 *o98 ·0039 *393 'OQI ·0182 *0365 '146 *293 *000976 '00195 *0039 *0078 0156 0312 •073 *0022 *0044 '000244 *000488 '0009.76 *00195 *0039 *0078 0175 *035 .070 IIIIII LACTIC Acm. Equivalent Gramme Molecule, CH3C(OH)HCOOH, 90. 44'0? i - | 198731 33.8 1526 26.0 : 19.5 88 i 14:4 650 10.6 III!!! (endinin ) 111111 III!!! II!!!! 111111 !!! 1 2 At 250 !!! II TABLE OF ELECTRO-CHEMICAL PROPERTIES. 463 0156 '0312 *0625 all für physik.Chemie, vol. ii. p. 749. I!!!!! |||||| I!!!!! I'0026 I'0052 L'0103 IIIlll 111111 10591 1032 976 251 8741 |||||| 111111 II lii TI!!! vo corino POTASSIUM LACTATE. Equivalent Gramme Molecule, CH3C(OH)HCOOK, 128.13. 102:61 | 10912 1062 1030 1008 977 - 1 945 1 111111 |||||| 111111 1 1 Ostwald, Zeitschrift für physil. Chemie, vol. i. p. 103.. 2 At 250 I!!!!! 111111 111111 *000976 79'2 *25 ·00195 ·0039 0156 I!!!!! I!!!!! III!! SODIUM LACTATE. Equivalent Gramme Molecule, CH,C(OH)HCOONa, 112'04. 81•11 8622; 842 77'1 820 74:6 7109 croreroru 111111 III!!! III!!! 111111 12 Ostwald, Zeitschrift für physik.Chemie, vol. i. p. 100. 2 At 250. 18 Reyher, Zeitschrift für physik.Chemie, vol. ii. p. 751. 793 69.4 OXALIC Am. "Equivalent Gramme Molecule, 2 (COOH)2, 45. - 24,34 | 2027 11 Ostwald, Journ. für P. 457. 1889 11111111 Illlllll ده ندوخ ܗ̇ ܘܲܗܗܵ Tiili 1792 1717 1638 !!!!!!!! IIII!!!! 11111111 IIII!!!! IIIIIII 1542 *140 •280 •560 I'122 2.239 4.455 *0125 025 '000976 ·00195 ·0039 *050 *100 *200 .400 *0078 'OIIO *0219 '0438 •0875 *175 *349 *0078 '0312 'O011 *0022 *0044 0088 *000244 *000488 '000976 *00195 '0039 *0078 *0156 '0312 *0175 *035 *070 *140 5417 464 SOLUTION AND ELECTROLYSIS. OXALIC ACID-continued. Equivalent Gramme Molecule, 3 (COOH)2, 45. •280 •560 30°7 1261 1085 906 26:4 22•1 179 14'1 ||||| | O142 736 578 75.82 !!!!!!!!! ſil!! 1111 111110 2 Lenz, Mémoire de l'Acad. de St Pé- tersbourg, vol. xxvi. 8 Berthelot, Annales de Chimie, vol. xxiii. p. 49. I212 IOSO 1288 I116 125 !!!!!!!!!!!!!! Net 1313 IIllllllllllllll II III III III Ilo |||| 21907 938 Pilllllllllll !!!!!!!!! 356.0 758 '0009 *009 *045 *000 • 180 *0002 *002 *OI '02 144 128 119 IIO 2331 1814 160g I Боб I 1381 !!!!! ||||| *04 POTASSIUM OXALATE. .. Equivalent Gramme Molecule, 3 (COOK)2, 83.13. 793 O 10 , 1 Kohlrausch, Wied. Annal. vol. vi. p. 150. I' Illes !!!! Till !!!!!!!! Tillillll 953 QOI 842 782 llll ||||||| l ILITI!!!!!!! 1111 1111 1111 Till IIIIII!! 1111 11111111 Illl llllllll 198 368 2 Lenz, Mémoire de l'Acad. de St Pé- tersbourg, vol. xxvi. 8 Berthelot, Annales de Chimie, vol. xxiii. p. 50. 4 Hittorf, Pogg. An- nal. vol.cvi. p. 371. ·0055 1186 *0068 ·0274 0548 '00082 0033 0066 otivio TABLE OF ELECTRO-CHEMICAL PROPERTIES. 465 TARTARIC ACID. · Equivalent Gramme Molecule, 1 C2H2(OH)2(COOH)2, 75. | 214081 1813 1513.| 1230 11 Ostwald, Journ. fiir Chemie, vol. xxxii. *00182 *00365 *0073 *0146 W. S. I!!! P. 340. من ن ن ن ن نن *0292 973 000244 | . '000488 '000976 *00195 *0039 *0078 '0156 0312 I'0016 •125 I '0042 1.0083 I'0165 1 '0334 *0585 crororororbitrorororororor IIIIIIIIIIIII 567 2 Berthelot, Annales de Chimie, vol. xxiii. p. 89. 3 At 25º. |||||||||||||| 422 Illlll contact collllllll |||||||||||| 223 309 99 IIIIIIIIIIIIIIIIIII ororerore TILMlllllllllllll 160 25 III||||||||ll|||lll Illllllllllllllllll 505 114 3069 7.26 *0015 2144 1867 •003 Owen on *015 *030 '0002 *0004 *002 '004 'OI .02 1224 963 |||||| 1111 69:6 49'4 370 |||||| •075 17 17 371 683 512 150 BENZOIC ACID. Equivalent Gramme Molecule, C6H3COOH, 122. 14333 24:6 ΙΙΙΙ 832 II|| :!!!!!!! Ill 1111111 1111111 1111 1111111 1111 !!!!!!! !!!!!!! Ill|lll 11 Ostwald, Journ. für Chemie, vol. xxxii. p. 343. : 2 Berthelot, Annales de Chimie, vol. xxiii. p. 44. 9.95 7.20 5.20 1111 1111111 60.22 8 At 25º. *00298 *00595 *O119 *0002441 *000488 '000976 *00195 *0078 *0156 0039 '0475 '095 *190 '00122 '0244 '061 '122 *0001 *002 '005 'OL 444 29'0 20.8 !!!! || !!!! !! 117' 99+ SOLUTION AND ELECTROLYSIS. SALICYLIC ACID. Equivalent Gramme Molecule, CGH(OH)COOH, 138. .0034 30083 .0068 66.61 599 51.2 ||| *000244 *000488 *000976 *00195 ‘0039 ·0078 0156 *0135 41.8 Ill IIIllll III!!!! crererererer 323 25.1 19:1 |||||| 2704 2313 1886 1461 1135 863 ||||||| Il 1111111 ||||||| II|| | Ostwald, Journ. für Chemie, vol. xxxii. P. 344. | 2 Berthelot, Annales de Chimie, vol. xxiii. p. 80. || IIII III II llo 2 0138 '001 171.22 *0345 NINT .0025 ·005 12807 99'4. 069 2307 1780 1375 ! 1039 |||| 8 At 25º. |||| 17 | 17 7501 .020 0034 34 3? 125 26.8 1 Ostwald, Journ. für Chemie, vol. xxxii. p. 345." 0135 '000244 *000488 *000976 *00195 '0039 *0078 *0156 0312 918 Illll 027 |||||||| |||||||| orororororororor ||||| METAOXYBENZOIC ACID. Equivalent Grainme Molecule, C.HA(OH)COOH, 138. - | 15503 1211 20:3 15'2 686 II2 507 372 5.99 4:31 |||||||| |||||||| 054 |||||||| 8.24 •108 •216 •432 III i II1lllll III|||||||| 12 Berthelot, Annales de Chimie, vol. xxiii. p. 82. *0138 *o01 Il 1111 3 At 250 I III *0345 '069 |||| I!!! *0025 ·005 *OI 71092 48'1 117 350 | 17 | 25.2 1171 I!!! Till |||| |||| •138 349 22.81 | 25 || 1! PAROXYBENZOIC ACID. Equivalent Gramme Molecule, C H (OH)COOH, 138. | 10292 17.2 25 1207 573 9:2 416 776 111! III 027 '054 •108 -216 •138 *0034 .0068 '000244 *000488. *000976 '00195 *0135 .027 I!!! | Ostwald, Journ. für Chemie, vol. xxxii. 1. p. 345. 12 At 25º. ||1l TABLE OF ELECTRO-CHEMICAL PROPERTIES. 467 •054 1 .0039 •108 · 0078 !!!! 18 Berthelot, Annales de Chimie, vol. xxiii. p. 84. •216 •432 '01 56 '0312 2:39 III III 1111 1111 III l III |||IIIII IIIII! 1111 1111 IIIllIIl *0138 08345 *001 *0025 !!!! 005 28.0 20'0 143 •138 020 11111111 IIII!!!! citio ci conda !!!!!!!! IIIIIII III!!!!! ORTHONITROBENZOIC ACID. Equivalent Gramme Molecule, C6H4NO2)COOH, 167.04. | 32802 3203 3037 2789 2453 45.9 2073 1688 29*3 1321 II!!!! II|IIII |||||||| IIII!!!! 1? Ostwald, Journ. für Chemie, vol. xxxii. p. 347. 2 At 250 II!!!!!! 53:41 p. 347. I!!!!! III!!!! METANITROBENZOIC ACID. Equivalent Gramme Molecule, C6H2(NO2)COOH, 167.04. | 24102 2021 35.8 1616 2707 1250 20.8 934 15.3 691 11•2 505 IIII!!! II|IIII UTI!!! I!!!! ||||||| I!!! III!!!! 2 At 25º. *000488 *00405 0081 •0162 *0325 ·065 •130 *0002441 *000976 *00195 ·0039 .260 *0078 *0156 '0312 •521 *00405 0081 0762 *0325 065 *000244 *000488 *000976 *00195 '0039 .0078 0156 •130 won O 30–2 54:67 *00405 '0081 •0162 *0325 *000244 *000488 *000976 *00195 I'll ill PARANITROBENZOIC ACID. Equivalent Gramme Molecule, CoH4(NO2)COOH, 167.04. | 24642 458 25 | 2009 37.1 25 1676 28.9 125 - | 1307 | 1111 III 1? Ostwald, Journ. für Chemie, vol. xxxii. p. 348. 12 At 250 - 468 SOLUTION AND ELECTROLYSIS. ORTHOCHLORBENZOIC ACID. Equivalent Gramme Molecule, CH CICOOH, 156:46. 67.4² 30462 | 1 Ostwald, Journ. für Chemie, vol. xxxii. 619 2794 1111110 1.IIIII 4431 53:8 44•7 35.5 27.6 25 25 III 1111110 IIIIIl. IIIlllo p. 349. |||||| 2018 nunun 1605 !!! 2 At 250, 25 - | 1246 | 1 11 Ostwald, Journ. für Chemie, vol. xxxii. c 000244 | *000488 •ooo976 *00195 *00391 III11 METACHLORBENZOIC ACID. Equivalent Gramme Molecule, CoH_CICOOH, 156:46. 4361 1 19712 349 1577 20' 9 25 946 2004 921 15'1 | 25 683 | ..!!!!! I !!!! NNN unun III 11111 P. 349. I!!!! I!!! 2 At 25° 11 Kohlrausch, Wied. Annal. vol. xxvi. P. 196. POTASSIC HYDRATE. Equivalent Gramme Molecule, KHO, 56•13. i 74711 794 845 | 898 1474 | 1567 1689 1795 1892 2011 2074 2205 2110 2243 2140 OOOO OO OO OOO OO OO OOCO |||||||||||||||||| üle locall|||llllll 2141 ||||||||||| |||||||||||||||||| Illlllllllllllllll |||||||||||||||||| III|IIII||lllllll |||||||||||||||||| 2 Ostwald, Journ. für Chemie, vol. xxxiii. p. 353. 3 Lenz, Mémoire de l'Acad. de St Pé tersbourg, vol. xxvi. 4 Kuschel, Wied. An- nal. vol. xiii. p. 289. 2124 2078 2209 I'OOI 2045 2174 211S TA I '0230 1841 1957 *0038 *0076 •0152 *0305 *000244 *000488 *000976 *00195 *061 ·0039 •122 " 0078 *0038 ·0076 *0152 *0305 '061 "000056 '000112 *000336 *000561 OOI12 *00336 *00561 '0112 *0336 *0561 •168 •280 *558 '00001 *00002 '00006 '0001 *0002 *0006 'OOI *002 .006 'OI *03 •I 2.743 5 376 | I '0440 1718 | 1826 TABLE OF ELECTRO-CHEMİCAL PROPERTIES. 469 qoros 1•1274 I'2109 | 104091 சுசு 18 | 0191 | 1314 | 1397 *0204 | 990 | 1052 *0273 / 423 450 ||| '000975 *00195 *00390 *0078 *0156 22882 231•2 233:1 232.6 230°7 228.9 crororororororonorer II||||||| சுசுசு ||||| con ile ill. |||||||||| *0625 •0312 |||||||||| ||| |||||||||| 111 1111|||||||||||| ||||||| 1'0026 L'0061 I'0121 I '0230 1111111 11||||||||||| 2253 2202 214:6 2004 '125 ||| |||||||||||||||| •25 *0424 82:58 2069 2066 0816 *103 2030 2162 158 I'0049 210 I'0077 292 I'olor 408 I'0191 586 10367 | 15.1470 •1537 206 '412 •825 ||||||| ||||||| TO ||||||| 2020 1908 1782 | 1894 1980 2105 2028 15 14.93 23:17 39.83 ·0055 *0109 *0219 0438 •0875 •175 -350 .697 1.386 2.743 4:467 I ei 1488 | 1'02251 1'0441 1°0850 I'1224 I'1569 1•1896 I'3320 | 1 Kohlrausch, Wied. Annal. vol. vi. p. 150. crererererer 18.ord 0221 SODIC HYDRATE. Equivalent Gramme Molecule, NaOH, 40'04. 15 1 8171 181 0194 / 1634 | 1737 18 0199 1488 1581 2447 '0209 1223 1300 3020 1007 1070 3264 0241 816 867 3259 ·0266 693 15 1896 *0452 |||||| Our A. W 2 Ostwald, Journ. für Chemie, vol. xxxiii. p. 355. 202 1111111 1111111 ||||||! 1.1.11111 II 11111 111.|||| : 111111111||||| 21501 *000975 *00195 *0039 •0078 *0156 . '0312 *o$25 211.62 216.7 215.2 21294 20500 |||||| !!!!!!! ||||||| 21007 I'0023 470 SOLUTION AND ELECTROLYSIS. Sonic HYDRATE--continued. Equivalent Gramme Molecule, NaOH, 40*04. *108 이 ​•125 25 I '0055 I'OI20 15 1993 1910 *080 !!!!!!! 3 Lenz, Mémoire de l'Acad. de St Pé- tersbourg, vol. xxvi. O|||||| •285 1954 I '0225 15 181.6 I'084 * Kuschel, Wied. Ar- nal. vol. xiii. p. 289. *127 *240 go o o o o lema lo ||||||ll|||lll *0319 ·0602 •1257 •1618 1777 11111111 111111° 1889 Entroierururur 1830 IIIlll |||||||| 56.78 1'0022 106 1.0056 217 15 287 I‘0121 424 I'0150 548 15 1022 | 140576 | 15 | 1805 III!!!!!!!!!!! !ול -642 1'012 1*274 2'515 4:893 •2564 1760 1871 1722 1883 1515 1610 1091 | 1797 !!!!!!!! | 15 |||||||| 115 I '0286 •6474 | 1-2947 1 1394 | 1481 | LITHIUM HYDRATE. Equivalent Gramme Molecule, LiOH, 24.02. - ) 1913 11- '000976 *00195 0039 *0078 *0156 *0312 *0625 *125 •25 .201 *402 *0023 *0094 '0188 *0375 *075 *150 *300 !!!!!!!!!!! 11 Ostwald, Journ. Für Chemie, vol. xxxiii. p. 356. 2 Kohlrausch, Wied. Annal. vol. vi. p. 151. Nei coono court 11111 11111111111 II!IIIIIIIIIII I||||||llll||||| !!!!!!!!!!! 11111 11111111111 11111 11111111111 8 Kuschel, Wied. A12- nal. vol. xiii. p. 289. 6942 I 1253 LAOR III!! 2108 !!!!! *0202 | 1054 2660 TABLE OF ELECTRO-CHEMICAL PROPERTIES. 471 | 251 '000976 *00195 *0039 IIIII!! •0078 111111111 II||| I!!!!!!!! crororonorer une IIIIIIII BARIUM HYDRATE. Equivalent Gramme Molecule, 1 Ba(OH)2, 85.5. 218:44 - | 232221 219.8 2336 2187 2325 215-9 2295 210:3 2235 2010 2044 1839 1955 1744 | 1854 111111111 II||||||| 1 Ostwald, Journ. für Chemie,vol. xxxii. p. 357. ? At 25º. 111111111 |||||||| 111111111 0312 *0625 2137 1923 •125 25 ·0059 •0118 ·0236 0472 11 Ostwald, Journ. fiir Chemie,vol. xxxii. *0039 ·0078 *0156 *0312 *0625 P. 357. IIIllli !!!!!!! T111111 1111111 IIII!!! STRONTIUM HYDRATE. Equivalent Gramme Molecule, Sr(OH)2, 60-75. 209.21 | 2224% 212.2 2256 21107 2250 20990 2222 2025 2152 196.5 2089 190°1 2021 II||||| 1111111 ||||||| III!!!! II|||| 2 At 25º. 378 I!!!!! 1||||| II!!!! TII|II| |||!11 CALCIUM HYDRATE. Equivalent Gramme Molecule, } Ca(OH)2, 37. 213-21 - | 22662 2154 2290 213.4 2268 2093 2225 200'2 2128 190-5 | 251 | 2025 I!!!! IIllll 111111 II!!!! 1 Ostwald, Journ. fiir Chemie, vol. xxxiii. p. 357. 2 At 250 '0083 *0166 *133 •532 .0036 *0072 '0144 *000976 *00195 *0039 .0078 *0156 *0312 '0288 *0575 •115 '000017 | *000034 *000102 - 00001 *00002 00006 AMMONIA. Equivalent Gramme Molecule, NHg, 17.04. 56041 595 700 744 | 690 733 70 000 111 I!! E 11 Kohlrausch, Wied. Annal. vol. xxvi. 1 p. 197. - 472 SOLUTION AND ELECTROLYSIS. AMMONIA-continued. Equivalent Gramme Molecule, NH3, 17.04. ATA OOOT7 Oc034 'COI02 0017. *0034 OI02 O17 1000. ZOOO. 9000. 100. llllll 200 100 I16 002 oo6 Or 11111111111) |||||| 2 Ostwald, Journ. für Chemie, vol. xxxiii. p. 358. | At 25. |||||||||| ISO. 085 85 。||||||||||||||| 12. ITI S"22 SSIS359 18766. 9446. oBBBBBBBBBBBBBBB%%%%%%%% 89 1111111111 || slilllllllll。 11llllllll 111111111llllll 35 1||lllllll llllllllllll||| 345 。二二二二二二二二二二二二二​||||| ||||||||||||||||||||||||| |||| | 25 53 Sor00. 3702 28 | SL6000. S6100. 6Eoo. 8Loo. 179 12-4 ||||||||||||||| 20132 0265. *053 i111|||||| |||||||||| ||||||||| 81. - - - - 901. - *212 B%; 6-13 427 3OI 2.IO I'46 「25 METHYLAMINE, Equivalent Gramme Molecule, CH NH,, 31.04. II482 900 CC0305 ( 1900. 6Eoo. 1946000. bioo. 8/oo. 9910. OI22 0245 049 ||||| 1111|| no conio 22222 11111 689 11111 11111 lllll. 11111 lllll lllll | 1 Ostwald, Journ. für Chemie, vol. xxxiii. p. 360. 2 At 25. 28。 TABLE OF ELECTRO-CHEMICAL PROPERTIES. 473 26.4 19:1 I!! ||||| 13:5 95 6:4 II!!! 204 1 44 IOI I!!!! ||||| ||||| I!!!! ||||| I!!! 204 *0088 *o0o976 1 *00195 *0039 936 Lii | Ostwald, Journ. für Chemie, vol. xxxiii. p. 360. •0175 '0078 *0156 *0312 ·0625 •125 |||||||||| 2 At 250 1111111111 Genererereren een ETHYLAMINE. Equivalent Gramme Molecule, C2H5NH,, 45'04. 112.01 | 11902 88.0 6609 711 50*2 36.9 26.8 1983 13.5 9:3 6'1 I!!!!!!!!! |||||||||| ||||||||| |||||||||| 11111111 |||||||||| |||||||||| !!!!!!!!!! •25 '000976 *00195 | Ostwald, Journ. für Chemie, vol. xxxiii. 821 p. 361. *0039 111111111 .0078 *0156 0312 *0625 II||||||| 326 111111111 jääradecer PROPYLAMINE. Equivalent Gramme. Molecule, C3H,NH,, 59'04. 97071 | 10382 772 59'2 44'3 2307 16.9 11:9 8.1 ||||||||| ||||||||| ||||||||| ||||||||| IIIIIIIII 1 2 At 250 IIIIIIIII IIII!!!!! je •125 •25 - 8752 - 11 Ostwald, Journ. für | Chemie, vol. xxxiii. *035 070 *140 •281 -562 *007! ·0283 *057 •0142 10009761 *00195 *0039 ·0078 I!!! ISOBUTYLAMINE. Equivalent Gramme Molecule, C4H2NH2, 73.04. 82:31 | 25 64°5 25 0:2 25 | 25 0536 onunun I!!! Till I!!! I p. 361. 12 At 250. 36.6 389 474 SOLUTION AND ELECTROLYSIS. ISOBUTYLAMINE“continued. Equivalent Gramme Molecule, C,H,NH2, 73.04. . I14 228 *4.55 SIM lllll lllll。 %93% 94864 1111|| 11111 - lllll。 111ll 。----- lllll AMYLAMINE. Equivalent Gramme Molecule, C5H, NH,, 87.04. 9751 IC362 774 | 200976 00195 1 Ostwald, Journ. für Chemie, vol. xxxiii. 823 *0039 0078 94 F11111111 %%%%%%% |||||||||| |||||||| O156 0312 0625 33'2 111111111 二11 ||||||||| lllllllll lllllllll 111111111 2 At 250, *0085 017 034 EP I36 272 54 242 ·125 17.2 II9 % DIMETHYLAMINE. 00105 200976 0039 20156 ||| 957 Equivalent Giramme Molecule, (CH)2NH, 45°04 J20-71 128321 1017 786 595 11 Ostwald, Journ. für Chemie, vol. xxxiii. p. 363. *0078 8 At 250. I40 ·281 llllllllll 0312 |||||| 92848409 %%%%%%%%%% 1111111111 llllllllll llllllllll 111111||||| 作辭B8 11llllll 1111111111 1111llllll 1111111111 ·562 *125° TABLE OF ELECTRO-CHEMICAL PROPERTIES. 475 *0071 *0142 DIETHYLAMINE. Equivalent Gramme Molecule, (C2H5),NH, 73.04. - 13822 | 1152 913 699 $6100. ·0285 -0078 ||||||||| '057 114 .228 *455 '910 ||||||||| |||||||| IIIIIIIII 1 Ostwald, Journ. für Chemie, vol. xxxiii. p. 363. 2 At 250. 525 ||||||||| I!!!!!!!! 111111111 111111111 381 IIIII!!!! 18.2 123 277 193 131 TRIMETHYLAMINE. Equivalent Gramme Molecule, (CH3)2N, 59'04. 56.81 6042 455 ·0058 *0231 29100. 946000. •0116 12 Ostwald, Journ. für Chemie, vol. xxxiii. P. 364. 2 At 250 6800. *0462 *0925 •185 ·0078 *0156 *0312 *0625 •125 1111111111 |||||||||| oinnilovicija coco II!!! I||||||||| !!!!!!!!!! * 1111111111 II||||||| |||||||||| |||||||||| •370 740 Til | 946000. 251 TRIETHYLAMINE. Equivalent Gramme Molecule, (C2H5)2N, 101.04. 111.61 11862 931 708 Hogy 96100. *0395 ·0039 Ostwald, Journ. fiir Chemie, vol. xxxiii. p. 364. 2 At 25. 640. •158 '0078 *0156 '0625 1111111111 |||||||||| con divinidio IIIIIII|||| II|||||||| 1111111111 zito. |||||||||| 1111111!!! •315 IIIIIIIII! IIIIIII!! |||||||||| 630 •125 •25 . INDEX. The numbers refer to the pages. Authors' names are printed in small capitals. The electrochemical properties of aqueous solutions of the substances of which the names appear in italics will be found tabulated in the Appendix. ABEGG and NERNST, theory of freezing point determinations, 153 Absolute electric charge on ions, 189 Absolute ionic velocities, 214; table of, 223 Absolute scale of temperature, 15. Absorption coefficients, 85, 87 Absorptiometer (Fig. 33), 84, 85 Accelerating influence of acids, 337 Accumulators or secondary cells, 263 ; electromotive force, 265; origin, 181 Acetic acid, 453 ; abnormal vapour pres. sure, 129; freezing point of solutions in, 156; ionic mobilities, 215, 218; ionization, 321; ionization constant, 341 Acetate of silver, solubility of, 93 Acetone, conductivity of solutions in, 331 Acids, accelerating influence, 337; elec- fusion curve (Fig. 20), 62; silver copper, 59, 60; fusion curve (Fig. 19), 60 Alternating currents, used in measure- ment of electrolytic conductivity, 199 Aluminium chloride, 420; sulphate, 445 Amalgams, in capillary electrometers and galvanic cells, 285; in concentration cells, 244; in dropping electrodes, 281; trical conductivities, 204, 337, 357 Action, secondary electrolytic, 194 - Additive properties of solutions, 332 Adiabatic relations of ideal gas, 7 ADIE, absolute value of osmotic pressure, 120 Affinity or avidity, coefficient, 205, 336, 342; measurement, 336; residual, 173 AITKEN, supersaturation, 43 Alcohol, ionization of solutions in, 322, 331; vapour pressures, 72, 74, 403 ALEXEJEFF, mutual solubility of liquids, 88 Alkalis, electrolytic decomposition of, 178 ALKEMADE, VAN RIJN, VAN, Š curves, 26, 63 Allotropic solids (Fig. 12), 45 Alloys, 59; eutectic, 60; mixed crystals, 69; freezing point, 60, 160; microscopic study, 60, 62, 68; rate of cooling, 68; structure (Figs. 43, 44), 144; copper and tin, 71; gold aluminium, 61, 62; vapour pressure of, 141 Ammonia, 471; ionization, 216, 322; solubility, 86 Ammonium bichromate, 450; chloride, 412; chromate, 450; iodide, 424; nitrate, 428; sulphate, 438 Amylamine, 474 Anhydrous solutes (Fig. 13), 50, 51 Animal electricity, 176 Anion, definition of, 180 Anode, definition of, 180 ARCHIBALD, equivalent conductivities at 0°, 325; freezing point, 153 ARMSTRONG, H. E., hydrate theory of solution, 170 ARMSTRONG, E. F., Report by, 403 ARRHENIUS, chemical activity, 336;. co- efficient of ionization, 322, electrolytic dissociation, 317; diffusion of electro- lytes, 380; freezing points, 153; heat of neutralization, 356 ; heat of ioniza- tion, 355; ionic fluidity, 224; maxima conductivities, 357; osmotic pressure of electrolytes, 317 ASTON and DUTOIT, equivalent conduc- tivities, 331 Available energy, see Energy Avidity, measurement, 336; table of rela- tive, 337 INDEX 477 AYRTON and PERRY, potential differences, 268 BUCHANAN, J. Y., boiling point of solu- tions, 138, 139; cryohydric point, lowering of, 146; freezing of sea water, 145; freezing point of sodium chloride solutions, 142; structure of ice, 145 BUNSLN, absorption coefficient, 85; con- firmation of Henry's law, 86; deter- mination of solubility, 84 BURCH, action of capillary electrometer, 283, electrometer as condenser, 282 BUSCEMI, temperature coefficient of fused salt cells, 237 Butyric acid, 460 BANCROFT, "the Phase Rule," 77, 402; potential differences, 388 Barium chloride, 415; hydrate, 471; nitrate, 432 BARNES, freezing points, 153; equivalent conductivity at 7°, 325 Battery, see Cell BECKMANN, boiling points, 137; freezing : point determinations, apparatus for (Fig. 45), 155; freezing points of con.. centrated solutions, 161; molecular weights in solution, 140; vapour pres- sures, 132, 133 BEETZ, electrolytes, resistance of, 198; conductivity of supersaturated solutions, 80 BEIN, electrolytic transport numbers, 210 BEKETOFF, precipitation of metals by hydrogen, 386 BEMMELEN, VAN, gelation, 394 BENDER, properties of solutions, 333 Benzine, freezing points of, solutions in, 156 Benzoic acid, 465 BERKELEY, Earl of, growth of crystals, 81; time required for saturation, 90 BERTHELOT, occlusion, 82 BERTHELOT and JUNGFLEISCH, solubility of succinic acid, 93 BERZELIUS, electrochemical theory, 191 BERZELIUS and HISINGER, electrolytic de- composition of salt solutions, 178 BINDEL, supersaturated solutions, 80 BLAGDEN, freezing points of solutions, 153 Bofling points, 135, 331; measurement of, bony Beckmann, 137; Buchanan, 138; Regnault, 138 ; Wade, 140 BONTZMANN, laws of osmotic pressure, 169 BOTTOMLEY, potential differences, 271 Boundary of two solutions, 219, 376, 382 Boloty, measurement of electrolytic con- ductivity, 198 Bofyle's Law, 7 BREDIG, specific ionic mobility, 229, 230 · BREDIG, COHEN and VAN 'T HOFF, transi- tion cells, 261 BREDIG, Noyes and OSTWALD, concentrated solutions, 162 Brompropionic acid, 459 BRÓWN, J., temperature coefficient of fused salt cells, 237; mercury drop- ping electrodes, 280; potential differ- ences, 271 BRÜHL, ionizing power of water, 364 BRUNI and PADOA, solid solutions, 403 BRUNNER, precipitation of metals by hydrogen, 386 Cadmium bromide, 422; chloride, 419; iodide, 424; nitrate, 433; sulphate, 443 CAILLETET, evolution of hydrogen by metals, 386 Calcium chloride, 416; hydrate, 471; nitrate, 432 Calorie, definition of, 1 Cane sugar, inversion of, 337; freezing point of solutions, 147 Capacity for heat of solutions, 171, 335 Capacity, specific inductive, of solvents, 362 Capillary action, electro-, 282 ; electro- meter, 282 CARLISLE and NICHOLSON, early experi- ments on electrolysis, 177 Carnallite, deposition of, 404 Carnot's engine, 12 CARRARA, dissociation of water, 363; equi- valent conductivities in pyridine, 331 Cathode, definition of, 180 Cation, definition of, 180 Cells, galvanic: amalgam, 285; bichro- mate, 1.82; chemical, 255; Clark's stan- dard, 184, 235, 261; Daniell's, 182, 233; effect of pressure, 239; electromotive force, 232, 235, 236, 285, 288, 382, 383; fused salt, 237; Grove's, 235, 237; irreversible, 235, 262; liquid, 382; mercury, reversible heat of, 238; re- duction and oxidation, 258; reversible 234, 235, 237; secondary, 263; Smee's 182; temperature coefficient of, 237; transition, 258; Weston's, 261 Cells, concentration : calomel, 250 ; von Helmholtz's theory, 242; hydrogen, 242; silver chloride, 249; silver nitrate, 245, 248; different electrodes, 242; differ- ent solutions, 245; double concentra- tion, 250; effect of low concentration, 253; ionization in, 255; migration in, 250; table of electromotive forces, 250 Cells, osmotic (Fig. 36), 96, 118, 168 Cells, resistance (Figs. 48 to 51), 201 Change of volume and osmotic pressure, 111 478 · SOLUTION AND ELECTROLYSIS CHARPY, alloys, 59 ; microscopic study of, solvents, 322, 330, 362; measurement 61 of, 198, 325; of mixed solutions, 88; Chemical affinity, see Affinity temperature coefficient of, 202, 408; Chemical combination, theory of solution, of supersaturated solutions, 80; of 169 water, 193, 358 Chemical constitution and mobility of Consolute components, 48 ions, 229 Consolute solid solutions, 63 Chemical potential, 25, 34 Contact electricity, 267 et seq. Chloric acid, 434 Contact potentials, 300; table of, 285 CHRISTY, contact potentials, 300 Contact of two solutions, 219, 376, 382 CLARK, LATIMER, standard cell, 184, 235, Contraction on formation, 171 261 Convergence temperature, 154 CLAUSIUS, on electrolysis, 205; latent - Co-ordinates, generalized, 18 heat equation, 38 Copper chloride, 419; sulphate, 443 Coagulation of colloidal solutions, 45, 395 Copper refining, 310 Cobalt sulphate, 445 Corpuscles, or negative ions, 191, 274 COHEN, hydrated solids, 53; transition CROMPTON, heat of neutralization, 352 point, 259 CRUIKSHANK, experiments on electrolytes, COHEN, VAN 'T HOFF and BREDIG, tran 178 sition cells, 261 Cryohydrates, 49 COLLINS, RICHARDS and HEIDROD, electro Cryohydric point, 142; lowering of, 146 chemical equivalent of silver, 185 Crystalline structure of alloys, 68, 71, Colloid, definition of, 371 144; of ice, 47, 144 Colloidal solutions, coagulation of, 45, Crystallization, 44, 81, 171, 392 395; nature of, 400; separation from Crystalloid, definition of, 371; separation crystalloids, 388 of, 380 Colour of salt solutions, 334 Crystals, mixed, 62, 69, 403 Combination, chemical, theory of osmotic Crystals, surface energy of, 45, 81 · pressure, 169 Cupric chloride, 419; sulphate, 443, COMEY, A. M., Dictionary of Chemical Current, alternating, used in measuring Solubilities, 93 electrolytic conductivity, 199 Commutator, revolving, 201; tuning-fork, Curves, concentration or solubility (Figs. 301 16 to 32, 34, 35, 52, 64, 66), 55 to 79, Complete cycles, 6 89, 91, 328, 404; conductivity (Figs. Complex cycles, 18 52, 64), 203, 328; electrocapillary Complex ions, 226, 322, 331 (Fig. 61), 288; fusion and solidification Complex, molecular, theory of solutions, (Figs. 16 to 25, 40, 64), 55 to 70, 125, 173 · 328; ionization (Fig. 64), 328; Phase Components, definition of, 35; one com Rule (Figs. 8 to 15, 31, 40), 39 tok 54, ponent, 39; two components, 48; 76, 125; vapour pressure (Figs. 26 to consolute, 48; two liquid, 58; two 30, 40, 41), 72 to 75, 125, 136; Š (Figs. volatile, 71; three, 76 7, 21 to 24), 26, 64 to 67 Compound, definition of, 48 Cyanacetic acid, ionization constant of, 342 Concentrated solutions, equation for, 162; Cycles, complete, 6; complex, 18 1 freezing point of, 160; freezing point CZAPSKI, temperature coefficient of cells, and osmotic pressure, 150; vapour 237 pressure of, 126 Concentration cells, 241; see Cells, Dalton's law, 48 concentration DANIELL, cell, 182, 233; nature of ions, Concentration curves, 55 ; see Curves Concentration, influence of, on equivalent Davy, Sir HUMPHRY, electrolysis, 178; conductivity, 223 electrolytic decomposition of alkalis, Concentration, ionic, 340, 346, 351, 365 178; polarization, 181 Conductivity, electrolytic, 197, 408; Decomposition, electrolytic, 178; of water, additive nature of, 207; equivalent, 178, 306, 307 202, 408; connexion with osmotic Decomposition voltages, 301; tables, 802, pressures, freezing points and vapour 308 pressures, 160, 316; influence of con- DE COPPET, cryohydric temperatures, centration (Fig. 12), 202, 203, 223, 143; freezing point of solutions, 153 322; of liquid films, 230; in various of supersaturated solutions, 80 192 INDEX 479 198 Density of solutions, 170, 333, 408; Eflorescence of crystals, 54, 58 of supersaturated solutions, 80 Electric charge of ions, 188, 189 Depression of the freezing point, 126; Electric endosmose, 292 see also Freezing Points Electricity, animal, 176; contact, 267 DES COUDRES, mercury concentration Electro-capillary action, 282, 294 cell, 244 Electro-chemical equivalents, 184; table DEVILLE and Troost, occlusion, 82 of, 187 DE VRIES, isotonic solutions, 119 Electro-chemical properties, table of, 407 DEWAR, occlusion, 82 Electro-chemical series, 177, 296, 298, 299 (Fig. 33), 85; boiling point (Fig. 42), Electrodes, definition of, 180; of different 139; capillary electrometer (Fig. 60), concentration, 242; dropping, 278, 281; 1282; electrolytic conductivity (Figs. platinum, preparation of, 199; tapping, 47 to 51), 200 to 202; freezing point 1 (Fig. 45), 155; ionic migration (Figs. Electrolysis, 176, et seq.; of gases, 187 54, 55, 56), 210, 217, 221; normal Electrolytes, additive properties, 332; electrode (Fig. 62), 295; osmotic cell coagulative properties, 395; conduc- ; (Fig. 36), 96; polarization (Fig. 63), 303 tivity of, 197; conductivity of and depres- Dialysis, 388 sion of freezing point, 160; diffusion of, Dichloracetic acid, 456 376; equilibrium between, 346; measure- DIETERICI, vapour pressure of sulphuric ment of conductivity of, 198; potential acid, 265 differences between, 381; "solution Diethylamine, 475 Diffusion, 369; constant of, 369; absolute of, 352 value, 371; tables, 372, 373; of electro Electrolytic conductivity, 197, 408 Electrolytic separations, 301 through membranes, 388; and osmotic Electrolytic solution pressure, 274, 280, pressure, 374; theory, 369, 374, 376 297, 385 Diffusivity or diffusion constant, 369 Electrometer, capillary, 282 Electromntive force, of galvanic cells, Dilution, effect of, 169; heat of, and 236, 238, 240, 243, 247, 257, 259, 381 osmotic pressure, 111; law of, 341, Electromotive series of metals, 177, 296, 343, 344, 350 298, 299 Dimethylamine, 474 Electrons, theory of, 191, 274 Disșipation of energy, principle of, 110 Electroplating, 178, 194, 307 Dissociation, electrolytic, theory of, 206, EMDEN, vapour pressure of solutions, 132 312; and chemical activity, 335; heat Endosmose, electric, 292 of, 354; and osmotic pressure, 159, 316; · Energy, available or free, 28, 29; appli- of water, 358, 362 cations to chemical change, 339; Dissociation, hydrolytic, 364 coordination of physical science, 165; ! Dissolution, heat of, 112, 171; table, 117 dilution of solutions, 169; electro- Divariant systems, 36 capillary action, 284; electromotive DOLEZALEK, theory of accumulators, 264, force, 235; heat of ionization, 354; 265 latent heat, 29; osmotic pressure, 103, DONDERS and HAMBURGER, temperature 113, 165 and osmotic pressure, 118, 119 Energy, conservation of, 1; internal, 19; DONNAN, colloid solutions, 402; Hall surface, 43, 81, 402 effect in electrolytes, 385 ENGEL and ETARD, influence of tem- Double concentration cells, 250 perature on solubility, 91 Double salts, 92; electrolysis, 195; Engine, Carnot's reversible, 12 deposition, 403 Entropy, 20 Dropping electrodes, 278, 281 Equilibrium, 10, 32, 205, 225, 339; DUNEM, theory of colloids, 394 conditions of, 25; electrolytic, 205, Dufort and Aston, conductivities of 225, 339, 346; false, 11, 37; labile, 42; solutions in acetone, 331; properties of phases, 33, 68, 78; in saturated. of solvents, 364 solutions, 78 Equivalent conductivity, tables of, 408 ECKARD, dialysis, 389 Equivalent conductivity, curves showing EDİLER and OBERBECK, potential differ (Fig. 52), 202, 203; influence of con. encès, 388 centration, 223; limiting value, 332; - 480 SOLUTION AND ELECTROLYSIS measurement at 0°, 325; in various solvents, 321, 330, 362 Equivalent, electro-chemical, 184; table of, 187 ERMAN, voltaic pile, 178 ERSKINE MURRAY, contact electricity, 272 Erard and ENGEL, influence of tempera- ture on solubility, 91 Ethereal solutions, lowering of vapour Ethyl alcohol, ionization in, 322, 330 Ethylamine, 473 Ethyl-sulphuric acid, 446 Ewan, T., freezing point of concentrated Free energy, see Energy Free surface of volatile liquid, 98 Freezing points, 40, 126, 141, 153, 317; of alloys, 59, 62, 69, 144, 160; depression of the, 123, 126, 142, 147, 149, 150, 156, 160, 162, 317, 320, 322, 328, 330, 400; diagrams (Figs. 16 to 25, 40, 64), 55 to 70, 125, 328; experimental methods (Fig. 45), 153, 155, 158; non-aqueous solutions, 156, 321, 330; connexion with electrolytic: conductivity, 159, 316 to 332; with osmotic pressure, 126, 147, 152; with vapour pressure, 122, 125 Friction coefficients, ionic, tables of, 379 Fuchs, electromotive force of polarizatioſ, 303 Fused salt cells, temperature coefficient of, 237 Fusion curves, see Freezing Point Diagrams EWING and ROSENHAIN, structure of alloys GALVANI, origin of electrolysis, 176; animal electricity, 176 Galvanic circuit, distribution of potential in (Figs. 58, 59), 275 Eutectic alloys, 60, 144 Evolution of gases in polarization, 305 EXNER, mercury-dropping electrodes, 280; single potential differences, 278 EXNER and TUMA, single potential differences, 278 Expansion, thermal, 171; of salt solutions, 333 EYK VAN, equilibrium of solid and liquid GAMGEE, colloids and crystalloids, 401 Gas, adiabatic relations of an ideal, 17;, electrolysis, 187, 189; polarization, 305; solubility in liquids, 84, 130; solubility in mixed solutions, 87; solubility in salt solutions, 87; solu- bility in solids, 81 Gas, battery, Grove's, 305 Gaseous film, 82, 269, 271 Gaseous pressure, identity with osmotic pressure, 104, 120, 166 Gelation, 394 Generalized co-ordinates, 18; forces, 19 GIBBS, chemical potential, 25, 34; eless, tromotive force of reversible cells, 235; growth of crystals, 45, 81; latent heat equation, 38; phase rule, 35; theory of osmotics, 109; transition cells, 258; surface energy, 81, 402 GILBAULT, effect of pressure on electro- motive force, 240 GLADSTONE, colour of salt solutions, 1335 GOCKEL, temperature coefficient of electro- phases, 68 EYKMAN, freezing points, 150, 161 False equilibrium, 11, 37 FARADAY, early experiments on electro- lysis, 179; laws of electrolysis, 182; polarization, 181; vapour pressures, 132 Faraday's laws, 182, 184, 332; in fused salts, 187; in gases, 187 Favre, occlusion, 82 Ferric' chloride, 421; equilibrium of phases (Fig. 17), 56; efflorescence of crystals, 54; hydrolysis, 366 Ferrous chloride, 420 Ferrous sulphate, 444 FICK, diffusion, 369, 371 Films, gaseous, 82, 269, 271; liquid, conductivity of, 230 FITZGERALD, osmotic pressure and surface tension, 100, 103 TirZGERALD and TROUTON, conductivity of electrolytes, 204 FITZPATRICK, electrolytic conductivity, 201, 330; tables of electro-chemical properties, 211, 407 Fluidity, ionic, 224, 356 coefficient of, 409 Forces, generalized, 19 Formic acid, 452; freezing points of solutions in, 156 Formic acid series, mobility of ions, 230 FOURIER, conduction of heat, 369 Fractionation, 75, 403 motive force, 237 GOODWIN, double concentration cells, 252 GORE, surface of contact of two solutions, 219 GORSKI and LASZOZYNSKI, equivalent don- ductivities, 331 GRAHAM, colloids, 391, 396; diffusion, 370, 372; occlusion, 82 Gram-molecule, definition of, 4 GRIFFITHS, freezing points of dilute solu- INDEX 481 tions, 158, 321 ; mechanical equivalent of heat, 1; molecular lowering of freez- ing point, 147 GROSHAUS, properties of solutions, 333 GROTTHUS, electrolytic chain, 180; electro- lytic decomposition, 179 GROVE, cell, 235; gas cell, 305 GULDBERG and WAAGE, the mass law, 205, 340 GUTAE and PATTERSON, electro-chemical equivalent of silver, 185 GUTHRIE, alloys, 59; cryohydrates, 49; equilibria of mixtures of salts, 76 Hall effect in electrolytes, 384 HALL and KAHLENBERG, equivalent con- ductivity at 09, 325 HAMBURGER and DONDERS, influence of temperature on osmotic pressure, 118 HARDY, coagulation, 398; gelation, 394 ; gels, 393 HAUTEFEUILLE and TROOST, occlusion, 82 Heat, latent, equation, 29, 30, 37, 125 Heat of dilution, calculation of freezing point from, 170; and osmotic pressure, 111; of sulphuric acid, 266 Heat of formation, determination, 238; table, 117 Heat of ionization, 354 Heat of precipitation, 117 Heat of reaction, 237 Heat of solution and solubility, 90, 115; and osmotic pressure, 112, of super- saturated solutions, 80; table of, 117 Heat, reversible, of cell, 237 Heat, specific, of supersaturated solu- tions, 80 HEIDENHAIN and MEYER, absorptiometer HEYDWEILER and KOLHRAUSCH, conduc- tivity of pure water, 193, 358 HISINGER and BERZELIUS, electrolysis of salt solutions, 178 HISSINK, equilibrium of solid and liquid phases, 68 HITTORF, chemical activity and conduc- tivity, 336; complex ions, 226; electro- chemical series, 300; electrodes of concentration cells, 254 ; electrolysis of double salts, 195; migration of ions, 208, 210, 383; secondary action in electroplating, 194 HOFF, VAN 'T, diffusion and osmotic pres- sure, 376; dilution law, 343; influence of pressure on solubility, 90; latent heat equation, 38; molecular depression of freezing point, 149; osmotic pressure, absolute value of, 103, 107; osmotic theory, 172 ; solubility of mixtures, 403; table of heats of solution or precipita- tion, 117 HOFF, VAN 'T, COHEN and BREDIG, transi. tion cells, 261 HOITSEMA, solid solutions, 83 HOITSEMA and ROOZEBOOM, occlusion, 82 HOLBORN and KOHLRAUSCH, equivalent and electrochemical weights, 186; trans- port numbers, 211 HOPFGARTNER, transport numbers, 210 Horn and MORSE, semi-permeable mem- branes, 406 HORSTORD, resistance of electrolytes, 198 HOSKING and LYLE, ionic viscosity, 406 HOULLEVIGNE and OSMOND, electrolysis of salts of iron, 196 Hydrated solids, 53 Hydrates, crystallization of, 171; forma- tion of, 57; isolation of, 171 Hydrate theory of solution, 170 Hydriodic acid, 422 Hydrobromic acid, 421 Hydrochloric acid, 410; solubility, 75, 84, 87 Hydrocyanic acid, 451 ; solutions in, 406 Hydroferrocyanic acid, 151 Hydrofluoric acid, 425 Hydrogels, 393 Hydrogen, concentration cell, 242 Hydrolysis, 364 Hydrolytic dissociation, 364 Hydrosols, 393 Ice, arctic, 145; crystalline varieties of, 47; structure of, 47, 144; Index, refractive, 171; and boundary of solutions, 121 Indicator diagram, 14 Internal energy, 19 Inversion of cane sugar, 337 31 (Fig. 32), 84 HEIM, electrical conductivity of super- saturated solutions, 80 HEIMROD, COLLINS and RICHARDS, electro- chemical equivalent of silver, 185 HELMHOLTZ, Von, electro-capillary action, 283; electric endosmose, 293, electro- motive force, 235; free energy, 28; migration in concentration cells, 250 ; osmotics, 109; potential differences, 279 HENDERSON and STROUD, measurement of electrolytic conductivity, 197 Henry's law, 85 ; confirmed by Bunsen, 86 HESS, law of thermo-neutrality, 352 HEYCOCK and NEVILLE, on alloys, 59 et . seq. ; copper and tin (Fig. 19), 71; depression of freezing point, 160 ; gold and aluminium (Fig. 30), 62, and (Fig. 43), 144; microscopic investigations, 59, 61, 62, 68, 71, 144 (Fig. 43); osmotic pressure, 244 W. S. 482 SOLUTION AND ELECTROLYSIS Inversion point, 41, 55, 259, 262 Iodides, mixture of, freezing point curve (Fig. 25), 69, 70 Iodopropionic acid, 460 Ionic concentration, 245, 253, 300, 308, 317, 326, 340, 348, 365, 397 Ionic fuidity, 224, 356, 379, 406 Ionic migration, theory of, 208, 213, 383 Ionic viscosity, 224, 356, 379, 406 Ions, charge on, 189; complex, 226, 322, 331; as condensation nuclei, 43; dis- sociation, in electrolysis, 206; fluidity, 224; migration, 207, 210; mobility, 211 to 226, 229, 230; nature of, 191 Ionization, 225, 316, 325, 328, 337, 341, 354, 358, 362, 406; heat of, 354; in various solvents, 330, 331, 362, 406 Ionization of dilute solutions at 0°, 321, 325, 328 Irreversible cells, 262 Isobutylamine, 473 Isobutyric acid, 461 Isohydric solutions, 346 Isomorphous salts, 92 Isotonic coefficients, 120 Isotonic solutions, 119 friction coefficients, 379; ionic mobility or velocity, 211; Ohm's law in electro- lysis, 177, 204; use of telephone, 199 KOHLRAUSCH, F. and W., electro-chemical equivalent of silver, 185 KOHLRAUSCH and HEYDWEILER, conduc- tivity of pure water, 193, 358 KOHLRAUSCH and HOLBORN, electro- chemical and equivalent weights, 186; tables of electrolytic transport numbers, 211 KONOWALOFF, vapour pressure of miscible liquids (Figs. 26 to 30), 72 to 75 KRAPIWIN and ZELINSKY, conductivity of solutions in alcohol, 330 KÜMMEL, electrolytic transport numbers, 210 KUSCHEL, electrolytic transport numbers, 210 JAHN, heats of formation, 238; reactions in electrolysis, 194; reversible heat in cells, 237, 238; temperature coefficient of cells, 237 JONES, H. C., freezing points, 153 ; ioni- zation at 0°, 328 JOULE, measurement of thermal equiva- lent of work, 1 JUNGFLEISCH and BERTHELOT, solubility of succinic acid, 93 KAHLENBERG, abnormal molecular weights LAAR VAN, electrocapillary phenomena, 287 Labile equilibrium, 42 Lactic acid, 462 LAMB, theory of electric endosmose, 294 LARVOR, diffusion, 374, 384; electro- in solution, 322, 332; chemical re- actions, 339; freezing point data, 330 KAHLENBERG and HALL, equivalent con- ductivity at 0°, 325 KAHLENBERG and SCHLUNDT, ionizing power of solvents, 363, 406 KELVIN, Lord (Sir Wm Thomson), capillary action, 100; dropping elec- trodes, 278; electromotive force and heat of reaction, 237; latent heat equation, 38; principle of classification, 110; similarity of laws for gases and solutions, 169; thermo-electricity, 272 KISTIAKOWSKY, electrolytic trausport numbers, 210 KOHLRAUSCH, F., alternating currents, 199; boundaries of solutions, 220; conductivity of solutions, 80, 199, 202; conductivity of water, 193; electrolysis of platinum chloride, 196; equivalent conductivity of solutions, 202; ionic capillary action, 283; migration of ions, 209; osmotic theory, 105, 109; thermo-electricity, 272 LASZOZYNSKI, conductivity of solutions in acetone, 331 LASZOZYNSKI and GORSKI, conductivity of solutions in pyridine, 331 Latent heat, and available energy, 29, 30; le Chatelier's theorem, 37, 38; and boiling point, 136; and freezing point, 142; osmotic pressure and heat of solution, 114; freezing point and vapour pressure, 125 Law of available or free energy, 28, 29 Law of diffusion, Fick's, 371 Law, dilution, 341, 344 Law of thermioneutrality, 352 Law, Henry's, 85 Law, the mass, 339 Law, Ohm's, 197, 204 Law, Volta's, 276 Laws, Faraday's, of electrolysis, 182 Laws of osmotic pressure, 103, 120, 166 Laws of thermodynamics, 1, 2 Laws of vapour pressure for mixed vapours, 71, 406 LE BLANC, decomposition point, 308; evolution of gases, 305; polarization, 301, 303, 304; single potential differ- ences, 387 Lead nitrate, 434 LE CHATILLIER, alloys, 59; latent heat, 38 LEHFELDT, electrolytic solution pressure, 299; electromotive force of concentration cell, 247 INDEX 483 LEHMANN, nature of amorphous bodies, 47 LENZ, electrolytic transport numbers, 210 LINCOLN, ionization in various solvents, 331 LINDER and PICTON, coagulative power of electrolytes, 395, 396, 399; nature of colloidal solution, 400 LIPPMANN, capillary electrometer, 282, 284 Liquid cells, 382 Liquid, free surface of a volatile, 98 Liquids, miscibility of, 88 Liquids, mixed, laws of vapour pressure MEYER, G., electromotive force of con- centration cell, 246; mercury dropping electrodes, 281 Meyer and HEIDENHAIN, absorptiometer (Fig. 33), 84 Microscopic study of alloys, 68, 71, 144 Migration of ions, 207, 383 Migration constants, 210, 212, 222, 408 Migration, elimination of, in concentra- tion cells, 250 Migration, ionic, theory of, 208, 383 Miscibility of liquids, 88 Mixture, definition, 48; solubility, 92 (Fig. 66), 403, 404 Mòbility, ionic, 214 to 226 Molecular bombardment, theory of, 167 Molecular complexes, 170 Molecular weight in solution, 140, 158, 316, 324 separation of, by fractionation, 74, 403; solubility of, in liquids, 88; under- cooled, 42, 392, 402 Liquidus curve, 66, 69 Lithium butyrate, 461; carbonate, 449 ; chlorate, 435; chloride, 414; formate, of permanganate, 98 MOND, RAMSAY and SHIELDS, Occlusion, 82, 83 Monobromacetic acid, 457 Monochloracetic acid, 455 Monovariant systems, 36 isobutyrate, 462; nitrate, 430; per- chlorate, 436; propionate, 459; sulphate, 440; trichloracetate, 458 LODGE, Sir OLIVER, measurement of ionic velocity, 216; potential differences, 270 LOEB and NERNST, electrolytic transport numbers, 210 LONGDEN, conductivity of metallic films, 231 LOOMIS, freezing points of solutions, 153, 321, 328 LYLE and Hosking, conductivity and fluidity of solutions, 406 255 MORSE and HORN, semipermeable mem- branes, 406 MOSER, theory of concentration cell, 242 NERNST, chemical cells, 255; concentra- tion cells, 248, 250, 382; diffusion, 281, 374, 376; electrolytic solution pressure, 274, 280, 385; equilibrium in solutions, 347; galvanic cells, 240; ionizing power of solvents, 361; liquid cells, 252, 382; metallic and electro- lytic conductivity, 184; reversible heat of mercury cells, 238; solubility in mixed liquids, 93; solubility of silver acetate, 93 NERNST and ABEGG, theory of freezing MACGREGOR, freezing point data, 330; NERNST and LOEB, electrolytic transport measurement of electrolytic conduc- tivity, 201; properties of dilute solutions, 333 Magnesium chloride, 417; nitrate, 433; sulphate, 440 Magnetic rotation of solutions, 171, 335 Manganese chloride, 420 MARIGNAC, thermal capacity of salt solutions, 335 Mass law of chemical action, 205, 339 MASSON, ORME, ionic velocities, 220; table, 221 Membranes, diffusion through, 388; perfect semipermeable, 102; semi- permeable, 95, 406 MENDELÉEFF, hydrates in solutions, 170 Mercury concentration cells, 243 Metachlorbenzoic acid, 468 Metals, electromotive series, 177, 296, 298, 299 Meta-nitrobenzoic acid, 467 Meta-oxybenzoic acid, 466 Methyl alcohol, ionization in, 331 Methylamine, 472 Methyl sulphuric acid, 445 numbers, 210 NEUMANN, single potential differences, 296, 387 NEVILLE, alloys forming mixed crystals, 69; freezing and melting point curves, 66 NEVILLE and HEYCOCK, see HEYCOCK and NEVILLE NICHOLSON and CARLISLE, early experi- ments on electrolysis, 177 Nickel chloride, 420; sulphate, 444 Nicol, additive properties of salt solutions, 334 Nitric acid, 426 484 SOLUTION AND ELECTROLYSIS Nitrobenzene, solutions in, freezing points of, 157 Non-electrolytes, freezing points, 153, 319; osmotic pressures, 104, 120; vapour pressures, 129 Non-variant systems, 35 Novak, ionization of water, 362 Noyes, electrolytic transport numbers, 228 NOYES, BREDIG and OSWALD, freezing points of concentrated solutions, 162 OBERBECK, polarization, 304 Occlusion, 82 OETTINGEN, Von, contact potentials, 300 Ohm's law in electrolytes, 197, 204 Organic cells and osmotic pressure, 118, 389 OSMOND, alloys, 59, 61 OSMOND and HOULLEVIGNE, electrolysis of salts of iron, 196 Osmotic pressure, 95, et seq., absolute value of, 103, 106, 109, 120, 166, 316 to 332; and boiling point, 122; cor- puscular, 274; and diffusion, 374 ; effect of concentration on, 117; effect of temperature on, 118; of electrolytes, 116, 120, 157, 159, 175, 316 to 332; experimental measurement, 95, 117, 406; and freezing point, 126, 152; and gaseous pressure, 103, 106, 109, 120, 166; and heat of solution, 112; of metallic solutions, 141, 160, 244; and organic cells, 118, 389; and surface tension, 97, 100, 390; theoretical laws of, 103, 120, 166, 316 to 332; and vapour pressure, 91, 98, 123, 127 Osmotics, theory of, 103 to 112, 120, 166, 175, 316 to 332 OSTWALD, additive properties of solutions, 333; acidity, measurement of, 336; colour of solutions, 334; conditions for production of current, 234; concentra- tion cells, 253; dilution law, 341, 344; dissociation of water, 360; heat of ionization, 357; ionic mobility, 229, 230; mass law, 340 ; solubility, 84, 85, 92; volume change of salt solutions, 334 OSTWALD, BREDIG and NoYES, concen. trated solutions, 162 OSTWALD and WALKER, measurement of vapour pressure, 133 Oxidation and reduction cells, 258 Oxygen, valency and ionizing power, 364 Padoa and BRUNI, solid solutions, 403 PALMAER, electrolytic solution pressure, PATTERSON and GUTAE, electro-chemical equivalent of silver, 185 PELLAT, electro-capillary action, 284 PELLAT and POTIER, electro-chemical equi- valent of silver, 185 Peltier effect, 238, 273 PERKIN, magnetic rotation in solutions, 335 PERRY and AYRTON, metallic potential differences, 268 PFEFFER, osmotic pressure, 95, 117, 120 Phase Rule, 32 et seq., 394, 402, 433 Phase, definition of, 33 Phases, equilibrium of, 33 Phenol and water, concentration curve (Fig. 18), 58 PICKERING, concentrated solutions, 163 ; densities of solutions, 170; freezing points, 153; hydrate theory of solution, 170, 171; permeability of membranes, 96, 172 Pile, Volta's, 176 PLANCK, diffusion, 281, 374, 384; electro- lytic dissociation, 317; galvanic cells, 240; liquid cells, 383 Platinum thermometry, 59, 147, 158 POINCARÉ, L., temperature coefficient of fused salt cells, 237 POISEUILLE, laws of, 293 Polarization, 181, 300, 303, 305; elimina- tion of 182, 198, 199; and contact electricity, 267 Polymerisation, gaseous, 161; at high concentrations, 161; in solutions, 364; i n solvents of benzene series, 159 Ponsor, convergence temperature, 154; freezing points of solutions, 161, 162, 328 Potassium acetate, 454; bichromate, 450; bromide, 422; butyrate, 460; carbonate, 448; chlorate, 434 ; chloride, 411; chromate, 450; cyanide, 451; fluoride, 426; formate, 452; hydrate, 468; iodide, 423 ; isobutyrate, 462; lactate, 463; nitrate, 427; oxalate, 464; perchlorate, 436; propionate, 458; sulphate, 437 ; trichloracetate, 457 Potassium chloride, ionization, 321, 327, 328 Potential, chemical, 25, 34; graphical method of representing (Figs. 7, 21 to 24), 26, 64 to 67 Potential differences, 267 et seq., 381; between electrolytes, 242 et seq., 381; in galvanic circuit (Figs. 58, 59), 275; single, 275, 294; tables of, 285, 296; summation of, 268, 276 Potential, thermodynamic, 23, 25, 64 POTIER and PELLAT, electro-chemical equivalent of silver, 185 281 PASCHEN, mercury dropping electrodes, 281 INDEX 485 POYNTING, depression of freezing point, 126 ; osmotic and gaseous pressure, 173; theory of osmotic pressure, 174 Pressure, osmotic, see osmotic pressure Pressure, effect on electromotive force of cells, 239; effect on metals, 41; effect on solubility, 83, 85, 90; vapour, see vapour pressure Pyridine, equivalent conductivity of solu. tions in, 331, 332 QUINCKE, coagulation, 399; electric en- dosmose, 292 Röntgen rays, charge on ions produced by, 189 ROOZEBOOM, allotropic solid (Fig. 12), 46, 47; alloys, 59; equilibrium of hydrates, 57; liquidus and solidus curves, 66; mixtures of iodides (Fig. 25), 69, 70; theory of solid solutions, 63, 68 ROOZEBOOM and HOITSEMA, occlusion, 82 Roscoe, distillation of nitric and hydro- chloric acids, 75 Roscoe and SCHORLEMMER, Text-book of Chemistry, 93 ROSENHAIN and EWING, structure of alloys (Fig. 44), 145 Rotation, magnetic, of solutions, 171, 335 ROTHMUND, electrocapillary action, 285 ROWLAND, mechanical equivalent of heat, 1 RÜCKER and REINOLD, conductivity of liquid films, 230 RUDOLPHI, dilution law, 343 RÜDORFF, freezing points of solutions, 153; solubility of mixtures, 92 Rule, the Phase, 32 et seq., 394, 402, 403 RUTHERFORD, velocity of gaseous ions, 189 RAMSAY, vapour pressure of amalgams, 141, 244 RAMSAY, MOND and SHIELDS, Occlusion, 82, 83 RANKINE, latent heat equation, 38 RAOULT, freezing points, 147, 153, 156, 161, 162, 328; polarization, 301; vapour pressures, 129, 132 RAOULT and RECOURA, vapour pressure of acetic acid, 129 RAYLEIGH, Lord, osmotic pressure, 106, 110; distillation, 403 RAYLEIGH, Lord, and Mrs HENRY SIDGWICK, electro-chemical equivalent of silver, 185 Rays, Röntgen, charge on ions produced by, 189 RECOURA and RAOULT, vapour pressure of acetic acid, 129 Reduction cells, 258 REED, C. J., accumulators, 263 Refining, copper, 310 Refractive index of solutions, 171, 335; used to determine boundary of solutions, SACK, conductivity of copper sulphate, 357 Salicylic acid, 466 Salt deposits, oceanic, 403 Salts, double, 92; electrolysis of, 195 Salts, isomorphous, 92 Salts and water, equilibrium of, 50 et seq., 403 Sand, electrolysis of mixed solutions, 399 Sandbanks, formation of, 401 Saturated solutions, 49 et seq., 78 et seq., 112, 143, 403 Saturation, time required for, 90 SCHEFFER, diffusion, 372, 380 SCHLUNDT, complex ions, 226; transport numbers, 332 SCHLUNDT and KAHLENBERG, ionizing power of solvents, 363, 406 SCHORLEMMER and Roscow, Text-book of Chemistry, 93 SCHULZE, coagulative power of electro- 221 REGNAULT, measurement of boiling point, 138 REICHER, transition point of sulphur, 46 REINDERS, equilibrium of solid and liquid phases, 68 REINOLD and RÖCKER, conductivity of liquid films, 230 Residual affinity, 173 Resistance of electrolytes, 197 et seq.; sec Conductivity Reversible engines, 12 Reversible processes, 8 RICHARDS, COLLINS and HEIMROD, electro. chemical equivalent of silver, 185 RIJN, VAN ALKEMADE, VAN, S curves, 26, 63 RITTER, action of accumulator, 181; electromotive series of metals, 177 ROBERTS-AUSTEN, Sir WILLIAM, gold-alu- minium alloy, 61 ROBERTS-AUSTEN and STANSFIELD, alloys, 59, 68 lytes, 395, 399 Sea-water, deposition of salts from, 405 Secondary action, 192, 194 Secondary cells, 263 Selenic acid, 446 Semi-permeable membranes, 95, 102, 168, 172, 406; perfect, 102 Series of metals, electromotive, 177, 268, 296, 298, 299 SETSCHENOFF, absorption coefficient, 87 SHAW, W. N., electric endosmose, 195, 294; electro-chemical equivalent of copper, 186 SHELDON and DOWNING, ionic velocity, 217 486 SOLUTION AND ELECTROLYSIS SHIELDS, hydrolysis, 366 STROUD and HENDERSON, measurement of SHIELDS, RAMSAY, and MOND, occlusion, electrolytic resistance, 199 82, 83 Structure of ice, alloys, etc., 143 SIDGWICK, Mrs HENRY, and Lord RAYLEIGH, Succinic acid, solubility of, 93 electro-chemical equivalent of silver, 185 Sulphur, allotropic forms (Fig. 12), 45 Silver, electro-chemical equivalent of, 184, Sulphur dioxide, solubility of, 86 185 Sulphuric acid, 437; densities of, 170; Silver acetate, solubility of, 93 heat of dilution, 266 Silver nitrate, 430; sulphate, 440 Sulphurous acid, 446 Single potential differences, 267 to 292, 294 Supersaturated solutions, properties of, 80 SKINNER, electrolysis of solutions in Supersaturation, 43, 44, 80 pyridine, 332 Surface energy or surface tension, 43, 44, SMALE, temperature coefficient of Groves' 80, 287; and potential difference, 283; gas cell, 237 osmotic pressure, 97, 100, 390 SMEE, galvanic cell, 182 Surfusion, 42, 45, 80, 155, 392 SMITH, S. W. J., electro-capillary action Systems, divariant, 36; monovariant, 36; 283 (Fig. 61), 288; mercury-dropping nonvariant, 35 ; one component, 39; electrodes, 281 two component, 49 Sodium acetate, 455; butyrate, 461; carbonate, 449; chloride, 413; ethyl Tables, accelerating powers, 338; avidities, sulphate, 446; formate, 452; hydrate, 337, 338; boiling points, 137, 331; 469; iodide, 424; isobutyrate, 462; conductivities of acids, 338; contact lactate, 463; methyl sulphate, 445; potentials, 285; cryohydric tempera- nitrate, 429; perchlorate, 436 ; pro tures, 143; decomposition voltage, 302, pionate, 459 ; selenate, 447 ; sulphate, 308; diffusion constants, 372, 373; 439; trichloracetate: 457. electio-chemical properties, 407; electro- Sodium sulphate, Rbase Rule diagram lytic solution pressure, 298; electro- (Fig. 15), 54; solubility curves (Figs. motive force of accumulators, 266 ; 16, 32), 55, 79; amalgam cells, 285, concentration cells, Solidifying point, see Freezing point 250, 252, liquid cells, 382, 383, mercury Solid solutions, 62 to 71, 83, 403 cells, 290; equivalent conductivities at Solids, allotropic, 45; amorphous, 47, 0°, 326, 327; equivalent weights and 392; hydrated, 53 electro-chemical equivalents, 187; freez- Solids, solubility in liquids, 89, 90 ing points, 149, 156, aqueous solutions Solidus curve, 66, 69 of alcohol, 163, cane sugar, 163, electra- Solubility, 27, 48, 55, 78; curves (Figs. lytes, 319, 320, 328, 330; non-aqueous 16 to 25, 32, 34, 35, 66), 55 to 70, 79, solutions in acetic acid, benzene, formic 89, 91, 404; of gases, 81, 84, 85, 87; acid, 156, nitrobenzene 157; heat of of liquids, 88, 92; of solids, 89, 90; ionization, 355, 358; heat of neutrali- tables of, 93, 94 zation, 356; heat of precipitation or Solute, definition of, 49; anhydrous, 50; solution, 117; hydrolytic dissociation, hydrated, 53 366; ionic friction coefficients, 379; Solution, 48, 77, 165; heat of, 112; . ionic mobilities, 211, 212, 215, 218, 221, table of heats of, 117; theories of, 165 222, 223; ionization constants, 242; Solvent, 49, 361, 406; specific inductive ionization of barium chloride, 330, capacity, 362, 406 potassium chloride, 328, of solutions in SORET, temperature, diffusion and osmotic alcohols, 331; migration constants or pressure, 376 transport numbers, 212, 222, 408 ; SPIERS, contact electricity, 271 potential differences, 96; . reversible SPRING, effect of pressure on metals, 41 heat of cells, 238; solubility, 93, STANSFIELD and ROBERTS-AUSTEN, alloys, 94; transport numbers or migration 59, 68 constants, 212, 222, 408; vapour pres- Stassfurt, salt deposits, 403 sures, 132, 133, 134, 137, 331 STEAD, alloys, 59, 68 TAMMANN, alloys, freezing point of, 160.; STELLE, complex ions, 226, 228; ionic amorphous solids, 47; crystalline varie- velocities, 221 ties of ice, 47; crystallization, 44; STEFAN, theory of diffusion, 372 osmotic pressure, 119, 120; pressure STREINTZ, accumulators, 264 and evolution of hydrogen, 386; vapour Strontium chloride, 415; hydrate, 471; pressures, 132, 134 nitrate, 431 Tartaric acid, 465 INDEX 487 TAYLOR, A. E., potential differences, 388 Telephone, used as indicator, 199 Temperature, absolute scale of, 15; co- efficient of cells, 237; coefficient of conductivity, 408; coefficient of fluidity, 409; convergence or equilibrium, 154 TERESCHIN, specific inductive capacity of solvents, 362 : Theory of chemical combination, 169; of direct molecular bombardment, 167; dissociation, hydrate, of solution, 170; of osmotics, 109 Theories of solution, 165 Thermal properties of electrolytes, 333, 335, 352 Thermodynamics, elements of, 1 to 31; laws of, 1, 2 Thermodynamic potential, 23, 25 Thermo-electricity, 272 Thermometry, platinum, 59, 147, 158 Thermo-neutrality, law of, 352 THOMSEN, affinity, 336; heat of dilution of sulphuric acid, 266; heat of neu- tralization, 352 THOMSON, JAMES, latent heat equation, 38 THOMSON, J. J., charge on ions, 189; corpuscles, 191; effect of pressure on cells, 240; electrolysis of gases, 187; ionizing power of solvents, 361 THOMSON, J. J., and MONCKMAN, filtration of potassium permanganate, 98 THOMSON, Sir WILLIAM, see KELVIN, Lord Three component systems, 76 TILDEN, solution and chemical action, 172 Tin, solutions in, lowering of freezing point, 160 TOWNSEND, J. S., charge on ions, 190 Transition cells, 258 Transition points 41, 55, 259 (Fig. 57), 261, 262 Transport numbers, 207, 210, 212, 408 TRAUBE, preparation of semi-permeable membranes, 95 Triangular diagram (Fig. 31), 76 Trichloracetic acid, 456 Triethylamine, 475 Trimethylamine, 475 TROOST and DEVILLE, Occlusion, 82 Troost and HAUTEFEUILLE, occlusion, 82 TROUTON and FITZGERALD, conductivity of electrolytes, 204 TUMA and EXNER, single potential differences, 278 VALSON, specific gravity of salt solutions, for, water and alcohol (Fig. 27), 74, 403, water and formic acid (Fig. 30), 75, water and isobutyl alcohol (Fig. 25), 72, water and methyl alcohol (Fig. 28), 74, water and propyl alcohol (Fig. 26), 74; measurement, 132; ethereal solu- tions, 132; and freezing points, 122; mixed solutions, 71, 403; and osmotic pressure, 98, 127; tables, 132, 133, 134, 137, 331 Vapour, supersaturated, 42 Velocity of the ions, 179, 188, 189, 208 to 230, 312, 376, 379; absolute, 214; measurement of, 216, 217; tables of, 215, 218, 221, 222, 223 Viscosity of solutions, 335, 409; ionic, 224, 356 VÖLLMER, conductivities in alcohol, 330, 333 Vapour pressure, abnormal, 129, 134; of amalgams, 141; calculation of, 130; of concentrated solutions, 126; curves 331 VOIGHTLÄNDER, diffusion, 372, 375 Volatile components, 88 Volatile liquid, free surface of, 98 VOLTA, contact electricity, 267; 'early experiments on electrolysis, 176 Volta's law, summation of potential differences, 268, 276 Volta's pile, 176, 178 Voltage decomposition, 181, 301, 308 to 311 Voltameter, silver, 184 Volume, change of, and osmotic pressure, 111; of solutions, 333, 336 WAAGE and GULDBERG, the mass law, · 205, 340 WAALS, VAN DER, equation of state for gases, 161 WADE, E. B. H., measurement of boiling points, 140 WALKER, J., vapour pressures, 132; hydrolysis, 365 WALKER and OSTWALD, measurement of vapour pressures, 133 WARBURG, mercury-dropping electrodes, 280; surface tension and electromotive force, 291 Water, conductivity of, 193, 203, 358, 362; decomposition of, in electrolysis, 178, 193, 306; ionization, 193, 203, 358, 362; preparation of pure, 193, 358; sea, freezing of, 143 WATTS, Dictionary of Chemistry, 93 WEBER, C. L., specific ionic velocity of copper ions, 216 WEBER, H., boundaries of solutions, 220 WEBER, H. F., diffusion, 371 Weights, equivalent and electro-chemical, 187; molecular, determination of, in solution, 140, 158; abnormal, 108, 159, 322, 332 488 SOLUTION AND ELECTROLYSIS WERNER, molecular weight of pyridine, 332 Weston cell, transition point, 261 WEYPRECHT, freezing of sea-water, 145 WHETHAM, W. C. Ď., coagulative power of electrolytes, 396; complex ions, 226; conductivity, 195, 201, 204, 325; hydrolysis, 367; ionization power of solvents, 362; mobile equilibrium in electrolytes, 225; preparation of plati. num electrodes, 200; specific ionic velocities, 217 WIEDEMANN, electrolytic conductivity, 198; endosmose, 292 supersaturation and condensation of water vapour, 43 WOELFER, boiling points of solutions in alcohol, 331 WOLLASTON, galvanism and electricity, 178 Wood, R. W., equivalent conductivity, 325 Work and energy, 3 WÜLLNER, vapour pressures, 132 Ścurves (Figs. 7, 21, 22, 23, 24), 26, 64, 67 ZELINSKY and KRAPIWIN, equivalent con- ductivities in alcohol, 330 ZENGELIS, electrodes of concentration. cells, 254 Zinc chloride, 418; sülphate, 441 WILDERMANN, freezing points, 153 WILLIAMSON, theory of chemical change, 206 WILSON, C. T. R., charge on ions, 189; CAMBRIDGE: PRINTED BY J. AND C. F. CLAY, AT THE UNIVERSITY PRESS. BOUND UNIVERSITY OF MICHIGAN . 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