LIBRARY OF THE UNIVERSITY OF CALIFORNIA. Class ELECTROCHEMISTRY I THEORETICAL ELECTROCHEMISTRY AND ITS PHYSICO-CHEMICAL FOUNDATIONS BY DR. HEINRICH DANNEEL Privatdozent of Physical Chemistry and Electrochemistry in the Royal Technical High School of Aachen TRANSLATED FROM THE SAMMLUNG GOSCHEN BY EDMUND S. MERRIAM, PH.D. Associate Professor of Chemistry in Marietta College, Ohio OF THE UNIVERSITY OF FIRST EDITION FIRST THOUSAND NEW YORK JOHN WILEY & SONS LONDON: CHAPMAN & HALL, LIMITED 1907 SRAL' Copyright, 1907 BY EDMUND S. MERRIAM 55 3 ROBERT DRUMMONI), PRINTER, NEW YORK INTRODUCTION. / . THE science of electrochemistry has come to have a far wider range of application than formerly. A com- paratively short time ago it comprised little more than methods of bringing about chemical reactions by means of electricity, and the utilization of chemical affinity for the production of an electric current. It has now become one of our most important aids in the investigation of some of the fundamental problems of general chemistry. The measurement of electromotive forces is the safest, and oftentimes the only, means of determining the chem- ical force with which reactions take place; conductivity measurements have given us an insight into the nature of solutions; electrochemistry has given rise to one of the most fruitful of the modern chemical theories, the theory of electrolytic dissociation. In practical as well as theoretical line's electrochemistry has been of immense value. Aside from the fact that many substances, such as the alkali metals, aluminium, magnesium, calcium carbide, etc., which can only be made with the greatest difficulty by purely chemical means, are easily manufactured with the help of elec- tricity, let us remember that electrochemistry gives us ' 1 6232:5 ia iv INTRODUCTION. a nearly perfect means of utilizing the enormous power of our waterfalls for chemical purposes, and enables us to store up and transport this energy which we receive from the sun. Finally electrochemistry gives us many compounds in a quicker, and therefore cheaper, way than the old purely chemical processes. Theoretical, or general chemistry, and electrochemistry are not separable; comprehension of one presupposes knowledge of the other. Therefore before we take up electrochemistry proper we will go over some of the physical and physico-chemical principles which form the basis of our present ideas in the field of electro- chemistry. We will then discuss the various theories of electrochemistry and give such illustrations as are nec- essary for their better comprehension. Experimental results and their applications, as well as methods of measurement, etc., will be contained in the second volume. The third will be devoted to the technical applications. TABLE OF CONTENTS. PAGE INTRODUCTION iii CHAPTER I. WORK, CURRENT, AND VOLTAGE. , i Kinds of Energy, and Their Relationships. Work Done by Natural Processes. Principles of Thermodynamics. Maximum Work and Free Energy; Determination of Same. Reversibility. Reaction Velocity and Chemical Force. Ohm's Law. Catalysis. Gas Laws, and the Performance of Work by the Expansion of Gases. Osmotic Pressure, and Osmotic Work. Semi-permeable Walls. Plant Cells, Quantitative Measurements. Work from Osmotic Pressure. Calculation of Chemical Work from Osmotic Pressure and van't Hoff's Equation. CHAPTER II. CHEMICAL EQUILIBRIUM, STATICS, AND KINETICS 32 Complete and Incomplete Reactions. Equilibrium. Law of Mass Action. Laws of Chemical Kinetics and Statics. Active Mass. Dissociation of Gases. CO and Os- Homogeneous and Heterogeneous Systems. Solution of Salts and Vapor Pressure. Change of Equilibrium with the Temperature. CO+O 2 . van't Hoff's Equation. CHAPTER III. THEORY OF ELECTROLYTIC DISSOCIATION 45 Freezing-point, Boiling-point, and Osmotic Pressure of Solu- tions. Dissociation. History of Electrochemistry, with the Dissociation Theory and its Basis. Faraday, Grotthus, Clausius, VI TABLE OF CONTENTS. PAGE Hittorf, van't Hoff, Arrhenius. Degree of Dissociation (Table) , Law of Mass Action. Applications of the Theory in Chemistry. Precipitation. Dissociation by Steps. Ions and the Dissocia- tion Constant of Water. Neutralization. Hydrolysis. Sapon- ification. Table of Dissociation of Water. Additive Properties. Physiological Applications. CHAPTER IV. CONDUCTIVITY 77 Ohm's Law. Specific Conductivity. Temperature Coeffi- cient. Metallic and Electrolytic Conductivity. Conductivity of Solutions. Charge on the Ions. Velocity of the Ions. Equiva- lent Conductivity. Conductivity of the Ions and Their Inde- pendent "Wandering." Water. Sulphuric Acid. Dissociating Power (Table). Strength of Acids and Bases. Distribution. Sugar Inversion. Decomposition of Ethereal Salts. Dissociation Constant and Ostwald's Dilution Law. Isohydric Solutions. Enforced Lowering of Dissociation and Solubility Product. Dis- sociation by Steps. Conductivity and Temperature. Measure- ment of the Transport Number. Absolute Ionic Velocities. Dielectric Constant. CHAPTER V. ELECTROMOTIVE FORCE AND THE GALVANIC CURRENT 115 Difference of Potential. Contact Electricity. Galvanism. Galvani, Volta, Daniell. Calculation of Electromotive Forces. Reversibility. Gibbs-Helmholtz Formula, and van't Hoff's Equation. Nernst's Formula. Fugacity. Solution Pressure. Electrolytic Potential. Daniell Cell. Gas Electrodes. Poten- tial of Alloys. Potential of Compounds. Electrodes of tHe Second Kind. Oxidation and Reduction Potential. Concen- tration Cells. Diffusion Cells. Applications of Nernst's For- mula. Solubility. Neutralization Cells. Secondary Elements, and the Accumulator. CHAPTER VI. POLARIZATION AND ELECTROLYSIS 151 Polarization. Polarization Capacity. Electrolysis of Water, Residual Current. Decomposition and Deposition Voltages. TABLE OF CONTENTS. Vll PAGB Overvoltage. Electrolysis of Mixtures. Faraday's Law. Table of Atomic and Equivalent Weights. Electrolysis. Secondary Reactions. CHAPTER VII. ELECTRON THEORY 169 LITERATURE 173 INDEX. *77 OF THE f UNIVERSITY ) OF sf^L'fORNVhs ELECTROCHEMISTRY, CHAPTER I. WORK, CURRENT, AND VOLTAGE. THE most important question ior scientific and technical progress is, How much work can a given chemical reaction perform ? This question is of equal or perhaps greater importance than the question as to what happens when two substances are brought together. If we know the work which a certain reaction can do, for instance the reaction CO + O = CO 2 , and the temperature co- efficient of its ability to do work, we know at once whether or not the reaction occurs and the conditions necessary for its occurrence. We see from the value of the energy, that this reaction, the oxidation of carbon monoxide, takes place at ordinary temperatures with great violence, in fact explosively; further, that the reaction is less complete the higher the temperature, and that at very high temperatures it even goes in the opposite direction; i.e., carbon monoxide not only will not burn, but carbon dioxide is decomposed into carbon monoxide and oxygen. We can distinguish six different kinds of energy: 2 ELECTROCHEMISTRY. i, mechanical energy; 2, volume energy; 3, chemical energy; 4, electrical energy; 5, heat energy, and 6, radiant energy. These different forms of energy are mutually transformable and if we have a suitable mechan- ism, the transformation is quantitative. Heat energy forms an exception to this rule ; the complete transforma- tion of heat into electrical or mechanical energy is theo- retically and practically impossible, although mechanical or electrical energy may be completely transformed into heat. The scientific unit of mechanical work is the erg ( = i dyne X i centimetre) and this is the unit of the so-called C.G.S. system. The practical unit is the kilogram-metre, which is the work necessary to raise 1000 grams through a height of 100 centimetres, or the work which a kilogram can do in falling a distance of i metre. A kilogram weight (not to be confused with the mass of a kilogram) is the force with which the mass of i kilogram ( = i litre of water at 4 C.) is attracted by the earth. A falling body attains as a result of the earth's attraction an acceleration of 980.6 cms. per second, so that a gram weight represents a force of 980.6 dynes. The unit of force = i dyne is that force which, acting on the mass of i gram, gives it an acceleration of i cm. per second. Acceleration is the increase of velocity per second. distance Velocity = ~. . A kilogram-metre is 100000 times as great as a gram-centimetre, i.e., = 98 060 ooo ergs. The unit of volume energy is the litre-atmosphere. When any body, for instance a gas, which always exerts a pressure on the walls of the vessel enclosing it (cf. p. 16) expands, the weight of the atmosphere above it is dis- WORK, CURRENT, AND VOLTAGE. 3 placed by an amount corresponding to the number of litres of expansion of the gas. The expanding gas therefore does work against the pressure of the atmosphere. (In general, every increase of volume taking place against a pressure, or every contraction brought about by a pres- sure, is accompanied by a gain or loss of work.) In the barometer the pressure of the atmosphere forces a column of mercury i sq. cm. in cross-section up to a height of 76 cms. Such a column of mercury weighs 1.0333 kilograms, since the specific gravity of mercury is 13.596. The pressure of one atmosphere therefore is 1.0333 kg. per sq. cm., or 103.33 kg. per sq. decimetre. If then 103.33 kilograms are raised i decimetre, i.e., if a body expands by i litre, the work done is the same as when i gram is raised i 033 ooo cms. i gr. cm. = 980.6 ergs; the value of i litre atmosphere is therefore 980.6X1033000 = i 013 200000 ergs. The ordinary unit of electric work is the watt-second. Watt is the "power" of an electric current of i ampere under the pressure of i volt. By power is meant the work done in unit time, i.e.,= work/time. An ampere is the amount of electricity measured in coulombs flowing through a conductor in unit time. A coulomb is the unit quantity of electricity. A coulomb in passing through a silver voltameter precipitates 0.001118 gr. of silver; a coulomb is the electric charge (cf. p. 53) on 0.01036 milligram equivalents of every ion and will precipitate this quantity of any ion on an electrode. A current of i ampere flows through a conductor when the quantity of electricity passing is i coulomb per second. An ampere is the tenth part of the unit of current in the C.G.S. system. 4 ELECTROCHEMISTRY. Electric pressure or difference of potential is ordinarily measured in volts. A volt is that pressure which suffices to send a current of i ampere through a resistance of i ohm (legal definition). One volt is equal to io 8 C.G.S. units. A Daniell cell has an electromotive force or difference of potential of i.i volts; a storage battery has 2.0 volts. A watt is i voltXi ampere (a power), and a watt-second is the work which a current of i ampere is able to do when flowing for i second through a resistance of i ohm. A watt-second is therefore io 8 Xio~ 1 = io 7 ergs. Heat energy is measured in calories. A calorie is the quantity of heat which is necessary to raise the temperature of i gram of water from 15 C. to 16 C. Since the specific heat of water is not independent of the tempera- ture, the quantity of heat necessary to raise the tem- perature of i gr. of water i C. is different at different temperatures.* The mechanical equivalent of heat has been determined by many investigators; we will use the value adopted by Nernst,f 42 600. The meaning of this number is as follows : If i gram falls 42 600 centimetres, or if i kg. falls 42.6 cms. and the total kinetic energy (vis viva) of the falling weight is converted by impact into heat, this quantity of heat is just sufficient to raise the temperature of i gram of water from 15 C. to 16 C., i.e., one calorie * Beside the above-defined calorie, which is the one most generally in use, there are the "mean calorie " = T ^ 7 the quantity of heat neces- sary to warm i gr. of water from o to 100, and the "zero-point calorie," the quantity of heat necessary to warm i gr. of water from o to i. The "kilogram calorie" is 1000 times the 15 calorie. f Theoretische Chemie, p. 12. Enke, Stuttgart. WORK, CURRENT, AND VOLTAGE. 5 is evolved. The energy of the i gram weight is then 42 600X980. 6 = 41 777 ooo ergs (980.6 is the acceleration due to gravity). There is no fixed unit for chemical energy, it is generally measured in volt coulombs. As yet there is also no common unit for radiant energy. With the help of the following table * it is easy to express a given quantity of work in any of the different units. Absolute Units, Ergs Electrical Units, Watt-seconds Heat- units, Gr. Calories erg watt-second = gr. calorie litre-atmosphere = kg.-metre horse-power-second = Gas constant R I I0 7 4.187X10' i.oi3X io 9 9.806X10' 7- 355Xio 9 8. 3155X10' io- 7 4.189 0.01013 9.806 735-5 8.3155 2.387XIO- 8 0.2387 i 24.19 2.341 I75-58 1.985- Litre- atmospheres Kilogram- metres Horse-power- seconds i erg i- watt-second i gr. calorie = i litre-atmosphere = i kg.-metre i horse-power-second = Gas constant R 9.86QXIO- 10 o . 009869 0.041342 I 0.09678 7-2585 0.0821 I.OI98X-IO- 8 o. 10198 0.4272 IO -333 i 75.00 0.848 i. 3 597Xio- 10 0.0013597 0.005696 0.13778 0.01333 0.011308 From the foregoing it is clear that an expression de- noting work is always made up of two factors. A summary of these will perhaps be of use in making the relationship clearer. * Table of H. Steinwehr, recalculated after Nernst, Zeitschr. f. Elec- trochemie, io, 629, 1904. ELECTROCHEM1S TRY. Mechanical work: Velocity Acceleration Force Work Power Work Weight Work of expansion Pressure Electrical work Current strength Distance Time * Increase of velocity Time = Acceleration X mass. = Force X distance. Work " Time' = Mass X length of fall X accelera- tion due to gravity. = Mass X acceleration due to gravity. = Increase of volume X pressure. Weight Surface * = Voltage X coulombs. Coulombs Electrical power Chemical work Time = Voltage X current. = Chemical potential X quantity of substance. The conceptions of chemical and electric potential will occur repeatedly and will be explained in their proper place. Work Done by Natural Processes. Fundamental Law. A II processes in Nature whtch take place of themselves can famish work, and only such proc- esses occur spontaneously, which, ivith the aid of suitable apparatus, can be made to perform work. Among such processes are the union of electric charges; movements WORK, CURRENT, AND VOLTAGE. ^ of liquid from a higher to a lower level; all movements of masses in general which occur spontaneously; further, chemical reactions; equalization of different tempera- tures, etc. The most important question for us is, how much work we can obtain from a given process under the most favorable conditions, the so-called " maximum work." In order to appreciate the meaning of this term we must review two laws concerning the relation between heat and work, the two principles of thermodynamics. First Law, Principle of the Conservation of Energy. Just as no substance can be created from nothing nor be absolutely destroyed (law of the conservation of matter), so energy can neither be created from nothing nor anni- hilated. "Perpetual motion," i.e., a machine which continually does work without having energy given to it in any way, is scientifically an absurdity. Many inventors who have had such an end in view have tried to achieve the impossible. A few illustrations will make the meaning of this law clear. We lift a weight of 10 kg. vertically from the floor through a distance of i metre. In so doing our muscles do 10 kg. metres of work. The weight has now a capacity for doing work, or potential energy, of 10 kg. metres, if we disregard the energy it may have had to start with. If we let the weight fall again it attains as a result of the earth's attraction a certain "vis viva" (the potential energy changes to kinetic energy) and when it strikes the floor this energy is converted into heat. If we measure the heat we find it to be 23.5 calories, and this, as we see from the table on p. 5, is just equal to the original 8 ELECTROCHEMISTRY. 10 kg. metres we spent in raising the weight. If we denote by U the change in energy resulting from the fall (in this case 10 kg. metres) and by W the heat generated by the impact of the weight on the floor, then U = W. We now tie to the falling weight a cord, lead it over a pulley, and fasten a 9 kg. weight to the other end, so that this last is raised a metre by the fall of the first; let the work necessary to raise this weight be A (in this case 9 kg. metres). We will now find that the heat developed by the impact of the first weight on the floor is 2.35 calories; if we denote this by W, then U=A+W. If we supply extra work to the process for instance, by accelerating either the 10 or 9 kg. weight by a blow this work A' must also appear in the heat developed, W=U-A+A'. In every case the change in the total energy plus the heat expended and work expended is equal to the work obtained plus the heat obtained. If we let a chemical reaction take place in such a way that no work is done, we obtain the change in total energy as heat, which in this case we call the "heat of reaction" (Warmetonung). In the combustion of coal we obtain with the help of a steam-boiler only about 20% of the heat of reaction as mechanical energy; the other 80% goes over into heat which is lost up the chimney and by radiation. If we obtain more work than that WORK, CURRENT, AND VOLTAGE. 9 which corresponds to the heat of reaction (which is possible in some cases) the extra heat must be supplied by the surroundings, i.e., the reaction mixture cools itself off. Second Law, Principle of the Transformation of En- ergy. We wish, of course, to know how much work we can get out of a given process under the most favorable conditions, i.e., what the maximum work is. Thomson, and after him Berthelot, proposed the law (principe du travail maximum) that the maximum work may be calculated from the heat of reaction, and that the two are equal. Helmholtz,* however, later proved that this is not the case. The. basis of Helmholtz's theory is the well-known fact that heat can do no work when it is at rest. Just as water can do no work when it is at rest and only does so when it falls from a higher to a lower level, and just as electricity can only perform work as it falls from a higher to a lower potential, so heat will only do work when it falls from a higher to a lower temperature/ If heat is to be converted into work we must have differences of temperature. To cite an illustration of Nernst's, we cannot utilize the enormous reservoir of heat in the sea to turn the propellers of the ocean steamers. One might conceive of the ships' engines taking heat from the ocean water, using it in the performance of work, i.e., in propelling the ship, and then returning it to the water in the form of friction. Experience shows that such a machine, which would not contradict the law of the * Thomson has accepted the views of Helmholtz, but Berthelot and many of the French scientists still cling to the principe du travail maxi- mum although it has been clearly shown to be incorrect. 10 ELECTROCHEMISTRY. conservation of energy, is unfortunately an impossibility; such a machine, however, has received the name of "perpetual motion of the second kind." By a simple thermodynamic cycle it can be shown that when an amount of heat Q at the absolute tempera- ture * T falls to the temperature T-dT* in the most favorable case the quantity of work dA to be obtained is By combining this equation with the equation U=A+W (cf . p. 8) we have ~-^p is, however, nothing else than the temperature co- efficient of the capacity for doing work, i.e., it is the amount by which A changes when the temperature is changed one degree. If we represent the temperature coefficient by a, then A-aT=U. The formula A U=T-^ is the exact expression in one equation of both laws of thermodynamics. * The gas laws make it probable that there can be no temperature lower than 273 C. 273 is therefore called the absolute zero of temperature. Temperatures counted from the absolute zero are de- noted by T; if / is the ordinary Celsius temperature, counted from the freezing-point of water, T=* 273 -H. f An infinitely small value, which is not zero, but approaches zero, is denoted by a prefixed d. dQ is an infinitely small quantity of heat, dU an infinitely small change of total energy, etc. WORK, CURRENT, AND VOLTAGE. II From this equation we can derive several very important results: i. The change in total energy U, which in chemical reactions is simply the heat of reaction, is only equal to the work obtainable, or, as it is often called, the "free energy," when the free energy is independent of the temperature, i.e., when a = o. 2. At the absolute zero ( 273 C.) A is always=Z7. 3. If a is positive, i.e., if the free energy increases when the temperature is raised, we may obtain more work than corresponds to the heat of the reaction. The excess must be supplied by the surroundings, and the reaction mixture cools itself off. This happens, of course, only when we do extract the maximum work. 4. If a is negative, excess heat results, and the system becomes warm, even when the maximum work is obtained. With the exception of No. 2, all these cases are realized. The Daniell cell furnishes a good illustration of these points. This affords electric energy as the result of the following equation: Zn + CuSO 4 = ZnSO 4 + Cu, i.e., copper is precipitated from a solution of CuSC>4 by zinc. A Daniell cell in using up 32.7 grs. of zinc gives at o C. electric energy equivalent to 25 263 calories; electrical measurements further show that the free energy increases 0.786 calorie per degree rise of temperature. /. aT = 0.786X273 = 213 calories. The heat of reaction is therefore / = 25 263-213 = 25 050 cal. Calorimetric measurements gave 25 055 calories, in excellent agreement with the calculated value. 12 ELECTROCHEMISTRY. The questions now arise, How do we determine the maximum work? or, How can we compel a reaction to do its best? To do this we must contrive an arrangement which converts chemical into mechanical or electrical energy, and which works so perfectly that there are no losses due to secondary causes, such as leakage, friction, radiation, etc. Further, the reaction must take place in such a manner that we may stop it at any time, and by putting back exactly the same amount of work we have already obtained from it, bring the system to its original condition. Such a process is called a "reversible" one. Absolute reversibility would be possible experimentally only if we ourselves were perfect beings; since, unfortunately, even electrochemists can make no such claim, we must content ourselves with approaching the above requirements of reversibility as closely as possible. An arrangement which fulfils these requirements very perfectly is the galvanic cell (battery). In it reactions often take place with practically perfect reversibility, and for this reason the scientific chemist should realize the importance of electrochemistry. The work which a reaction can do is the point which has a special interest for us. One of the chief aims of electrochemistry is to obtain work from chemical reactions, such, for instance, as the combustion of coal; the reaction between zinc and copper sulphate or between lead, lead peroxide, and sulphuric acid. Another aim is the com- pulsion of chemical reactions by means of electrical work, as in the manufacture of aluminium from its oxide, or the preparation of bleaching solutions from common salt. In the first case we are satisfied when we know the maximum work which the given reaction can do; in the WORK, CURRENT, AND YOLTAGE. 13 second we must learn the maximum work of the reverse reaction. If we have a solution in which two reactions may take place, for instance a solution of FeSC>4 and CuSC>4, and wish to obtain the copper electrolytically, we must know which of the two reactions takes place easier; i.e., how much work is sufficient to precipitate the copper on the cathode, but does not suffice to precipitate the iron. In other words, we must know the work necessary for each reaction. If we know the maximum work of a reaction we know also, as already stated, whether it will take place of itself or not. If we know, for instance, that the displacement of copper by zinc according to the equation Zn + CuSC>4 = Cu + ZnSO4 can perform work, we know from this fact that the reaction will go on of its own accord, and that therefore the reverse reaction which requires the ex- penditure of work will not occur spontaneously; that is, zinc cannot be precipitated by copper from a zinc salt solution. Another example is the following: When we dissolve hydrogen peroxide in water we observe no reaction; decomposition according to the equation H 2 O 2 =H 2 O + O apparently does not take place of itself. It would there- fore appear probable that the reverse reaction would occur spontaneously. However, if we pass oxygen gas into water, H 2 O2 is not formed in measurable amounts. Accordingly the only way of deciding which of the two reactions, decomposition or formation, is spontaneous, is to measure the work involved. It is found that work is necessary for the formation of H 2 O 2 ; work can be done by its decomposition and therefore this reaction goes on of 14 ELECTROCHEMISTRY. itself. A similar case is found in detonating gas. Hydro- gen and oxygen may be kept together many years without the visible formation of water. In this case, also, the only means of determining which reaction is spontaneous is by measuring the work. The reason why we do not observe either a decomposition of the H 2 O 2 or a formation of H 2 O lies in the slowness of the reaction. Reaction Velocity and Chemical Force. At the end of the last paragraph mention was made of the slowness of a reaction, and we must now see what bearing the reaction velocity has on the work of a process. In utilizing a chemical reaction for the production of work the first point to be considered is the speed with which the reaction proceeds. A reaction which can furnish a million kg. -metres can be of no use to us if it requires a milliard years before it is completed, nor, on the other hand, if it only requires a fraction of a second, for our machines are too imperfect to take care of such a power, and the greater part would be lost in the form of heat. The reaction 2H 2 +O 2 = 2H 2 O at ordinary temperatures goes too slow, and at high temperatures, too fast (explosively). An electrochemical arrangement, however, enables us to regulate the velocity within certain limits, and so quantitatively obtain the work of the re- action. A law similar to Ohm's law regulates the velocity of chemical reactions. impelling force Reaction velocity =. -. , . . chemical resistance We can always calculate the impelling force from the WORK, CURRENT, AND VOLTAGE. 15 work which the given reaction can do, but we know very little about chemical resistance. In most reactions, prob- ably in all, the chemical resistance increases as the tem- perature decreases, and would appear to become infinite at the absolute zero, where all chemical action would cease. In many cases we can reduce the chemical resistance; this may be done, for example, in the case of H 2 O formation by constructing a gas cell. The chemical resistance is also lowered by raising the temperature, or by bringing finely divided platinum into the gas mixture. The platinum does not take a visible part in the reaction, for it is the same after the reaction as before. But by the simple presence of platinum we can increase the reaction velocity at ordinary temperatures till explosion occurs. Such substances which diminish chemical re- sistance are known as catalytic agents or catalyzers. Their presence changes neither the impelling force nor the nature of the reaction. In technical work there are many reactions which, were it not for suitable catalyzers, would go so slowly as to be commercially worthless. We need only mention the " contact process" for sulphuric acid, in which a number of catalyzers have found appli- cation in bringing about the union of sulphur dioxide and oxygen.* * The reader will find a collection of the most important technical reactions in which catalysis plays an important part in an address of Bodlander's, delivered before the Berlin International Chemical Congress, which has appeared with other collections in "Der deutsche Verlag." Compare also Ostwald's article on Catalysis in Science and the Arts, in the Zeitschrift fur Electrochemie, 7, 995, 1901. 16 ELECTROCHEMISTRY. The Gas Laws. Work Obtainable from the Expansion of Gases. We will later find that the method of calculating the work obtainable from the expansion of a gas is also applicable in calculating the work done when substances in a solution change their concentration. We will there- fore briefly go over the gas laws and put them in a form from which the work obtainable is easily calculated. 1. Boyle's Law. At constant temperature, when the volume of a gas is changed, the pressure varies inversely as the volume; that is, p-v = B, constant. If we bring into the volume of i litre successively one, two, three, . . . grams of oxygen, the pressure increases in the proportion one, two, three, . . . ; i.e., each gram of oxygen presses on the walls of the containing vessel as though it were present alone. 2. Gay-Lussac's Law. If the pressure on a gas is kept constant and the temperature raised, the gas expands per degree centigrade by an amount which is 0.003663 times ( = -2T-g-) the volume it occupies at o C. If the volume at o C. is v , its volume (v) at the temperature r C. is V = v (i + 0.003663 T). On the other hand, if the volume is kept constant during the heating, the pressure increases. Boyle's law holds for any given temperature, and it therefore follows by combining these two equations that ^ = MI +0.0036637). WORK, CURRENT AND VOLTAGE. i? If both pressure and volume vary, we obtain for the product at the temperature T C. p-V = pQ-V (l +0.0036631-). This equation holds on the supposition that a gas exerts no pressure at the absolute zero, and affords a means of calculating this temperature. The value thus found is 273 C. If T represents the absolute temperature ( = 273 + T) (cf. p. 10) we obtain the equation ^ pv = L -- T. 273 3. From section i it is seen that each gram of a gas exerts a pressure on the walls of the containing vessel as though it were present alone. This applies also to a mixture of two or more different gases, and the pressure of a gas mixture is therefore equal to the sum of the pressure which each gas would exert by itself. This single pressure of each gas which goes to make up the. total is called the partial pressure of the gas in question. ILLUSTRATION: The pressure of the atmosphere at sea-level under normal conditions is 760 mm. of mercury, and this is made up of the partial pressures due to nitro- gen, oxygen, carbon dioxide, water-vapor, and the rare gases. Air contains about 79.2% nitrogen, 20.8% oxygen, and about 0.04% carbon dioxide. The partial pressure of nitrogen is therefore 760 - mm. of mercury, 20.8 and that of oxygen 760- - mm. 4. When gases combine to form a chemical compound the volumes which react are either equal or stand in a simple numerical proportion to one another, and the i8 ELECTROCHEMISTRY. same is true of the resulting product if it remains in the gaseous form. These facts form the basis of Avogadro's Hypothesis (1811), which states that under the same conditions of temperature and pressure the unit volume of alt gases contains the same number of molecules* ILLUSTRATION: 2 grs. of hydrogen, 32 grs. oxygen, 44 grs. carbon dioxide, 28 grs. nitrogen always occupy the same volume when the temperature and pressure of each has the same value. At atmospheric pressure and o C. this volume is 22.42 litres. Or if a mol of any gas at o C. is confined in the volume of i litre, it exerts a pressure of 22.42 atmospheres on the containing walls. The equation of section 2, therefore, when applied to i mol, becomes litre atmospheres. 273 273 This factor 0.0821 which is the same for all gases is a very important one. It is called the "gas constant" and is denoted by the letter R. If we consider n mols instead of one the equation is of course pv = nRT. ILLUSTRATION: The average volume of i mol of the different gases at o C. and i atmosphere pressure has been found to be 22.42 litres. Atmospheric nitrogen gave a somewhat different value, 22.34. This led to an investigation into the purity of atmospheric nitrogen and resulted in the discovery of argon and the other rare gases. * A mol or gram-molecule is that number of grams of a substance which is equal to the molecular weight, i mol of Zn=65-4 grs. Zn. i mol (^2=35.45 + 35.45 grs. = 70.9 grs. chlorine, i mol CuSO 4 = 63.6 + 32X64 grs. = 158.6 grs. CuSO 4 , etc, WORK, CURRENT, AND VOLTAGE. 19 To calculate the work obtainable from an expanding gas one must remember that work = pressure X change in volume, provided during the process the pressure does not change. If the volume is kept constant and the pressure changes, the work is = volume X pressure change. If we let a gas under constant pressure and tempera- ture expand from the volume Vi to volume v 2 the work obtained is A=p(v 2 -vi). Or if a quantity of gas at constant temperature and constant volume has its pressure raised from pi to p 2 then A=v(p 2 -p l ). ILLUSTRATION i. Let us consider a cylinder v;hose cross-section is one square decimetre and whose height is about 3 metres, at the bottom of which is i mpl = i8 grs. of water. Suppose the water is converted into vapor at o and under the atmospheric pressure. Neglecting the volume of the liquid water (0.018 litre) and remembering that at o and atmospheric pressure i mol of every gas occupies the volume of 22.42 litres, we find that the weight of the atmosphere above the cylinder is raised through a distance of 22.42 decimetres. Since the work which is necessary to overcome the pressure of i atmosphere through the volume of i litre is r litre-atmosphere, we find the work on evaporation A =22. 42 litre-atmospheres. If n mols are evaporated the work is of course n- 22.42 litre-atm. = n- 231. 60 kg.-metres, or 542.34 calories (cf. Table 5). 20 ELECTROCHEMISTRY. ILLUSTRATION 2. If we decompose by electrolysis i gr. -molecule of water, we obtain 2 grs. of hydrogen and 1 6 grs. of oxygen = i mol hydrogen + J mol oxygen; these occupy under standard conditions 33.63 litres, That is, in order to liberate the gas into the atmosphere we have done 33.63 litre- atmospheres of work, aside from the chemical work necessary to decompose the water. This consideration frequently enters into the calculation of the work necessary in such reactions where a gas is evolved or absorbed. If we let the hydrogen and oxygen again combine, the volume decreases by 33.43 litres; i.e., the atmosphere in this case does 33.43 litre -atmospheres of work, which we can obtain as electrical work by using a gas-battery. In general it \i\\\ not be true that the volume alone or the pressure alone varies. If we have a quantity of gas and increase its volume at a constant temperature, the pressure falls off at the same time according to the equa- tion pv = constant. To calculate the work we need the help of differential calculus, and find the following result: When a mol of a gas expands from vi to ^ 2 the work obtainable is * A=RTln-. Vi Osmotic Pressure and Osmotic Work. It has been shown by van't Hoff that the gas laws mentioned above also apply to substances in dilute solu- tions. * Ln is the symbol of the "natural logarithm." To change it to the Briggs or common logarithm it must be multiplied by 0.4343. The derivation of the above equation is here given for the benefit of those WORK, CURRENT, AND VOLTAGE. 21 The pressure of a gas is to be looked upon as its endeavor to expand. Gases expand as far as they can, i.e., they distribute themselves through the whole of the volume at their disposal if there is a medium present through which they can pass. Such a medium is the vacuum or any space filled with other gases. When their expansion is hindered by a medium through which they cannot pass, such as an air-tight wall, they exert on this wall a pressure. All other substances behave in this respect similar to gases. All have the tendency to distribute themselves as much as possible, but can only do so in a suitable medium. Water is a suitable medium for cane-sugar. Sugar tries to distribute itself in this medium to the greatest possible degree, i.e., it dissolves in water. If a layer of pure water is carefully put over a solution of who have studied calculus. When the gas expands from v to the vol- ume v + dv, the pressure decreases from p to p dp; the work obtained, dA therefore lies between pdv and (p dp)dv. In comparison with p, dp is infinitely small and can therefore be neglected; i.e., dA = pdv. If we insert the value of p which is obtainable from p-v=RT in this equation we obtain v This, integrated between the values i)\ and v 2 , gives A = RTln^. Vi Since v z :v\= p\: p 2 , the equation can also be written P2 If n mols of gas are used, the equation is 2 2 ELECTROCHEMIS7R Y. sugar, the sugar has an opportunity for further expansion, and it accordingly diffuses upwards against the force of gravity till the concentration at all points is the same. If the two layers are separated by a wall which is permeable to water but not to the sugar molecules, the process is reversed, the sugar no longer diffuses upwards, but draws water through the wall to itself. If the vessel containing the solution is closed on all sides, very little water can enter, since a hydrostatic pressure is soon developed which prevents the further entrance of water. This tendency to expand has therefore the nature of a pressure, and is called the osmotic pressure of the sugar solution. The relation between osmotic and gas pres- sure is clear when we remember that the gas corresponds to the dissolved sugar and the solvent (water) to the vacuum. If we avoid the development of hydrostatic pressure, by allowing the containing vessel to give way, the solution actually draws in a great quantity of water. To test this conclusion experimentally we require a substance which is permeable to water but impermeable to the dissolved sugar molecules. A diaphragm built of such a substance is called "semi-permeable." We will first go over the history of our knowledge con- cerning osmotic pressure and at the same time become acquainted with many terms and laws which will be met later on. It is well known that plant cells which have become dry and need water can take up water when they are put in contact with it, without losing any of the cell contents. The walls of plant cells are therefore semi- permeable membranes. The first investigations on the WORK, CURRENT, AND VOLTAGE. 23 osmotic pressure of the solution in plant cells were made 'by physiologists. The cells were placed in salt solutions, and it was found that salt solutions of a particular con- centration were in equilibrium with the cells, i.e., the cells neither expanded nor contracted. If they were put in a more dilute solution, they took up water and expanded; put in a more concentrated solution they gave off water and became smaller. Solutions which were in equilibrium with the cells were called " iso tonic " or " isosmotic " solutions. It was discovered that solutions of similar salts were isotonic when they had the same molecular concentration; * for instance, normal solution of KNO 3 , NaNOs, KC1, NaCl are approximately isotonic. Cell Wall ,_ Protoplasmic Sac Nucleus As Fig. i shows, the cells are surrounded by a cell wall which is permeable to solutions as well as water ; within this is the protoplasmic sac which is permeable to water but not to the salts dissolved in the cell solution. Th.e cell solution is called the "protoplast," and the proc- ess of expansion or contraction is called "plasmolysis.'' A fact was further discovered which was later explained by the theory of electrolytic dissociation, namely, that * Measured in mols per litre. Cf. remark on p. 18. ELECTROCHEMIS TR Y. dilute solutions of the above-mentioned inorganic salts have an osmotic pressure which is practically twice as great as solutions containing an amount of organic sub- stances urea, sugar, etc. equal in molecular concentra- tion to that of the inorganic salts. It should be mentioned here that the osmotic pressures were later measured in atmospheres and that the ordinary plant cells which contain dissolved glucose, malates of calcium and potas- sium, sodium chloride, etc., have an osmotic pressure of about 4 to 5 atmospheres. Certain cells used for storage purposes in plants such as the sugar-beet have a pressure of 15 to 20 atmospheres. In young plants the pressure is still higher. The cells of bacteria have an especially high osmotic pressure, . which fact may perhaps explain their great physiological action. Plant cells could only be used in making comparative measure- ments; in order to measure the pressure directly in atmospheres, it was necessary to construct an artificial protoplasmic sac, i.e., a semi-perrneable membrane. A membrane composed of copper ferrocyanide is impermeable to sugar and most salts, but readily permeable to H 2 O. Traube made such a membrane -by FIG. 2. putting a solution of K 4 Fe(CN),} in a carefully cleaned porous cell and placing the cell in a dilute solution of CuSO4- The two substances diffuse toward each other in the cell wall WORK, CURRENT, AND VOLTAGE 25 and form, on meeting, a precipitate of Cu2Fe(CN)6, thus making a durable semi-permeable wall. Using this cell, measurements were made as follows (cf . Fig. 2). A sugar solution was put in the cell; the open end was closed by a rubber cork, through which passed a long glass tube, and the whole was placed in pure w r ater. The osmotic pressure of the sugar in solution causes water to be drawn in through the walls of the cell till the hydro- static pressure of the column of water in the upright tube is as great as this drawing force, i.e., as great as the osmotic pressure of the solution. The hydrostatic pressure is easily calculated from the specific gravity of the solution and the height of the water column in the tube. An experiment made by Ramsay at the suggestion of Arrhenius affords a striking comparison of osmotic pressure with the action of gases. He made an air-tight cell the bottom of which consisted of a thin sheet of Pt, attached a manometer, filled the cell with nitrogen, and placed the whole in an atmosphere of hydrogen. Plati- num is impermeable to nitrogen but permeable to hydro- gen, consequently hydrogen is drawn into the cell just as H 2 O is drawn through the copper ferrocyanide membrane, and the increase of pressure can be read off on the manometer. The first quantitative osmotic measurements were made by the physiologist Pfeffer. He measured the osmotic pressure of sugar solutions of various concentrations and obtained the following table. Concentration of sugar in grams per 100 c.c i 2 2.74 4 6 Pressure in atmospheres. ... 0.704 i-34 i-97 2 -7S 4.06 Pressure per gram of sugar . 0.704 0.67 0.72 0.69 0.68 26 ELECTROCHEMISTR Y. From these figures it is clear that the pressure is pro- portional to the percentage of sugar in the solution, or inversely proportional to the volume which contains a Constant gram of sugar in solution p= ; p v = Constant, which is the expression of Boyle's law. Pfeffer found further that the osmotic pressure rises with a rise in temperature, as the following table shows. t Pressure Difference Observed Calculated 6.8 o 664 atmosphere o . 665 atmosphere + 001 13-7 o 691 0.681 o OIO 14.2 o 671 0.682 + on 15-5 684 0.686 + 002 22. O o 721 o. 701 o 020 32.0 o 716 0.725 + 009 36.0 o 746 -735 o Oil The calculated pressures in the third column were obtained from the value for a i% solution, according to the equation ^=0.649(1+0.003671:) atm.; for an n% solution, p = n- 0.649(1 +0.003677). At 13.7 C. the pressure of a 4% solution was 2.74 atmospheres, while the formula gives 2.73. If we calculate from this the value of the osmotic pressure for i gram- molecule of sugar = 342 grs. in i litre we obtain the equation (Gay-Lussac's law), WORK, CURRENT, 4ND VOLTAGE. 27 where p is the osmotic pressure in atmospheres, v the volume in litres, and T the absolute temperature. Gay- Lussac's law, therefore, holds for the osmotic pressure of sugar ; that is, the sugar exerts the same osmotic pressure as it would exert gaseous pressure if the H 2 O were absent and the sugar in the form of a gas. We will now describe a few experiments which strik- ingly illustrate the action of osmotic pressure and at the same time form a transition to considerations on the relation between osmotic pressure and the freezing- or boiling-points of solutions. i. When a crystal of Feds .is thrown into a dilute solution of K 4 Fe(CN)6 a membrane of Prussian blue is formed on the outside of the crystal. Inside this mem- brane the concentration of FeCls is very high, and water is drawn in from the outer solution, and the membrane is extended till it can no longer stand the pressure from within. It breaks at some point and concentrated solu- tion from within bursts out. A fresh membrane is at once formed around this and the process is repeated so that a tree-like structure of Prussian blue gradually grows up from the crystal. Solution Water FIG. 3. 2. If a, wall of ice is placed in a rectangular vessel (Fig. 3) in one side of which is water and in the other a solution, the ice wall will appear to move toward the 28 ELECTROCHEMISTRY. side where the water is, because on the one side ice melts in contact with the solution, while water crystallizes out on the other side. This ice wall is in a way a semi- permeable wall which is permeable to water. (An important point in calculating the depression of the freezing-point.) 3. The atmosphere can also be considered as a semi- permeable medium. If two beakers, one of which con- tains a sugar solution and the other water, are placed in a confined space, it will be found that water distils over from the second to the first. The atmosphere can be considered in this case "as a wall permeable to water but not to sugar molecules. (Important in calculating the elevation of the boiling-point.) 4. The so-called " Schlierenapparat " of Tammann is an arrangement for observing the concentration changes on a semi-permeable wall. If a drop of a concentrated solution of K 4 FeCy 6 is carefully brought into a dilute solution of CuSO4 by means of a pipette, a membrane of Cu2FeCy2 is at once formed around the drop. Water will be drawn in through the membrane on account of the higher osmotic pressure of the salt inside, and as a result the CuSCU solution in the immediate vicinity of the drop becomes more concentrated and this heavier solution can be seen falling in a stream away from the drop. If no descending streams are observed, the two solutions are iso tonic.* We have seen (p. 27) that the gas laws hold for dilute solutions. Just as gases can do work on expanding, * For further methods of measuring osmotic pressure, as well as freezing- and boiling-point changes, see any of the larger text-books of physical chemistry, as Nernst, p. 132 ff. WORK, CURRENT, AND YOLTAGE. 29 k so a dilute solution can be made to perform work when it is being further diluted, since dilution is nothing more than the distribution of the dissolved substance through a greater volume, i.e., expansion. If v is the volume in which n gram- molecules of a simple substance, for instance cane-sugar, are dissolved, and if the osmotic pressure of these molecules is lowered by dilution from pi to p2, the work which may be obtained is (cf. p. 20) or, since osmotic pressure and concentration are directly proportional, A=nRTln-, c 2 or, finally, since the osmotic pressure varies inversely as the dilution, ( Dilution = volume per gram-molecule = -. I \ concentration/ Vo A=nRTln-. Vi With the help of this equation it is possible in most cases to calculate the work obtainable from chemical reactions. Calculation of Chemical Work from Osmotic Pressure. van't Hoff's Equation. We will take a reaction of the form i.e., a reaction in which m mols of the substance A unite with n mols of thesubstance B, forming o mols 3 ELEC TROCHE MIS TR Y. of the substance C and q mols of D. For instance in the reaction 4SbCl 3 + 5H 2 O = Sb 4 O 5 Cl 2 + loHCl, m = 4, n= 5, = 1, and q= 10. Further, let the small italic and Greek letters represent the concentrations before and after the reaction and we have the following scheme : Disappearing Substances. Resulting Substances. A. B. C. D. Concentration before reaction. . . Concentration after reaction Number of reacting molecules. . . . a a m b f n C r d 9 1 As the reaction goes on, the concentration of both A and B sinks. Lowering of a concentration or pres- sure can do work. For the substance A this work is for B it is mRTln-, a The concentrations of C and D are increased by the progress of the reaction. The work to be gained from this cause is negative, i.e., to increase their concentration requires work; consequently -oRTln-=oRTln-> f C 7 WORK, CURRENT, AND YOLTAGE. 31 The total work of the reaction is therefore This is the so-called " energy equation " of van't HofL This equation becomes still simpler when we introduce the laws of mass action. When the reaction goes to completion, i.e., till equilibrium between all the reacting rd q substances prevails (cf. following chapter), and # = - ^ represents the equilibrium constant, then Product of active masses* of disaDpeariie: substances A = RTlnK+RTln Product of active masses O f resulting substances ' When all the substances have the same concentration at the start, then A=RTlnK. * In this equation by "active mass" of a substance is meant the con- centration of the same raised to a power represented by the number of molecules with which it enters into the reaction. CHAPTER II. CHEMICAL EQUILIBRIUM, STATICS, AND KINETICS. THE first equation on page 31 gives the work of a reaction when it is interrupted at a particular point where the concentrations are a, /?, 7-, d. We will now consider the far more important question, how much work a reaction can afford when we let it go on till it stops of itself. We have a fundamental distinction to make between the so-called complete and incomplete reactions. An example of a complete reaction is the conversion of water into steam at atmospheric pressure and tem- peratures above 100, when the water " phase" completely disappears. The freezing of water below o is likewise a complete reaction. Water is turned completely into ice, there is no unfrozen remainder. The evaporation of water at temperatures below 1 00 and at atmospheric pressure is an example of an incomplete reaction. In this case water will evaporate till the partial pressure (cf. p. 17) of the water-vapor attains a value which is just the same as the vapor pres- sure of water at the temperature which prevails. When such a concentration of the water-vapor is attained just as much water evaporates as is formed by condensa 32 CHEMICAL EQUILIBRIUM, STATICS, AND KINETICS. 33 tion of the vapor, i.e., visible evaporation has stopped. We say the liquid water is in equilibrium with water- vapor at the corresponding vapor pressure. If too little water is present, it will of course evaporate completely. A classical example of an incomplete reaction is the " ester formation." When one mol each of alcohol and acetic acid are brought together they unite to form ethyl acetate and water, but the reaction is not complete; it stops when f mol of ester and mol of water have been formed and J mol of alcohol and J mol of acid remain unaltered. The reaction has reached equilibrium when the concentrations have attained these values. We will have to do principally with the incomplete reactions. It was formerly thought that such reactions were exceptional, because the end concentrations were too small to be measured chemically. For instance, before Davy's time certain substances were considered absolutely insoluble. It was believed that when solutions of barium chloride and sulphuric acid were mixed, barium sulphate was absolutely removed from the solution. According to this idea such a reaction would be complete. In reality there is no such thing as an absolutely insoluble substance, although in many cases the solubility is so small that chemical methods are unable to measure it. The precipitation of substances is in reality an incomplete reaction. It was formerly thought that when zinc in excess was put in a solution of copper sulphate absolutely all the copper was precipitated out of the solution. But this is not the case, the reaction goes on till the concen- tration of the copper salt is io~ 40 . Of course it is out of the question to even demonstrate by chemical means the presence of copper in such a dilute solution, but certain 34 ELECTROCHEMISTRY. electrochemical methods enable us to approximately measure such low concentrations. All such reactions in which one metal is precipitated by another are in- complete. They are also reversible. We saw above that alcohol and acetic acid unite to form ethyl acetate and water. When we dissolve a mol of ethyl acetate in i mol of water the reverse reaction occurs, i.e., alcohol and acetic acid are formed. But this reaction is also incomplete, and will come to the same state of equilibrium as the first, i.e., will stop when J mol of ethyl acetate has been converted into acid and alcohol. Such reactions which can occur in either direction are denoted by two arrows in place of the equality sign: C 2 H 5 OH + CH 3 COOH <=> CH 3 COOC 2 H 5 + H 2 O. We have defined an incomplete reaction as one which ceases of itself when equilibrium is reached. This definition requires some modification: when equilibrium is reached the reaction does not actually cease, but the two reactions, from left to right and the reverse, both go on with the same velocity, so that although a continual reaction is going on the composition of the equilibrium mixture remains constant. We must likewise assume a similar condition of affairs before equilibrium is reached. Both reactions take place, but the velocity in one direction is much greater than in the other, so that this determines the direction of the total reaction which we observe. Keeping in mind these considerations we will have little difficulty in understanding the very important law of mass action. Let us take the reaction of page 29, CHEMICAL EQUILIBRIUM, STATICS, AND KINETICS. 35 in which the concentrations of A , B, C, D are represented by a, b, c, d respectively. The kinetic theory * and also practical experience teach that the reaction from left to right can be expressed by the equation vi = kia m b n , i.e., is proportional to the product of the active masses of the reacting substances. In the same way the velocity of the reverse reaction can be expressed: But the actual apparent velocity is the difference between these two single velocities: V=V!-v 2 = kia m b n - k 2 cd q . This is the law of chemical kinetics. When equilibrium is attained Vi = v 2 and the total velocity V becomes o. Consequently when the equilibrium concentrations are a? If j- = K represents the equilibrium constant of the #1 , reaction, then * The kinetic theory assumes that the molecules of all substances are in a continual state of motion; a reaction can only occur when two or more molecules collide. See Nernst, Theoretische Chemie, 1903, p. 427. ( 36 ELECTROCHEM1S TR Y. This is the law of chemical statics. It states that for every incomplete reaction there exists a state of equilibrium when the reaction ceases of itself, and this condition is regulated , by the active masses * of the disappearing substances and of those being produced. The equilibrium constant remains the same no matter what the concentra- tions of the reacting substances were at the start. For instance, in the reaction CH 3 COOH + C 2 H 5 OH <=> CH 3 COOC 2 H5+H 2 O * We must explain the conception of "active mass" somewhat more definitely. By the active mass of a substance is meant its volume con- centration; in the case of a solution it is the ordinary molecular concen- tration (gr.-mols per litre). In the formulae of the law of mass action, the energy equation, etc., the active mass of each molecule which takes part in the reaction is used; the concentration a of the substance A, for instance, appears m times since m molecules of A take part in the reaction. If a solvent takes part in a reaction, as for instance water in the ester formation or in hydrolysis, its active mass should also be intro- duced. In dilute solutions, however, the change in the active mass of water is so slight that for practical purposes it may be neglected, and its active mass be considered as a constant (in all such calculations the change in active mass is the important point rather than the absolute value itself). In very concentrated solutions the change in active mass of the solvent can no longer be neglected, but in most of the electro- chemical reactions of importance, concentrated solutions play a minor part, and we may nearly always consider the active mass of the solvent as constant. The active mass of a solid in contact with a solution in which the solid reacts is constant. The active mass of a metal in a galvanic cell, or of a soluble sub- stance in excess in a solution saturated with respect to this substance, is constant, for as soon as any more of the substance is formed or used up the concentration of saturation is at once reproduced by further precipitation or solution of the solid, and the active mass remains un- changed. CHEMICAL EQUILIBRIUM, STATICS, AND KINETICS. 37 if we start with i gr.-mol each of acid and alcohol, equilibrium is reached when J mol of acid and alcohol is left and mol of ester and water are formed. K is therefore K " If instead of taking one mol each, to start with, we take any concentration we please, the reaction will go on in any case till the ratio of the concentrations is J. For instance, if we take 2 rnols of acid to i of alcohol, there will of course be more than J mol of acid left over. If x represents the amount of acid and alcohol which has been used up when equilibrium is reached the quantity of ester and water formed is also x. In equilibrium, then, we have 200 mols acetic acid, i x mol alcohol, and x mol each of ester and water, then ^ -- = K=. From this quadratic equation x 4 we can calculate x, and then know how far the reaction has gone. Another classical example is the formation of hydriodic acid from iodine vapor and hydrogen, according to the reaction H^-I-^^^HL Here we can* use instead of the concentration the partial pressures of each gas, which are directly proportional to the concentration. If P with the corresponding indices represents each particular partial pressure, then 'HI ELECTROCHEMISTR Y. A further example is the reaction and Ppci 5 The last two equations have to do with the breaking up or " dissociation " of gases. All cases of dissociation equilibrium whether in gases or in solution are calculated in a similar way. A very important example is the dissociation of carbon dioxide. The union of carbon monoxide with oxygen is an incomplete reaction; thus, 2CO 2 <=O 2 + 2CO, and the equilibrium conditions are given by K X Pi 2 = P% X Pa 2 , where PI, P'2, PS are the partial pressures of the three gases respectively. If the constant K has been determined at some particular temperature and pressure, the dis- sociation can be calculated by the above equation for any pressure at this particular temperature. The follow- ing table gives the percent to which carbon dioxide is dissociated into carbon monoxide and oxygen not only for different pressures but also for temperatures between 1000 and 4000. Pressures in Atmospheres O.OOI O.OI O.I i 10 100 1000 0.7 o-3 0.13 0.06 0.03 0.015 1500 7 3-5 !-7 0.8 0.4 0.2 2000 40 12.5 8 4 3 2 -5 2500 81 60 40 T 9 9 4.0 3000 94 80 60 40 21 10 35 96 85 70 53 32 15 4000 97 90 80 63 45 25 CHEMICAL EQUILIBRIUM, STATICS, AND KINETICS. 39 The table shows that at high temperatures it is im- possible to burn carbon monoxide completely to the dioxide, and that for this reason we are unable to utilize at high temperatures the full energy of the combustion of carbon; we can see from the table about how far the combustion goes in different processes. In the iron blast-furnace the temperature is about 2000 and the partial pressure of carbon dioxide is about 0.2 of an atmosphere. Under these conditions CO 2 is about 5% dissociated, and as a result the efficiency of the furnace is slightly impaired. In illuminating flames which also have a temperature of 2000 or more, the partial pressure of CO 2 is only about o.i of an atmosphere owing to the large quantity of hydrogen. The dissociation of CO 2 can then exceed 10%, and the temperature is cor- respondingly lower, while the illuminating power, which varies enormously with the temperature, is very appreci- ably decreased. In the case of explosives the temperature is probably between 2500 and 3000, but here the pres- sure of CO 2 is several thousand atmospheres, and the dissociation very small, so that the combustion is prac- tically perfect. The law of mass action has been found to hold for a great number of reactions ; for further details, reference is made to the text-books of theoretical and physical chem- istry by Nernst, Ostwald, and others. As yet we have only considered reactions between substances which were in the same physical condition, i.e., in " homogeneous systems " when all were either liquid or gaseous. We will now consider the " heterogeneous " systems. For the first illustration we will take the solution of a salt. If we bring solid salt in contact with water it dissolves: 40 ELECTROCHEMISTRY. NaCl solid <= NaCl dissolved . The equilibrium equation is ^C s ' olid = C dissolve d; but the solid salt does not change its concentration C solid as solu- tion goes on ; its quantity may diminish but the remaining solid salt always keeps the same density or concentration. Csolid is therefore also a constant, and for equilibrium we have KI = C d i sso i ved . This equation, however, is nothing less than a statement that at equilibrium the concentration of the dissolved salt is constant, i.e., every salt has a constant solubility. What has been said for ordinary salt is true for all solid substances. They do not change their concentration as solids although they may lose in weight. This fact is expressed when we say the active mass of a solid substance is constant (cf . note, p. 36). 2. Another classical example is the dissociation of calcium carbonate : CaCO 3solid <= CaO solid + CO 2gaS eous. Here, too, we can include the active mass of the solid substances in the constant of equilibrium and obtain where p c o 2 is the pressure of the carbon dioxide, and is proportional to its concentration. This is simply a statement that the dissociation pressure of marble, i.e., the pressure with which it evolves CO 2, is a constant at constant temperature. The same remarks apply also to liquids. When liquid water evaporates, part of it disappears as such, but the density of the' remaining water, i.e., its concentration (mols per litre), is not changed. We obtain in this case also CHEMICAL EQUILIBRIUM, STATICS, AND KINETICS. 41 in other words, the vapor pressure of water has at con- stant temperature a fixed value. Change of Equilibrium with the Temperature. In the previous considerations it has been understood that the temperature remains constant. If we consider a reaction at different temperatures, as for instance the formation of carbon dioxide (cf. table, p. 38), we 1000 2000 J Temperature FIG. 4. 3000 J 4000 J find that the equilibrium constants are different for each temperature. These facts are clearly shown by the accompanying curves (Fig. 4). The abscissae represent temperatures, and the ordinates give the per- centage to which carbon dioxide is dissociated. At low temperatures the combustion for all practical purposes is complete, and the gas mixture contains practically 100% CO 2- But the higher the temperature, the less complete is the combustion. At a temperature of 3000 when the pressure of CO 2 is one atmosphere the com- 42 ELECTROCHEMISTRY. bustion is only 60% of the whole; the dissociation increases with increasing temperature, till finally at very high temperatures carbon monoxide and oxygen combine to a very slight extent. However, since this reaction, either at high or low temperature, is not absolutely complete, the curve which represents the relation between degree of combination and temperature can never actually touch the two horizontal lines representing o% and 100% dissociation, but can only approach them asymptotically. This is best seen in the curve for o.ooi of an atmosphere. The relations which hold for this particular reaction are true for all incomplete reactions; similar curves can be obtained in all cases. From what has been said it can be seen that the chem- ical facts with which we are acquainted are somewhat a matter of chance, since they are governed by the tem- perature and pressure which happen to prevail on our planet. We are accustomed to say that coal burns, uniting with oxygen to form carbon dioxide, and this is true for the comparatively low temperatures of our stoves or blast-furnaces. But if we lived on a body whose temperature like that of the sun is in the neighbor- hood of 10000 our chemical text-books would say that carbon and oxygen do not combine. Carbon dioxide would be an unknown substance to an inhabitant of the sun, since at that temperature it is almost completely dissociated. Water is an unknown body on the sun, since the equilibrium of the reaction 2H 2 + O 2 ^2H 2 O at the sun's temperature lies at a point where the concentration of the water is immeasurably small. We consider a mixture of hydrogen and oxygen unstable, but an in- habitant of the sun would consider water an exceedingly CHEMICAL EQUILIBRIUM, STATICS, AND KINETICS. 43 unstable compound if he could ever succeed in obtain- ing it. Our experimental chemistry is the chemistry of the earth; we cannot write a " chemistry of the universe" until we know the equilibrium constants of all reactions at all temperatures. For since all reactions proceed toward the point of equilibrium we could then know the direction in which any reaction would go at any tempera- ture. We are indebted to J. H. van't HofT, the master of the science of physical chemistry, for the method of solving this important problem. An expression derived by him and known as " van't HofF s Equation " gives the relation between the equilibrium constant, the heat of reaction, and the temperature. This expression, obtained by inte- grating a differential equation,* is: In this equation T\ and T 2 are two absolute temperatures, KI and K 2 the equilibrium constants of the given reaction at these temperatures, In represents the " natural log " (see p. 20, note), R is the gas constant 1.991 cal. (see table on p. 5), and q is the " heat of reaction " (see p. 8). If we know the last-named value and determine the equilibrium constant for any particular temperature we can calculate the equilibrium for any other tempera- ture. The table on page 38 has been calculated in this * The equation is derived from the second law of thermodynamics (p. 9) and the energy equation (p. 31). By combining them the differ- dlnK -q ential equation -rr^ ~7^, 1S obtained. 44 ELECTROCHEMISTR Y. way, sLice it is experimentally impracticable to measure the equilibrium at a temperature of 4000. On the other hand, if we know the equilibrium constant of a reaction at two different temperatures we can calculate the " heat of reaction." The equilibrium constant of the reaction where a- solid substance dissolves in water is equal to the concentration at saturation (see p. 40). If Ci=2.SS and 2 = 4. 22 are the solubilities of succinic acid at o C. ( = 273) and 8.5 C. ( = 281.5), then q ( i i \ Inci Inc 2 = ( 7^ 777- ) . 2\li lz/ From this equation we can calculate q\ and find the value 6900 cal. The reaction mixture cools itself off, since q is negative. Berthelot found experimentally 6700 cal. as the heat of solution, in very good agreement with the calculated value. CHAPTER III. THEORY OF ELECTROLYTIC DISSOCIATION. A NUMBER of experimental facts which we will mention later on has led to the supposition that in the water solution of a salt only a certain fraction of the salt plays a part in electrochemical processes. This active part varies with the nature of the salt, the temperature, the dilution, and the nature of the solvent. (Solutions in solvents other than water have not as yet been system- atically investigated.) The rest of the salt remains in- active and has nothing to do in transporting the electric current. For instance, if we measure the conductivity of a sodium-chloride solution, we find that all the salt does not take part in conducting the current, but only a fraction; in the case of a normal solution of NaCl this active part is of the whole; in a normal solution of AgNO 3 it is only 58%. It is this same fraction which is active in in- fluencing the electromotive force of an electrode; for instance, in a normal AgNO 3 solution it is 58% of the total salt present. Of every .TOO molecules in the above NaCl solution 67 are in a condition different from the remaining 33, and the same is true of the 58 molecules in every 100 in the AgNO 3 solution. This active part of the whole is found from the conductivity and measurement 45 46 ELECTROCHEMISTRY. of electromotive forces, and also from measurements of the osmotic pressure and changes in the freezing- and boiling-points of the solutions, and all these methods give practically the same values. The chemical conduct of dissolved salts seems to indicate that these 67 or 58 molecules are just the ones which enter into chemical reactions. In cases where no molecules are present which can transport, the current, or if they are present in very small amounts, chemical reactions do not take place, or if they do, are extremely slow. A salt on dissolving in water must therefore suffer some change, and the physical conduct of solutions shows that the change is very profound. Like all soluble substances, a dissolved salt depresses the freezing-point of water and raises the boiling-point. When i gr.-mol of a substance like urea, or boric acid, or sugar, which does not conduct the current, is dissolved in i litre of water, the freezing-point of the solution is 1.86. 1.86 is called the "molecular lowering of the freezing-point " of water. If, however, we take a solution of i gr.-mol of a salt in i litre, which does conduct the current, we find that the freezing-point is lowered more than 1.86. It seems as though that part of the salt which does not take part in the conductivity acts normally in lowering the freezing-point, but the rest which is the active agent in conducting the current acts as though its component radicals had parted company and were each existing separately in the solution. For instance, in a normal solution of NaCl, 33% of the salt affects the freezing-point as cane-sugar would, lowering it 1.86X0.33 = 0.614; but the remaining 67% acts as though it had broken up into Na and Cl atoms and thus affects the THEORY OF ELECTROLYTIC DISSOCIATION. 47 freezing-point twice as much as an equal molecular quantity of sugar would do, so that the lowering from this cause is 2 X 67 X 1.86 = 2.49. The total lowering is therefore 2.49 + 0.614 = 3.104 instead of 1.86. In a normal AgNOs solution 42% has the usual effect, but the rest has twice the normal effect, as if this part of the AgNO 3 had broken up into Ag and NO 3 radicals. In a N - solution of H 2 SO4 about 75% of the acid takes part in conduction. The remaining 25% acts as usual in de- pressing the freezing-point, but the 75% has triple the usual effect, as though it had broken up into H+H + SO 4 . The o.i normal acid acts therefore in regard to its con- ductivity as though it were 0.075 normal, but with respect to its freezing-point as if it were 0.25 normal. The relations which hold for the lowering of the freez- ing-point are true also of the rise of the boiling-point or lowering of the vapor pressure. A gram-molecule of any non-conducting substance when dissolved in i litre of water raises the boiling-point a certain fixed amount, no matter what the substance is, provided only that it gives a non-conducting solution. But a o.i normal solution of H 2 SO 4 raises the boiling-point as though 75% of the acid had decomposed with the formation of three new substances, i.e., as though the solution Were 0.25 normal. The osmotic pressure is affected in just the same way. On p. 26 we saw that a normal solution of cane-sugar exerted an osmotic pressure of 22.42 atmospheres. A nopnal solution of other non-conducting substances has the same value, but a conducting salt solution has a much higher osmotic pressure. The ratio of this higher pres- sure to 22.42 is the same as the ratio of the abnormal 48 ELECTROCHEMISTRY. to the normal lowering of the freezing-point. Here again the conducting molecules act as though they had broken up into their component radicals. These facts, as well as many others of a physical and chemical nature, leave little room for doubt that a de- composition or " electrolytic dissociation " actually takes place when a salt is dissolved in water, and that only the dissociated atoms or molecules (known as " ions ") are the active agents in conducting the electric current or determining the electromotive force of an electrode. The percentage of the salt which undergoes decomposition is called the " degree of dissociation." Aside from the fact that many chemical reactions can only be explained on this supposition, the theory of elec- trolytic dissociation finds its principal support in the fact that all the different methods give concordant results for the degree of dissociation. At the present time it is impossible for the electrochemist to do without the theory of electrolytic dissociation. To illustrate these facts we give the following table of measurements. The numbers state how many molecules are formed from one molecule of the dissolved salt as the result of electrolytic dissociation. The question now comes up: " What is the nature of this separation?" It cannot be an ordinary separation, since the union of atoms in forming a compound is generally accompanied by a great production of energy. On decomposition this energy would have to appear again, which is apparently not true in this case. It seems, therefore, that the chemical affinity which has brought about the union of the atoms has been compensated for in some way so that the atoms are at liberty to separate, THEORY OF ELECTROLYTIC DISSOCIATION. 49 DEGREE OF DISSOCIATION AS DETERMINED BY OSMOTIC AND ELEC- TRICAL METHODS. Salts Concentra- tion Degree of Dissociation Osmotic Freezing- point Conductivity KC1. . NH 4 C1 Ca(N0 8 ) 2 K 4 Fe(CN) 6 . . . MgS0 4 LiCl o. 14 o. 148 0.18 o-35 6 0.38 0.13 0.18 o. 19 0.184 0.188 0.0018 i. si 1.82 2.48 3-9 i- 2 5 1.92. 2.69 2.79 2.78 2.47 I .20 1.94 2.52 2.68 2.67 2.56 5-92 1.86 1.89 2.46 3-7 i-35 1.84 2-51 2.48 2.42 2.41 SrCl 2 - MgCl 2 . . CaCl 2 CuCl 2 Na 6 C 12 O, 2 .... Because of the electromotive effects and the conductivity we assume that the chemical affinity has been changed to an electrical affinity, in that the atoms take on charges of positive and negative electricity. The neutral compound dissociates into positively and negatively charged atoms or radicals, which are known as " ions." In what follows we will review briefly the history of the theory, and at the same time explain the different con- ceptions which have been introduced. History of Electrochemistry. The Theory of Electrolytic Dissociation and its Foundations. In order to understand the foundation of the theory and its advantages a theory which at present is an in- dispensable part of theoretical chemistry we will follow its development historically. We will not, however, confine ourselves strictly to the history of the theory of 50 ELECTROCHEMISTRY. electrolytic dissociation, but will also take up that of electrochemistry in general and use this opportunity to learn some of the important laws of electrochemistry. The dissociation theory has met with more opposition than most theories of a purely hypothetical nature, probably because at first sight it seems to clash with our " chemical sense." But is not the atomic theory that matter is divisible until the final indivisible particles known as atoms are reached still more antagonistic to our " chemical sense " ? And yet we find ourselves quite at ease where the atomic theory is concerned. Possibly the reason for this is that the physical and nathematical knowledge required for the comprehension of the dis- sociation theory is not necessary to an understanding of the atomic theory. We are probably justified in saying that most of the opponents of the theory of electrolytic dis- sociation refrain from accepting it on grounds of con- servatism which is simply another name for inertia while others oppose it as they do the atomic theory, because they are unwilling to accept anything which they have not seen c. tested by experiment. The dissociation theory had its beginning a long time ago. Nicholson and Carlysle * found, and Davy f confirmed the facts accurately, that solutions which conduct do not remain unchanged by the passage of the current, as the metals do, but are decomposed; that is, the chemical affinity which has brought about the union of the elements in the salt is simply overcome by the action of electricity. The fact that the products of the decomposition are * Nicholson, Journ. of Nat. Phil., 4, 179 (1800). t Gilbert's Ann., 7, 114, 28, i and 161 (1808). THEORY OF ELECTROLYTIC DISSOCIATION. 51 attracted to the electrodes, where they are deposited, proves that they were already electrically charged before deposition, as otherwise there would be no attraction; and further, the elements which move toward the negative electrode must be charged positively and those which go to the positive electrode must be negatively charged. Fig. 5 is a facsimile of one of Faraday's drawings in which he has written the terms now in common use. These words were made at his suggestion by the philol- ogist Whewell. He called the negative " electrode " Fig. 5. the " cathode," and this is the electrode toward which the " cations," or the metallic elements in the " electrolyte," move; the " anode " is the electrode toward which the " anions " move. The whole process was named " elec- trolysis." * f About 1833, Faraday discovered the law of equivalent deposition, now generally known as Faraday's law. He * Faraday's spelling of "cathion" is wrong. The word anode is derived from the Greek words dvd=up and o<5oS=road; cathode is ro~n Kard= down and 66 oS (the th in this case comes from the aspirate in oSo 1 *). The word ion is from ^eyai=to go, and the corresponding words are cation and anion. Cation should have no h. $2 ELECTROCHEMISTRY. showed: ist, that the amount of the electrolyte which is decomposed is proportional to the quantity of electricity which has passed through the solution; and 2d, that when the same current is passed through two different electrolytes the amounts of the different substances set free are chemically equivalent. ILLUSTRATION: This law can be expressed as follows: Equal quantities of electricity precipitate equal quantities of all substances in electrolysis. By equal quantities of substances is meant not equal quantities in grams but in gram equivalents. A current of i ampere precipitates per second 0.01036 milligram equivalents of any substance; for instance (cf. table on p. 163): 107.93X0.01036 = 1.118 mgr. of silver, or 35.45X0.01036 = 0.368 mgr. of chlorine, or 127 X 0.01036 = 1.3 1 6 mgr. of iodine, or i4.o4 + Xi6)Xo.oio36 = o.643 mgr. of NO 3 . In the case of substances whose valence is greater than i we must divide the atomic weight by the valence. One ampere-second deposits 61.6 -^ X 0.01036 = 0.32 94 mgr. of copper, or (32.06+4X16) , ^^ Xo.oio36 = o.5 mgr. of SO4, or X 0.01036 = 0.0935 mgr. of Al. 3 Since the precipitation of metals or radicals is governed by the law of equivalents, it follows that equivalent THEORY OF ELECTROLYTIC DISSOCIATION. 53 quantities of different compounds are decomposed by one and the same quantity of electricity. Thus i ampere- second decomposes Xo.oio36 = 0.0933 mgr. of water, or Since i ampere-second deposits 0.01036 mgr. equiva- lents or 0.00001036 gr. equivalents, it is seen that 96 540 ampere-seconds are required to deposit i gr. equivalent; or since i ampere-second = i coulomb, 96 540 coulombs are required. This fact proves that one equivalent of each and every ion carries the same charge of electricity. Faraday's law applies not only to water solutions, but also to solutions in other solvents, and to salts in a fused state, and holds for all temperatures. The fact that the decomposition products of the electro- lyte, as hydrogen and oxygen, appear at points some distance apart, caused at first a great deal of difficulty. It was evident that the two products could scarcely be derived from the same molecule of water or dissolved substance, but must come from different ones. Several theories were at first proposed to account for the facts; for instance, the theory that the two substances hydrogen and oxygen were not derived from the water at all; that electricity itself was nothing less than an acid. Von Grotthus * attempted to clear up the difficulty. He assumed that the anion which was being deposited came from the molecule which was nearest to the anode; * Ann. d. chem. u. Physik, 58, 64 (1806), 63, 20 (1808). 5 4 ELEC TROCHE MIS TR Y. the cation which was being deposited came from the molecule nearest to the cathode. Just at the instant when these were deposited on the electrodes the re- mainder of the decomposed molecule appropriated the atom or radical it had lost from its neighboring molecule, this in turn robbing its next-door neighbor. This view was also apparently held by Faraday. The first to point out the shortcomings of this theory was Grove.* From his study of the oxygen-hydrogen cell, which derives its energy from the union of these two elements, he concluded that a decomposition of the water molecules is not necessary for the evolution of oxygen and hydrogen, but that the molecules are present from the start in a decomposed state. Clausius f then followed up this idea : if a force is necessary to decompose the molecules, electrolysis should not be possible at very low voltages. But the electrolysis of silver nitrate between silver electrodes takes place at voltages which are far below the voltage which corresponds to the energy of formation of silver nitrate; that is, we decompose at the expense of a small amount of work a salt which is formed with the liberation of a great deal of energy, a fact which conflicts with the principle of the conservation of energy. Clausius concludes therefore that " the supposition that the components of the mole- cules of an electrolyte are firmly united and exist in a fixed orderly arrangement is wrong." A few years earlier Williamson { had expressed a somewhat similar view. He proposed the hypothesis * Phil. Mag., 27, 348 (1845). f Poggendorf's Ann., 101, 338 (1857). J Liebig's Ann., 77, 37 (1851). THEORY OF ELECTROLYTIC DISSOCIATION. 55 that in hydrochloric acid " each atom of hydrogen does not remain quietly attached all the time to the same atom of chlorine, but that they are continually exchanging places with one another." If this is the case, then the two radicals must be present separately for a certain length of time, and this time will be longer the farther apart the molecules are, or, in other words, the more dilute the solution is. This hypothesis was adopted by Clausius, but at that time no experimental means were known for determining how much of the electrolyte was dissociated, or, in other words, to determine the ratio of the time during which the molecules were dissociated to the time during which the atoms remain united. About this time Hittorf's* importantwork was published. Hittorf found that during electrolysis changes of concen- tration occur at the anode and cathode, and concluded that these changes could only be explained by assuming that the anions and cations move with a different velocity. At the same time Kohlrausch discovered the lawf of the " independent wandering of the ions." He found that in dilute solutions the conductivity of a given salt is additively composed of two values which are peculiar to the different ions; that is, the potassium ion plays the same part in conducting the current whether it is present with the chlorine ion or the NOs ion. If we add to the conductivity of the potassium ion that of the chlorine ion, which is also independent of the nature of the cation present with it, we obtain the conductivity of potassium chloride. This result shows that any one ion troubles * Ostwald's Klassiker, Nos. 21 and 23. i f See the chapter on Conductivity. 5^ ELECTROCHEMISTRY. itself very little about the nature of any other ions which may also be present in the solution. Electrochemical theories had reached this point when van't Hoff in his classic work applied the gas laws to solutions. We saw (pp. 20 and 46) that the gas laws no longer hold when we consider a salt whose solution con- ducts the electric current. If p is the osmotic pressure and v the dilution, i.e., the volume in which a gram-molecule is contained, then pv = RT for non-conducting solutions (cf. p. 26). In the case of conducting solutions van't HofT found it necessary to multiply RT by a factor i, so that for this class of solutions p-v = iRT. Arrhenius calculated from Kohlrausch's measurements that only a part of the total number of molecules of a dissolved salt is active in conducting the current, and that this part is i i; i.e., if 2 = 1.7, then 70% of the total dissolved salt takes part in conduction. Arrhenius then concluded: " If we must assume that free ions are present in the solution, as Clausius and Williamson have shown, and if the osmotic and other methods show that many more molecules seem to be present in the solution than we have introduced, then we may assume that the salt is dissociated, not as Clausius believed, to a very slight extent, but to such a large extent that this will account for the deviation from the van't HofT gas laws." Now, since only a part of the dissolved salt and not the whole is active in conduction, and since this part corresponds to the extra molecules which van't Hoff has shown to be present, Arrhenius drew the conclusion that the electrolyte is dissociated into ions, the amount of disso- ciation depending on the concentration of the solution and nature of the salt, and that the ions are the only ^E IV:RSITY ) OF J OF ELECTROLYTIC DISSOCIATION. 57 active agents in conducting the current. This theory has become indispensable to electrochemistry, and has also become of great help in our understanding of general chemistry. When we bring ordinary salt in contact with water, it dissolves, but at the same time the reaction * takes place. This is the equation of an ordinary chemical reaction and like all reactions finally reaches a condition of equilibrium. In the case of a normal solution of NaCl, the reaction goes on till 67% of the salt has dissociated into ions, i.e., the degree of dissociation is 67%. Such a reaction must follow the law of mass action (p. 35). If x represents that part of a gram-molecule which is dissociated when the volume of the solution is v (in the above case # = 0.67), then at equilibrium the concentration T /y* of the undissociated molecules will be - , but the v ' oc concentration of each kind of ions will be - and the law v of mass action requires T x #2 ' 4. = ~^2' * The ions were formerly denoted by Na and Cl to indicate that we have to do with a positively charged sodium ion and a negatively charged chlorine ion; substances whose valence is greater than i were denoted + + by Cu and SO 4 , indicating that the copper or SO 4 ions carry twice the charge of the sodium or chlorine ions. For typographical reasons it has become customary to replace the + by and the by ' , printed above and to the right of the symbol. 5 3 ELECTROCHEMISTRY. \ or, in general, if Q is the concentration of the ions and c s that of the undissociated molecules, then n being the number of ions which results from the disso- ciation of i molecule of the salt. K is called the " disso- ciation constant " of the salt. The following examples will show how the dissociation occurs : AgN0 3 ^ Ag'+NCV; Na 2 SO 4 <= Na' + Na' + SO 4 "; But " dissociation by steps " may also occur, as: BaCl 2 <=BaCl- In many cases we cannot decide from the formula of a salt how it will dissociate. In the case of KHSO 4 the following reactions are possible: or KHSO 4 <=K' or KHSO 4 <=H' By measuring the " transport number " we can generally determine what the ions are, and Hittorf has applied this method in a number of cases where the composition of the ions was doubtful. If we put some potassium silver cyanide KAg(CN) 2 at the bottom of a U tube and pour THEORY OF ELECTROLYTIC DISSOCIATION. 59 water into each arm of the tube, the cations will move to the cathode and the anions to the anode when a current is passed through the tube. After the current has passed for some time we find on analyzing the contents of each half of the tube that no silver has wandered toward the cathode, but has gone in the opposite direction toward the anode. This shows that the silver forms part of the anion, and that the dissociation occurs thus : In a similar way it has been shown that the chromium in the chromates belongs to the anion just as sulphur belongs to the SO 4 ion. In the case of many acid salts, provided the solution is not too dilute, the hydrogen goes as part of the anion to the anode. Acid potassium sulphate then would dissociate It must not be understood, however, that no further dissociation takes place. In the above instance of KAg(CN)2 the dissociation constant K of the reaction [KAg(CN) 2 ] has a very large value, and the dissociation is nearly complete. On the other hand the dissociation constant [Ag-][CN'f Al [Ag(CN) 2 '] * The concentration of a substance is denoted by enclosing its sym- bol in brackets. 60 ELECTROCHEMISTRY. of the reaction Ag(CN) 2 ' <=* Ag- + CN' + CN' is very small, so that this second dissociation only takes place to an exceedingly small extent. In such a solution we have very many potassium ions and " complex " silver- cyanogen ions, but free silver ions and cyanide ions are present in exceedingly small amounts. It follows therefore that the current is conducted almost entirely by the potassium and complex ions, while the others on account of their scarcity are practically without effect on the conductivity. As a result we find in the above experiment no silver in the cathode arm of the U tube. Some other typical forms of dissociation are: Aids <=* Al- ' ' + Cl' + Cl' + Cl', '* K 6 Fe 2 (CN)i2 + K' + K'-f K From one molecule of potassium ferricyanide seven ions are formed, and the dissociated part has seven times as great an effect on the osmotic pressure or lowering of the freezing-point as the simple molecules. Other typical examples will be given in the following chapters. * This equation seems to the translator to be incorrect, as Ostwald's "Basicity Rule" shows ferricyanic acid to be tribasic. See Jahn, Grundriss der Elektrochemie, 2d edition, p. 146. THEORY OF ELECTROLYTIC DISSOCIATION. 61 Applications of the Dissociation Theory in Chemistry. In this chapter we cannot enter into details but must limit ourselves to a few examples which will show the usefulness of the theory of electrolytic dissociation and how we can apply it in our work and calculations. At the same time we will touch on a number of physico- chemical questions, a clear understanding of which is necessary to our further study of electrochemistry. The supporters of the theory of electrolytic dissociation assume that most of the reactions of inorganic chemistry, which, in comparison to organic reactions, take place in a very short space of time, are reactions between the ions. The precipitation of silver chloride from a silver-nitrate solution by ordinary salt was formerly explained by the following equation: AgN0 3 +NaCl <=> AgCl+NaN0 3 . If we assume that all the salts except the solid AgCl are dissociated into their ions the reaction becomes or subtracting those ions which occur on both sides of the equation, Ag' + CF^AgCl. The essential reaction is the union of silver ions and chlorine ions to form insoluble silver chloride. The old explanation that " chlorine and silver react in solution to form silver chloride" is not strictly correct. In terms 62 ELECTROCHEMISTRY, of the theory of electrolytic dissociation " chlorine ions and silver ions can only exist together in a water solution in very small concentrations; if the product of their concentrations, measured in mols per litre, should exceed i.2Xio~ 10 solid silver chloride is deposited until the product of the concentration of the ions is reduced to this value." Chloroform, for instance, contains no chlorine ions, since it is a non-conductor of electricity, and therefore can- not be electrolytically dissociated; therefore it does not precipitate silver chloride from a solution. The same is true for sodium chlorate> NaClOs, which dissociates according to the formula A solution of this salt contains chlorate ions, but no chlorine ions. In a solution of KAg(CN)2, which dissociates after the formula KAg(CN) 2 ^ K'+Ag(CN) 2 ', so few silver ions result from the further dissociation, Ag(CN) 2 ' <=> Ag- + CN' + CN', that they can remain in the presence of a large amount of CY ions without being precipitated. This accounts for the fact that NaCl will not precipitate AgCl from a solution of KAg(CN) 2 . Before the birth of the theory of electrolytic dissociation no satisfactory explanation had been given. The theory explains the slowness of reactions between organic substances on the ground that they are not THEORY OF ELECTROLYTIC DISSOCIATION. 63 dissociated to any measurable extent, and the same is true of reactions between solid substances. A mixture of solid NaCl and AgNO 3 from which water is carefully excluded does not react; but as soon as it comes in contact with water the two salts dissolve, are at once dissociated into their ions, and reaction starts. Salts in a state of fusion are also dissociated so that under such circumstances reaction can easily take place. The old dictum " corpora non agunt nisi fluida " is pretty generally true, but not absolutely, since solid substances do react, but with extreme slowness. Among the salts we must include the salts of the metal hydrogen, i.e., the acids. These are generally very strongly dissociated in water solution. Just as potassium salts have the common property of giving off -potassium ions, so all the acids have the property of sending hydrogen ions into solution, as, for instance, HOMH'+Cl', or or H 3 PO 4 <= H- + H 2 PO 4 ' =* H- Acids like sulphuric acid which can furnish two hydrogen ions per molecule are called dibasic, those which can furnish three hydrogen ions tribasic, etc. The examples just given show that the dissociation of a molecule is not necessarily complete but may take place by stages, or " stepwise." The bases are also to be reckoned among the strongly 64 ELECTROCHEM1S TR Y. dissociated salts. Just as a common characteristic of the chlorides is their ability to furnish chlorine ions, so the bases have the common property of furnishing hydroxyl or OH ions. Acids and bases therefore are simply two particular kinds of salts. Their exceptional importance in chemistry due to the fact that their char- acteristic ions are also the ions of the most universal solvent, water. A chemical science based on a solvent which contained neither H* nor OH' ions would there- fore be wholly unable to distinguish acids or bases from salts. We thus arrive at a now and exact definition of an acid or a base. Acids are salts which are capable of forming H* ions in solution; bases are salts which furnish OH' ions. We must now consider the dissociation of water, which is one of the most important results of the dissociation theory and the most convincing proof of its value. We can consider water as a dibasic acid which dissociates as follows: or also as a mon-acid base, since it can furnish OH' ions. The second step of the acid dissociation which gives rise to O" ions is very slight, i.e., the concentration of O" ions is exceedingly small. The first dissociation of water into H* and OH' is also very slight but of very great chemical importance. The reaction like every other chemical reaction is governed by the law of mass action, thus: THEORY OF ELECTROLYTIC DISSOCIATION. 65 The equilibrium constant K is known as the " dissociation constant of water." (Enclosing a symbol in brackets is the conventional way of indicating the concentration of a substance.) Now, the dissociation of water is very slight, so that the active mass of water is practically unchanged by the dissociation, and we may therefore consider it a constant and include it along with the reaction constant without causing any appreciable error ; then where k is the product of the concentrations of both ions. In neutral water neither H' nor OH' is present in excess. The two concentrations are equal, so that if CQ repre- sents the concentration of either ion in neutral water, The last equation but one must always hold, no matter what the concentrations of H* or OH'OH' may be, i.e., whether the solution is acid, neutral, or alkaline. A number of different methods which we will consider in the following have given io~ 7 as the value of CQ at about 22. Therefore [H'][OH']=io- 14 . In an alkaline solution, which contains' 17 grams of OH ions per litre, [OH']=i, and [H'] must then be io~ 14 ; in such a solution, then, we would have a concentration of i gr. of hydrogen ions in 100 billion litres. In a o.ooi ormal acid solution [H'] = .ooi and [OH'] = io~ n , etc. A further application of this formula is as follows: if we mix i mol of HC1 and i mol of NaOH in a litre of water, the product [H']X[OH'] at first will be=i, a 66 ELEC TROCHE MIS TR Y. much larger value than is possible. H" and OH 7 will therefore combine till the value of [H'j [OH'] becomes io~ 14 . The equations for this and other simple reactions of neutralization are: Na' + OH'+H' + Cl' = H 2 0+Na- + Cl', After subtracting the ions which appear on both sides there remains in every case The process of neutralization therefore is always based on the same fundamental reaction, provided of course that the reacting base and acid are in a solution so dilute that they are both completely dissociated into their ions. As a result, the heat of reaction of every neutralization must always be the same, and must be independent of the nature of the particular acid or base used. This fact has long been known, but previous to the evolution of the dissociation theory no satisfactory explanation had been given. The following table gives some experimental results: Acid and Base. Heat of Neutralization. Hydrochloric ac Hydrobromic Nitric Hydroiodic Hydrochloric i ( 1 1 id ai id sodium hydn < < t ( C ( lithium potassium barium calcii'm 3xide .... 13 700 13 700 I 3 700 13800 I 3 700 13800 13800 13 900 THEORY OF ELECTROLYTIC DISSOCIATION. 67 Hydrofluoric acid is only slightly dissociated in solution, consequently in the reaction HF + K' + OH' <=> K- + F' + H 2 HF must become further and further dissociated as the reaction goes on. The dissociation of HF of course follows the law of mass action K 1 [HF] = [H'][F'] and as the H* ions combine with OH' ions to form water new ones are supplied by the undissociated HF. The heat evolved by the dissociation of the hydrofluoric acid appears as an excess over that evolved by the union of H' and OH'. The neutralization of hydrofluoric acid evolves 16 270 calories. The difference between this and the ordinary heat of neutralization, 16 270 13 70x3 = 2 570, is the heat of dissociation of HF. The question now arises, when either the acid or base has a very small dissociation constant, how will this affect the neutralization? Like all chemical reactions, that of neutralization goes on till a particular condition of equilibrium is reached. When we mix solutions of NaOH and HC1, they do not combine completely to form NaCl, some free NaOH and HC1 remain, but their quantity is so small that it cannot be measured. The incompleteness of some reactions of neutralization, however, can be measured, as, for instance, that of acetic acid. From conductivity measurements, or, better, from the influence of sodium acetate on the velocity of the saponifi- 68 ELECTROCHEMISTRY. cation of methyl acetate,* it has been found that a mixture of o.i N acetic acid and o.i N sodium hydroxide combine to the extent of 99.992%, i.e., 0.008% of NaOH and CH 3 COOH remain in a free state. We may now ask, is it possible to calculate this percentage of free acid or hydroxide from the dissociation constant of acetic acid? A o.i N solution of sodium acetate in H 2 O must be decomposed into free acid and base to exactly this same amount (0.008%) and this decomposition of a salt by water is known as " hydrolysis." The calculation of the dissociation constant of organic acids from the dissociation constant of water and the degree of hydrolysis of the salts of the acid, or the reverse, has recently become of such importance for organic chemistry that we will give a numerical illustration of the method to be followed. The Hydrolysis of sodium acetate: acetic acid disso- ciates according to the equation CH 3 COOH <= H- + CH 3 COO', and the constant of the reaction is given by ' K![CH 3 COOH] - [IT] [CH 3 COO']. From conductivity measurements the value of KI has been found to be 0.000018. The relation between [H*] and [OH'] is governed by the dissociation constant of H 2 0,K 2 , at 25: * The velocity of this reaction is proportional to the concentration of th6 OH' ions present, which accelerate the saponincation catalyt- ically. THEORY OF ELECTROLYTIC DISSOCIATION. 69 Further, there must be just as many positive ions present in the solution as there are negative ions, i.e., [H-] + [Na-] = [CH 3 COO'] + [OH']. The two sodium compounds present, NaOH and CH 3 COONa, can be considered as completely dissociated at this degree of dilution, i.e., practically all the sodium is present in the form of Na' ions. This concentration is then o.i N, since we took that much Na in the form of sodium acetate. Finally we must remember 'that the amounts of NaOH or CH 3 COOH which do not combine in the reaction of neutralization or which are set free by the hydrolysis are equal. Since the NaOH is completely dissociated, while the CH 3 COOH is only dissociated to such a small amount that its total concentration is not appreciably affected, we may consider [OH'] = [CH 3 COOH]. We ha^e then four equations : (1) o.ooooi8[CH 3 COOH] = [CH 3 COO'][H']. (2) [H'][OH']=i.2Xio- 14 . (3) [H-] + [Na'] = [H-] + o.i =[CH 3 COO']+[OH']. (4) [CH 3 COOH] Substituting the value of [CH 3 COO'J from (3) in equation (i) gives o.ooooi8[CH 3 COOH] = [H']([H-] + o.i A solution of CH 3 COONa reacts alkaline; there must therefore be more OH' than H' present, so that [H*] is 7 o ELECTROCHEM1S TR Y. certainly less than 10 7 . This value is so small that it may be neglected in comparison with o.i (at the most this would only introduce an error of about 0.0001%). Substituting the value of [H*] from equation (2) and then introducing for [OH'] its value from equation (4), we finally obtain -r n NX 14 o.oooo I 8[CH3COOH]=- H3COOH] (o.i-[CH 3 COOH]). On solving this quadratic equation we find for the con- centration of CH 3 COOH, [CH 3 COOH] = 0.0000081. That is, of the o.i CH 3 COONa, 0.0000081 or 0.0081% has decomposed into free acetic acid and sodium hydrox- ide; this agrees very well with the value 0.008 found by experiment. We may also reverse this process and from the ex- perimental value 0.008 calculate the dissociation constant of water. . In this way we find : C = i.iXio- 7 at 25. The following table contains the " degrees of hydrol- ysis " of certain salts at 25 when present in o.i normal solution : Salt. Degree of Hydrolysis. Sodium carbonate 3-17 % Potassium phenolate. . . 3-5 " cyanide. . . . I . 12 Borax 0-5 " Sodium acetate 0.008 " THEORY OF ELECTROLYTIC DISSOCIATION. 7 1 It is seen that the hydrolysis may amount to several per- cent. It is well known that a solution of potassium cyanide smells of prussic acid, which can only result from a " hydrolytic dissociation " of the salt. A solution of ammonium carbonate smells strongly of ammonia; the odor in this case being due to the free NH 3 resulting from hydrolysis. The slow evolution of carbon dioxide from a solution of sodium carbonate is another instance. Still another example is the conduct of certain salts of bismuth, which precipitate bismuth oxide on being diluted; in this case the hydrolysis is so great that the solubility of the oxide is thereby exceeded. Let us now go back to the calculation of the dissociation constant of water. The first method was by measuring the hydrolysis of sodium acetate; a second method consists in measuring the velocity of the reaction of "saponifi cation. " When ethyl acetate and sodium hy- droxide are brought together, sodium acetate and ethyl alcohol are formed according to .the equation CH 3 COOC 2 H 5 + NaOH <=> CH 3 COONa + C 2 H 5 OH. In this reaction the ester CH 3 COOC2H 5 is said to be saponified by the base NaOH. The velocity of this reaction is dependent on the concentrations of the reacting substances and is further catalytically accelerated by the presence of H' ions (cf. p. 15). On the other hand, the number of OH' ions present also influence the velocity, and it has been found experimentally that the OH 7 ions saponify an ester 1400 times as fast as the H' ions. It is easy to see that when we successively diminish the con- centration of the OH' ions, the velocity of the reaction will reach a minimum when the concentration of the H' ions 7 2 ELECTROCHEMISTRY. is 1400 times as large as that of the OH' ions. If this minimum is determined experimentally and the amount of free acid at that point determined, we have In this manner van't Hoff has calculated the dissociation constant of water, and obtained as the value of c , c = i.2Xio~ 7 at 25. A third method for calculating the dissociation of H 2 O consists in measuring the electromotive force of the acid- alkali cell; that is, of an element made of up two platinum electrodes saturated with hydrogen, one of which is placed in an acid and the other in an alkaline solution. We shall see later that the electromotive force of a metal when placed in a solution of one of its salts depends not only on the nature of the metal but also on the concentration of the ions of the metal present in the solution For any one metal the electromotive force varies inversely as the logarithm of the concentration of the ions of the metal in solution. We may consider a platinum electrode saturated with hydrogen as an electrode of the metal hydrogen, and its electromotive force is therefore depen- dent on the concentration of the hydrogen ions in the solution. If we measure the electromotive force of the acid-alkali cell and determine by titration the concentration of the H' ions on one side and that of the OH' ions on the other, we can calculate from this result the concentration of the H' ions in the alkaline solution. In a normal solution of NaOH where the concentration of the OH' ions is nearlv = i it has been found that the concentration THEORY OF ELECTROLYTIC DISSOCIATION. 73 of the H* ions is about i.44Xio~ 14 .. That is, in this solution [H'][OH']= 1.44X10-1*, or The conductivity of pure water furnishes a fourth method. The measurements made by Kohlrausch on the purest water obtainable have given the following figures: co = o.78Xio~ 7 at 18 and ~" 7 at 25. (The method by which these results were obtained will be discussed later, in the chapter on Conductivity.) These four independent methods have given the following results for the dissociation of water: i.iXio" 7 , i.2Xio~ 7 , and If we take the constant for 25 as ^T=i.2Xio~ 14 , we can calculate the value of the constant for other temperatures by means of van't Hoff's equation, since the heat of the reaction H v -t-OH r = H 2 O is 13700 cal. From these results it has been calculated that the conductivity of the purest water should increase 5.81% per degree rise of temperature. Kohlrausch found that the increase was 5.32%. The following table gives the dissociation of water at different temperatures : Temperature = 2 10 18 26 34 42 5 2.48 TOO 8-5 c Xio 7 = o-35 o-39 0.56 0.80 i . i 1.47 i-93 74 ELECTROCHEM1S TR Y. A number of purely chemical problems which cannot be satisfactorily explained without the help of the theory of equilibrium will be discussed in the chapter on Con- ductivity, after we have learned the different methods of measuring dissociation constants. Among these are: influence of the strength' of acids and bases on the saponi- fication of esters, on the inversion of sugar, and on the hydrolytic dissociation of salts; distribution of an acid between two bases, or of a base between two acids; rapidity of solution of metals, carbonates, and oxalates in acids; the influence of dissolved salts on one another, etc. The dissociation theory disposes of the question whether a reaction occurs when solutions of salts which have no common ions are brought together; for instance, are KC1 and NaBr formed when solutions of KBr and NaCl are mixed? The absence of any evolution or absorption of heat would go to show that no reaction takes place. The dissociation theory shows that the question is meaningless. Before mixing, the solutions contain the ions K*, Na', Cl' and Br'; and after mixing, the resulting solution contains the same ions unchanged. No reaction can have occurred. According to the dissociation theory it is self-evident that the properties of such mixed solutions are additively built up of the properties of the original solutions. The specific gravity, for instance, is simply obtained from the specific gravities of the original solutions. We can go one step farther, since the specific gravity of a solution of a single substance is additively made up of values peculiar to the ions. If we know the number representing the effect of each ion on the specific gravity, we can calculate THEORY OF ELECTROLYTIC DISSOCIATION. 75 by simple addition the specific gravity of a mixture of any ions, i.e., the specific gravity of a solution of any salt. In a similar manner it has been shown that the compressibility, the capillarity, the internal friction, the index of refraction, the magnetic rotation of the plane of polarization, and the light absorption of solutions are additive properties. These few examples have shown some of the applications of the dissociation theory to chemical phenomena, and will suffice for the present. We need only mention that the conduct of indicators in titration has been explained satisfactorily by the dissocia- tion theory. Also many analytical reactions, such as the precipitation of metallic sulphides by hydrogen sulphide, can easily be understood from a knowledge of the solubility products and the state of dissociation. (Cf. chapter on Conductivity, p. 103). Finally a few words must be added on the application of the dissociation theory to physiological problems. The theory has widely increased our knowledge of the poison- ous action of certain classes of substances. The acids are more poisonous and have a greater physiological action according as their dissociation constant is great or small. The ions of mercury are very poisonous. If a salt con- taining mercury is taken into the stomach, the poisonous effect is more intense the higher the salt is dissociated. Corrosive sublimate is exceedingly poisonous, while the slightly soluble calomel which gives rise to few mercuiy ions is less poisonous although physiologically active. Cyanide of mercury, on the other hand, which contains the two active poisons' mercury and prussic acid, is itself not very poisonous. This is accounted for by the fact that cyanide of mercury is practically undissociated, as 7 6 cLEC TROCHE MIS TR Y. has been shown by conductivity measurements. An every-day example of the application of the osmotic theory to physiology is the following: The cells of the human body contain dissolved substances and have therefore a certain osmotic pressure. When a wound is washed with water, the cells, whose walls are " semipermeable," draw in water and burst, giving rise to continued bleeding. To avoid this the wound should be washed with a solution whose osmotic pressure is the same as that of the solution in the cells. Such a solution is the 2% solution of boric acid. If a 2% solution of NaCl were used, this would cause smarting, since NaCl is completely dissociated and has twice the osmotic pressure of the boric acid, which is practically undissociated. A i% solution of salt, the so-called " physiological salt solution," is there- fore used for cleansing wounds. Washing out the nose with water causes pain, but this may be avoided by the use of a 1% solution of common salt. A swimmer knows that it is unpleasant to open the eyes under fresh water, but in sea-water, which has nearly the same osmotic pressure as the solution in the cells of the eye, the eyes may be kept open for a long time without smarting. CHAPTER IV. CONDUCTIVITY. JUST as water strives to descend from a higher to a lower level, or as heat tends to pass from a higher to a lower temperature, so electricity tends to sink from a higher to a lower "potential." In these three cases the tendency is greater, the greater the difference in level, or in " potential," and consequently the quantity which falls in unit time is governed by the difference of potential. A quantity of water is measured in litres, a quantity of heat in calories, and a quantity of electricity in coulombs. The quantity of water flowing in a given time is governed by the size of the pipe through which the water flows, as well as by the difference in level. The quantity of water per unit of time is greater, the greater the cross-section of the pipe; and smaller, the longer the pipe. This quantity can be measured by determining the number of litres per unit of time which flows in at the top or out at the bottom of the pipe. This same amount must also pass any cross-section of the pipe in unit time. The amount of water is further dependent on the friction of the water against the material of which the pipe is made. In other words, it is directly proportional to the reciprocal of the value of this friction, which we might call the 77 78 ELECTROCHEMISTRY. conductivity for water of the pipe material. Exactly similar relations hold for the conduction of heat and of electricity. When two quantities of electricity which have a different potential are connected by a conductor, a certain quantity of electricity per unit of time will pass through the .conductor. This amount per unit of time, or current, will vary directly with the cross-section of the conductor and inversely with its length and with the friction which the material of the conductor offers to passage of the electricity. These relations are expressed in Ohm's Law : Amount of electricity in coulombs Eq Current = - J - = * = -i. . Time Iw In this formula E represents the impelling electromotive force, or difference of potential, q the cross-section of the conductor, / its length, and w is a value which varies from substance to substance, and expresses the resistance which each .substance offers to the passage of electricity. The current is therefore proportional to the electromotive force and the cross-section, and inversely proportional to the length and specific resistance, w is called the " specific resistance "; it is the reciprocal of the conductivity for the unit of cross-section and length, and is the resistance which a cube of the conductor i centimetre in thickness offers to the passage of the current. If we put 'a difference of potential of i volt on two opposite sides of this cube and find that the current flowing is i ampere, it follows from the above equation that the specific resistance of the conductor is i. The reciprocal of the specific resistance is the specific conductivity. The specific conductivity CONDUCTIVITY. 79 of a substance is i when a difference of potential of i volt will send a current of i ampere through a cube of the substance i centimetre in diameter. The specific resistance is then i ohm. A distinction was formerly made between good, bad, and medium conductors. This distinction, however, can- not be adhered to, since we have conductors of every order of magnitude. The following table gives the specific conductivity of a number of substances : SPECIFIC CONDUCTIVITY IN RECIPROCAL OHMS or A CENTIMETRE CCBE AT 18. K 18 is the specific conductivity; o ls = is the specific resistance; <7 18 '= K 10 ooo (T 18 gives the resistance of a wire i metre in length and i square millimetre in cross-section; a is the temperature coefficient; if T is the temperature, then <7 T =a ls [i + a:(T 18)]. The figures apply to pure soft metals. *1S- * ' a. Silver , , Copper + 0.0037 Aluminium 587 ooo Zinc 76 800 + 0.0037 Mercury 10 420 0.0000958 o. 13 0.958 + 0.00092 Manganine Nickeline Gas carbon * HoSO 30%. . 23 800 23 800 200 o . 000042 o . 000042 o . 0050 0.49 0.42 0.42 5 + o . 00003 + 0.00023 o . 00003 to o . 00008 Slate * . 1 oo o 000014 w. /^ Wood charcoal * ... Benzol * o . 00004 7 eVio- 10 26 ooo i 300 ooo ooc Hard rubber * ?. 5 Xio- 16 4Xio 15 Approximate values. Silver is the best conductor known, although copper, which is used most extensively, is not far behind. Alu- 8o ELECTROCHEMISTRY. minium, which has lately come into prominence as a material for power transmission cables, conducts only about half as well as copper, but has the advantage of lightness. Impurities in a metal always diminish its conductivity, consequently all alloys have a lower conductivity than the metals themselves. Thirty percent sulphuric acid has at 1 8 a conductivity of about f, at 40 of about i; i.e., a centimetre cube of sulphuric acid of this strength has a resistance of i ohm. A complete list of substances could be given whose resistances lie between those of nickeline and hard rubber, which shows that all degrees of resistance are possible. The temperature coefficient of the resistance of all the metals and most of the alloys is positive, i.e., the resistance increases as the temperature rises. In the case of practically all liquid conductors the temperature coefficient of the conductivity is positive, and in the case of water solutions its value would indicate a conductivity of zerjo at about 30. It is impossible to make a sharp distinction between good and bad conductors, but another very important distinction can be made. All conducting substances may be divided into two classes : the first includes all substances which remain unchanged by the passage of the current; in this class belong all the metals, practically all solid conductors and a few liquids. The second class com- prises all substances which are definitely changed by the passage oj the current; to this class belong the electrolytes, i.e., salt solutions and salts in a state of fusion. The rule has been proposed that a substance shows metallic conduction when the temperature coefficient of its conductivity is negative; electrolytic conduction hen the coefficient is positive. This rule, however, does CONDUCTIVITY. 8 1 not always hold, for gas carbon, which conducts like a metal, has a positive temperature coefficient of conductivity (or negative temperature coefficient of resistance). Cer- tain solutions show a negative temperature coefficient of conductivity. Even among the metals there are certain alloys which have a positive temperature coefficient of conductivity. The difference between the two kinds of conductivity will be clearer if we assume that in a metallic conductor the atoms touch each other, and there are everywhere present bridges over which the electricity may pass. In an electrolyte the dissolved substances which conduct the, current are more or less widely separated, so that if electricity is to pass from one atom to another these atoms must first traverse a certain distance in order to come in contact. A rise of temperature causes metals to expand and thus the contact between the atoms becomes less intimate and the resistance increases. In the case of electrolytes, however, the rise in temperature diminishes the friction to which the atoms are subject in their motions and the conductivity increases. Conductivity of Solutions. In the study of electrochemistry we have to deal princi- pally with solutions of salts in water, and we will therefore consider more closely the mechanism of the conduction of electricity through a solution. We saw on p. 58 that salts when dissolved in water dissociate into electrically charged ions. When two electrodes are connected with the poles of a battery so that one is charged positively and the other negatively and the electrodes dipped into a solution of any salt, the. 82 ELECTROCHEMISTRY. positive electrode exerts an attractive force on the nega- tively charged ions and a repelling force en the positively charged ions, while at the other electrode the positive ions are attracted and the negative repelled. As a result the negatively charged anions move to the positively charged anode and the positively charged cations go to the cathode. At the electrodes the ions are discharged; i.e., they neutralize a part of the electricity with which the electrodes are supplied, and either remain as neutral matter on the electrode or enter into further reactions. The charges on the electrodes which have been neutralized by the ions are of course immediately renewed by the battery. As a result of the pull exerted on the ions by the charges on the electrodes the ions move through the solution, and since -they themselves are electrically charged they thus transport a current through the solution. As was seen on p. 52, each gram equivalent of any ion always carries the same amount of electricity, 96 540 coulombs, i.e., the anions carry 96 540 coulombs of negative electricity per mol, and the cations the same amount of positive electricity per mol. When i mol of K' ions and i mol of CY ions pass through a plane perpendicular to the direction of the current in one second, then 2 X 96 540 coulombs are transported and the current strength is 193 080 amperes, since it makes no difference whether positive electricity moves in one direction or negative in the other. If instead of i mol i/iooooo mol passes through the plane per second the current is only 1.931 amperes. We must now consider the all-important question: What is the relation between the conductivity of an electro- lyte and the number and nature of the ions? CONDUCTIVITY. 83 Let us consider two metallic plates, serving as electrodes, placed parallel to each other at a distance of i centimetre ; between these we pour the solution to be considered. Since all the ions are either attracted or repelled by the electrodes, and since they all take part in transporting the current, the conductivity of the solution will be greater the more i;ms there are between the electrodes; two equivalents of the ions will give twice the conductivity of one equivalent.* The conductivity will also depend on the amount of electricity which each ion can carry; this, however, is the same for all ions since they all carry 96 540 coulombs per equivalent. Finally, the conductivity is dependent on the velocity with which the ions move, i.e., is conditioned by the different degrees of friction which the ions must overcome as they move through the solution. If we represent by L the conductivity of our solution, by r the friction, and by m the number of equivalents present, then mX 96540 If we represent by A the reciprocal value of r multiplied by 96 540, then when m=i, i.e., when we are dealing with i equivalent of the ions, L = A. A is called the equivalent conductivity. The equivalent conductivity of a salt is therefore equal to i when an electromotive force of i volt * " Gram equivalent," or simply "equivalent," is the number of grams of the substance obtained by dividing the atomic or molecular weight by the valence, i.e., it is mol (see p. 18) divided by valence. In other words, it is the weight in grams of a substance which carries a charge of 96 540 coulombs. The atomic weight of the bivalent element zinc, for instance, is 65.4 and its equivalent is 32.7 grs, 84 ELECTROCHEMISTRY. suffices to send a current of i ampere between two elec- trodes which are i cm. apart, when the solution be- tween the electrodes contains i gram equivalent of each ion of the dissolved salt.* In this definition no account is taken of the volume of the solution between the electrodes, the only provision is that they are i cm. apart. Whether the gram equivalent is present in a small or large volume of solvent the pull exerted on the ions by the electromotive force of the electrodes w r ill always be the same, and the same is true of their velocities and electric charges. What has just been said in regard to the salts can be applied to each kind of ion. The conductivity of any sort of ion will be high according as its concentration is high and the less the friction is which the ion has to overcome in moving through the water. Let k' represent the conductivity of the cation, m' the number of equivalents present, U its velocity (reciprocal of the friction), and 96 540 U = 1 ', and let &', m', V, and / ' be the corresponding values for the anion, then Conductivity of the cation =k' = m' Uq6 540 = m'l ', " " anion =k f = m'Vg6 $4o = m'l but k = ma(l ' + l '). Thus far we have not considered any particular volume of solution between the electrodes. The specific con- ductivity of our solution (cf. p. 79) is ic = , where q is the cross-section. Since in this particular case / = i, the volume of the solution, v = q and k = KV. Further, the con- centration in mols per c.c. is v or or if 7) = i mol per c.c., A^ is called the equivalent conductivity of the salt for the concentration i). This equation is used very often to determine the degree of dissociation. We measure the specific conductivity of the solution and divide this by if the equivalent concentration of the solution, i.e., - = A v and CONDUCTIVITY. 87 this gives the equivalent conductivity. We then introduce the values for / ' an d /o' from the table mentioned on p. 85 and obtain A is the equivalent conductivity of the salt when it is completely dissociated into its ions. From what has been said it is clear that the value of AQ = I Q ' + IQ can only be found when a = i; that is, when all the dissolved molecules are dissociated into their ions. Such solutions, however, do not exist in reality, since the reaction of dissociation is incomplete and proceeds until a state of equilibrium is reached. Nevertheless the law of the independent wandering of the ions holds for solutions when dissociation is net complete. Dissociation is, in a way, an additive property, and there is a law of independent dissociation of the ions which, while not as exact and of such general application as the other, is still of great use in calculation. It states that the degree of dissociation of a dissolved substance may often be calculated from numbers which are peculiar to each ion. From the two laws it follows that the values of a/ * and a/o' are definite for a given concentration. Let al Q ' = lc and alrf = l c ' be the conductivities of the ions at the concentration c and we obtain for the equivalent conductivity at the concentration c: i.e., the equivalent conductivity at the concentration c is equal to the sum of the conductivities of the ions. It must always be kept in mind that the degree of dissociation 88 ELECTROCHEMISTRY. is always included in the values of l c ' and / ^Ag> fa> ^NO 3 , and without further data the single values cannot be found. The fifth necessary equation is furnished by measuring the " transport number," which gives the value of V For the transport number of KC1, fa IK + lei The value 0.503 has been found by experiment. * Kohlrausch and Holborn, Leitvermogen des Elektrolyt. Teubner, Leipzig. f The letter n means "normal." o.i n is tenth normal; 3 n is three times normal; etc. CONDUCTIVITY. From this, and from the conductivity of a normal KC1 solution, A KC i = lK + l C i = ()8.2 ) the value of / C1 is found to be 49.4. With the help of this figure we obtain the following values for the conductivities of the five unknown quanti- ties IK /Cl /Na /N0 a /Ag 48.8 49.4 25.0 41.0 26.8 In exactly the same way the values for / may be found for other concentrations, for instance, for o.oi n they are 61.3 62.0 40.5 56.8 51.9. It must not be forgotten that these numbers represent not the velocities of the ions alone, but the velocities multiplied by the degree of dissociation. In order to determine the values of / * and / ' we must t- 1 Concentration Dilution FIG. 6. know the value of A Q . This cannot be measured directly, since dissociation is complete only at an infinite dilution. If we plot the value of A in its dependance on the con- centration we obtain a curve similar to Fig. 6. In this the abscissae represent the dilution and the corresponding equivalent conductivities are plotted as ordinates. As 90 ELECTROCHEMISTRY. the dilution increases the curve approaches asymptotic- ally a maximum which we cannot reach experimentally, but which may be found by extrapolation. In this way it is possible to determine the value of A Q . Since the transport number remains essentially the same for all concentrations we may use the value found to calcu- late /o, l f =nA and A /o'=/o". Pure substances conduct poorly: the specific con- ductivity of ordinary distilled water at 18 is about io" 6 . But even this low conductivity is not the conductivity of pure water, but is due almost entirely to small amounts of dissolved substances. Although the amount of these dissolved impurities may be so small as to escape any chemical tests, still they have a very marked influence on the conductivity. Glass may be dissolved to a very slight extent Dy water, also carbon dioxide from the air when dissolved in water furnishes ions which may impart a marked conductivity to the water. By very careful distillation and other methods, Kohl- rausch was able to obtain water so pure that its specific conductivity was only 0.0384 Xio~ 6 . Probably a part of even this low figure is due to dissolved impurities, but in any case not a very large part, as the following calcula- tion shows: From the specific conductivity K ( = recip- rocal of the resistance of a centimetre cube of water) and the values of the velocities of the ions H* and OH', we obtain as the number (m) of H' and OH' ions in i c.c. of this water m = o. f jSXio~ w . In i litre, then, the CONDUCTIVITY 9 1 concentration of H* and OH' ions is o.ySXio" 7 at 18. The fact that several other methods for determining the value of this concentration have given as an average 0.78 Xio~ 7 at 18 proves that 0.0384X10" must be very nearly the actual conductivity of absolutely pure water, A number of other pure substances behave in a similar way at ordinary temperatures. They have a very low conductivity and consequently can contain very few ions. For instance, pure anhydrous sulphuric acid is very weakly dissociated according to the scheme when the two pure substances H 2 O and H2SO4 are mixed; i.e., if H 2 SO4 is dissolved in water, the resulting solution conducts more or less readily. According to the views developed in the preceding pages, the reason for this is that the pure substances alone contain very few ions, but mixing or dissolving the two sub- stances in some way gives rise to the formation of a large number of ions. An instructive example of this general fact is furnished by the conductivity of sulphuric acid of different strengths. The accompanying curve (Fig. 7) shows the relation between the concentration and conductivity of H 2 SO 4 , conductivity being plotted on the vertical axis and con- centration on the horizontal. At the concentration zero, i.e., in pure water, the con- ductivity is practically zero. As the concentration of H2SO4 increases, the conductivity increases rapidly and at 32% reaches a maximum. It then falls off until at 82% a minimum is reached, the solution at this point having a composition corresponding to the formula H 2 SO4-H 2 O. 2 ELECTROCHEMISTRY. This monohydrate is to be considered as a comparatively poor conductor. When more sulphuric acid is added the curve rises again (the following solutions may be considered as a solution of H 2 SO 4 in the hydrate, H 2 SO 4 -H 2 O), at 92% reaches a maximum and then falls off practically to o at 100%. If SO 3 is added to the anhydrous H 2 SO 4 a 10 .20 30 40 50 60 70 80 90 100 FIG. 7. new curve with another maximum is obtained, as shown in the figure above 100%. Solutions of all other conducting substances behave in a similar way, although frequently the solubility is not high enough to allow the maximum conductivity to be attained, as the curve for NaCl shows (Fig. 7). The more soluble LiCl, however, shows the maximum. The question now arises, does a conducting solution, i.e., one containing many ions, always result from the mixture of two different substances? This must be answered in the negative. The dissociation depends on the nature of the two components of the solution. Water possesses the property of forming with most of the CONDUCTIVITY. 93 acids, bases, and salts solutions which conduct very well; i.e., it compels the dissociation of these substances. We say that water has a great "dissociating pow r er"; but all substances dissolved in it are not necessarily dis- sociated. For instance, sugar, urea, boric acid, and many organic substances when dissolved in water give non-conducting solutions, which therefore contain no ions. Another class of substances, the alcohols, are good solvents, though by no means as good as water; their solvent power decreases with an increase in molecular weight. Liquid ammonia is almost as good a solvent as water; it dissolves many substances and gives solutions which conduct very well. In order to compare solvents with respect to their dissociating power two points must be kept in mind. The conductivity of a solution is dependent not only on the degree of dissociation of the dissolved electrolyte but also on the resistance or friction which the ions must overcome in moving through the solution. A solvent of low disso- ciating power may give a solution of higher conductivity than a second solvent whose dissociating power is greater. If the friction which the ions have to overcome in one solution is low enough, this may more than compensate for the larger number of ions in the other solution. Water and liquid ammonia are two such solvents: the first possesses the higher dissociating power, but the latter presents much less resistance to the movements of the ions, as might be expected from the mobility and volatil- ity of liquid ammonia. Nernst has proposed the following explanation of the ability of different solvents to dissociate dissolved salts 94 ELECTROCHEMISTRY, into the ions. The electrostatic attraction of the oppositely charged ions must evidently tend to diminish the dissocia- tion of a given salt, and acts in opposition to that force which strives to dissociate the compound, and whose nature is as yet entirely unknown. The rivalry between these two opposing forces regulates the actual equilibrium of dissociation. The dissociation must therefore increase if the electrostatic attraction is diminished. The study of static electricity has shown that two bodies having opposite charges of electricity attract each other with a force which varies inversely with the dielectric constant of the medium which surrounds the bodies. According to this view those solvents which have the highest dielectric constant must have the highest dissociating power. This rule, which was proposed simultaneously by Thomson and Nernst, holds very well in most cases, as is shown by the following table of Nernst.* Medium Dielectric Constant Electrolytic Dissociation Gases I .0 Immeasurable at ordinary temperature Benzol 2-3 Conductivity extremely low, very slight dissociation indicating Ether 4.1 Perceptible conductivity of electrolytes dissolved Alcohol 2 S Moderate dissociation Formic acid 62 Strong dissociation Water 80 Very strong dissociation * The values of the different dielectric constants and a table showing the relation between the dissociating power and a number of the physical properties of the different solvents will be given in Book II. CONDUCTIVITY. 95 Apparently most of the physical properties of solvents, such as " association," dissociating power, etc., are in some way connected. Dutoit and Aston have found that solvents with a high dissociating power are in general inclined to polymerization in the liquid state. Polymeri- zation is generally noticed in the case of substances which contain an element of variable valence, such for instance as NH 3 , which contains the tri- or pentavalent element N or H 2 O, which contains the di- or tetravalent element oxygen. The occurrence of these elements in a compound therefore would seem to be connected with the dissociat- ing power. Aside from the dissociating power and internal friction there are other influences at work concerning whose nature we are completely in the dark. Formic acid, for instance, has a dielectric constant of 62, and accordingly should have a high dissociating power, nevertheless HC1 dissolved in formic acid gives a practically non-conducting solution, although salts like NaCl, KBr, etc., conduct very well in formic acid. In this case the hydrochloric acid probably unites directly with the formic acid and is therefore unavailable for conducting purposes. In gen- eral the dissociation depends not only on the solvent but also on the nature of the dissolved substance. The tendency of the different elements and 'radicals to take up an electric charge a tendency which makes itself evident in the electromotive force of the elements and the ease or difficulty with which they may be deposited on an electrode, plays an important part in determining the relative dissociation. The tendency of elements to pass into the ionic condition is closely related to the general chemical properties of the elements, and thus the degree 9 6 ELECTROCHEMISTR Y. of dissociation becomes an important factor in determining the chemical activity of a dissolved substance. We must therefore consider the relations of dissociation somewhat more fully. As we have seen on p. 87, the degree of dissociation is calculated according to the equation a. = f. The folio w- ^o ing table shows how the degree of dissociation of certain typical electrolytes when dissolved in H 2 O changes with the concentration. C= l/V o w O M o M o & HN o % W HM 1 S3 HH HOOD HO O ED O.OOOI 0.99?* 0.990 0.992 0.992 0.989 0.308 0.28 O.OOI 0.992 0.998 0.979 -973 0.962 o-959 0.890 0.118 o. 119 O.OI 0.974 -973 0.941 0-931* 0.886 0.873 0.664 0.041 0.041 O. I 0.924 0.860 0.861 0.830 o-759 0.713 0.418 0.013 0.014 I 0.792 0.786 -755 0.628 o-579 o-534 0.241 The first vertical column contains the concentration c (reciprocal of the dilution), the others contain the degree of dissociation of the different substances at these particular concentrations. HC1 is dissociated the most, and the dissociation of the other strong monobasic acids as HNO 3 , HC1O, HBr, HI, etc., follows that of HC1 closely; the bases NaOH. KOH, LiOH, T1OH, etc., are also just as highly dissociated. The i : i salts are slightly less dissociated; still less the 1:2 salts, while the 2:2 salts like ZnSO 4 are the least dissociated.* * By a i : i salt is meant one derived from a monobasic acid and a CONDUCTIVITY. 97 The strength of the acid and base from which the salt is derived has considerable influence on the degree of dissociation. The K salt of the weak acetic acid is less dissociated than the corresponding salt of the stronger hydrochloric acid. This fact is still more evident when we compare the acids and bases themselves, for instance, acetic with hydrochloric acid: ammonia with potassium hydroxide; etc. Since the H* ion is common to all acids and always has the same tendency to take up an electric charge the difference in the degrees of dissociation can only be due to the fact that chlorine has a much higher tendency to pass into the ionic condition than the acetic- acid radical, i.e., it has a higher " electro-affinity." Strength of Acids and Bases. The degree of dissociation is of the highest importance in determining the chemical activity of an acid or base. The common characteristic of all acids is the formation of H* ions in a water solution, consequently in all re- actions which may be brought about by any acid and which therefore depend on the presence of the H* ion, the concentration of the H* ion is of decisive importance. In a similar way the common property of all bases is their ability to form OH' ions in a water solution, consequently the bases will act more vigorously according as their degree of dissociation is high or low. The strength of a base or acid makes itself felt in the reaction of distribution. If we add to a solution of NH 3 monacid base; 1:2 are derived from a monobasic acid and diacid base, or vice versa, as BaCl 2 , or Na 2 SO 4 , etc. 2:2 are such as ZnSO 4 , MgCO 3 , etc. 98 ELECTROCHEMISTRY. and KOH an amount of HC1 which is less than sufficient to neutralize both bases, this acid will be distributed between the .two bases. Both potassium and ammonium chloride will be formed, but more of that salt whose base is the stronger. In the same way a base is distributed between two acids, so that the larger part falls to the lot of the stronger acid. Further, if we add to the salt of a weak base, such as NKUCl, the stronger base KOH, a redistribution of the HC1 takes place, the KOH takes the acid from the ammonia, the latter is set free and may be driven out of the solution by boiling. Still further, if we add hydrochloric acid to a solution of sodium acetate the HC1 displaces the acetic acid. In all these cases, however, the displacement takes place only till a state of equilibrium is reached, and this equilibrium is determined by the value of the dissociation constants of the acids and bases.* It has been found that the ratio of distribution is equal to the ratio of dissociation of the two acids or bases at the dilution in question. The strength of an acid also makes itself felt in a certain class of reactions which are " catalytically " ac- celerated by the presence of H* ions. Such a reaction is the inversion of cane-sugar into levulose and dextrose, which causes a good deal of trouble in the refining of sugar, since the two resulting compounds are very hard to crystallize. The reaction proceeds very slowly in a neutral solution, but is greatly accelerated by the presence of acids. This catalytic * For the relation between the dissociation constant and the distri- bution, cf. Nernst, Theoretische Chemie, 1903, p. 506. CONDUCTIVITY 99 acceleration is greater according to the number of H* ions which a given acid can supply; in other words, the acid accelerates this reaction more or less according as it is ( strongly or weakly dissociated. If the acids are arranged in the order of their conductivity this same order represents also their relative activity in accelerating the inversion of sugar. A similar case is furnished in the decomposition of the ester: CHaCOOCsH,, + CH 3 COOH + C 5 H lo . This reaction is accelerated to a different degree by strongly and weakly dissociated acids. The strength of a base regulates the velocity of the reaction of saponification. The higher the dissociation of a base the faster it will saponify the ethereal salts of the fatty acids. As yet we have considered the connection between the dissociation and strength of an acid or base only in a qualitative way. How can we obtain definite quantitative relations ? The law of mass action applies to the reaction of disso- ciation, as it does to all reactions. If we write the equation for the dissociation of acetic acid, CH 3 COOH ?=* CH 3 COO+H', and apply to this the mass-action law we have c a represents the concentration of the undissociated molecules and Ci that of the ions. (In any solution the concentration of the two different kinds of ions must 100 ELECTROCHEMISTR Y. necessarily be equal.) K is the dissociation constant. If the value of K is known for any acid or base the value of the dissociation may be at once calculated for any dilution, and also the conductivity, if the values of / ' and / ' are known, van't Hoff and Reiche give the following table for acetic acid: MOLECULAR CONDUCTIVITY OF ACETIC ACID AT 14.1. V A v iooa Observed rooa Calculated 0.994 1.27 0.402 0.42 2.02 1.94 0.614 0.6o 15-9 5-26 1.66 1.6 7 18.9 5.63 I. 7 8 I. 7 8 K= 0.0000178 1500 46.6 14.7 JS- log #=5.25-10 3010 64.8 20.5 20.2 4)= 316 7480 95-i 3 O.I 30.5 15000 129 40.8 40. I [ 316 100 100] The first column contains the dilution in litres per mol, the second the observed molecular conductivities A v , the third the value of a calculated from the conductivity measurements by means of the formula cc = -~. In the ^o fourth column are the values of a calculated from the equation Kv(i a)=a 2 , using 0.0000178 as the value of K. The equation c s = Kci 2 is identical with this since c 8 = - and c\= . In regard to the physical signifi- cance of K the following may be said: in the case of a binary electrolyte (i.e., one which dissociates into two ions) K is equal to half the concentration at which the electrolyte is 50% dissociated.* * This is readily shown by substituting 0.5 for a in the equation. CONDUCTIVITY. 101 Strange to say, this law, which was first derived by Ostwald and is known as the Ostwald dilution law, holds only for electrolytes which are weakly dissociated. It does not at all fit the case of highly dissociated salts. A possible reason for this is the following: in calculating the dissociation we tacitly assumed that the mobilities of the ions V and / Cd 2 Cl 2 " + Cl' + Cl' 3 ', etc. This polymerization of the molecules is the cause of many of the deviations from the laws of solutions. CONDUCTIVITY. 107 Conductivity and Temperature. The temperature has a great effect on the conductivity of the electrolytes, and the temperature coefficient is practically always positive, i.e., the conductivity increases as the temperature rises. Two causes must be dis- tinguished. , The dissociation of most salts decreases as the temperature rises, and this decrease though generally small should lower the conductivity. On the other hand, the mobility of the ions is much increased and this tends to increase the conductivity. The temperature coefficient of most salts hi water has such a value that at about 30 the conductivity would be zero. Since the fluidity of water (reciprocal of the internal friction) follows a temperature formula which also gives zero as the value for 30, it seems clear that the influence of temperature on the conductivity is due to the effect of the temperature on the internal friction of water. At ordinary temperatures the temperature coefficient of dilute solutions of salts is from 0.02 to 0.023, i- e -> tne con " ductivity is raised by 2 2.3% for i degree rise in tempera- ture. For acids and some acid salts the coefficient is 0.009 to 0.016, for alkalies it is 0.019 to 0.02. The temperature coefficient depends but little on the concentration. In nearly all cases it decreases slightly as the concentration rises, and then rises again at higher concentrations. With certain salts such as the chlorides and nitrates of K and NH4 the decrease persists even in the stronger solutions.* * A classic work on the conductivity of the electrolytes is the book by Kohlrausch and Holborn, published by Teubner of Leipzig, which Io8 ELECTROCHEMISTRY. The high temperature coefficient of substances which conduct electrolytically is of especial importance in the case of solid salts. At ordinary temperatures these are practically non-conductors, but at higher temperatures the conductivity increases greatly, and salts in a state of fusion are among the best conductors. Even solid substances when highly heated may show considerable conducting power. A good example is furnished by the " glower " of the Nernst light. The Transport Number. We will consider first a binary electrolyte, say NaCl. If we send a unit quantity of electricity through this solution both ions take part in transporting the current? and since the concentrations of the two ions are equal and the pull exerted by the electrodes is the same for both, the part taken by each in the conduction will be proportional to the velocity of the ions. If E' is the quantity of elec- tricity transported by the anion and E' the part transported by the cation, then E'+E' = E and E':E' = V:U, where U and V are the velocities of the cation and anion respectively. We then obtain E':E=V:U+V and E':E=U:U+V. The phenomena attending the passage of the current will be better understood from Fig. 8. A tube which is divided into three compartments by two porous dia- phragms contains at one end the anode and at the other contains the theory of the methods of measurement and extended tables. CONDUCTIVITY. 109 the cathode. At first the electrolyte has the same con- centration throughout the tube as is indicated by the upper series of signs. Every sign represents a gram- molecule of salt, the + signs represent the cations, and the signs the anions. Let us assume that the velocity of the cation is to that of the anion as 5:3. We send 16 F* through the solution, which results in the separation of Before Anode Diaphragms FIG. 8. Cathode 1 6 mols of cations at the cathode and 16 mols of anions at the anode. In the actual transporting of the current the ions take part in the ratio of their velocities, i.e., E-:E' = icF: 6F E".E = ioF:i6F E':E = 6F:i6F. While the + ions all move 5 units of length in one direc- tion the ions move 3 units in the other. The final distribution is shown by the lower series of signs of Fig. 8. It is seen that 16 mols have been set free at each electrode, the concentration in the middle compartment * In honor of Faraday the charge on i gr. equivalent of ions or 96 540 coulombs is represented by F. i 1 o ELECTROCHEM1S TR Y. remaining unchanged, while that in each electrode com- partment has changed to a different degree. The changes in the salt concentration in each of the electrode com- partments are to each other as the velocities of the ions which have left those compartments. In this case the change at the cathode is to the change at the anode as the velocity of the anion is to the velocity of the cation cr as 3 is to 5. The value of -^ can therefore be found by sending a known quantity of current through a suitable form of apparatus and determining before and after the concen- trations in the electrode compartments. The fact that the concentration in the middle compartment does not change is a proof that diffusion has not influenced the result.* The above method only applies when the ions are precipitated or otherwise removed from the solutions. If instead of the ion which has transported the current, some other ion is set free, it is necessary to calculate by Faraday's law (p. 52) how much of the first ion should have been removed by the electrolysis and subtract this from the concentration found before we can tell how the concentration has been affected by the wandering of this ion. If the original concentration is c, and the concentrations after electrolysis are c' at the cathode and c f at the anode, so that the losses at the electrodes are c c' and c c f respectively, then V:U=c-c':c-c f . * For more detailed information concerning the methods of measure-* W ent and calculation of re^ul^ cf, 5Q9fe JJ, CONDUCTIVITY. ill U: V is the ratio between the velocities of the two ions. Hittorf (1856), who was the first to investigate this subject, V called the fraction ,. ,y ==n the "transport number of V U the anion." Since ,, v and rr, v together are equal to one, =in is the transport number of the cation. With the help of this new term we may now summarize the most important formulae concerning the conductivity of an electrolyte. If y represents the concentration in mols per c.c., a the degree of dissociation, then a y is the concentratiorrbf the ions and the specific conductivity K is K =arjF(U+V). Putting 1 ' = FU and 1 Q ' = FV (cf. p. 84), then K=ar)(l '+I '). Now the molecular conductivity is A = and we obtain A = a(lo'+lo). At very great dilutions a = i, conse- quently if we represent by A the molecular conductivity at extreme dilutions then AQ = IQ'+IQ'. l ' = nA and I Q ' = (I n)A . These last equations are the mathematical expression of Kohlrausch's law of the independent wandering of the ions, H2 ELECT ROCHE MIS TR Y. Absolute Velocity of the Ions. The velocities or mobilities /' and /' are based on the ohm as the unit of resistance (cf. p. 79). In order to obtain U and F, the acutal velocities in centimetres per second with which the ions move in a field where the fall of potential is i volt per centimetre, we must remember that each gram equivalent of ions carries with it 96 540 coulombs, and since the conductivities V and /. For the vacuum DC = i and is but slightly greater than i for the different gases. In water the attraction is -gV of that in a vacuum, i.e., the dielectric constant of water is 80. The capacity of a condenser, i.e., the quantity of electricity which it is necessary to add in order to give the two plates a difference of potential of i volt, varies directly with the dielectric constant of the medium which occupies the space between the two plates of the condenser. If c is the capacity when air is used, the capacity is cDC * For details cf. Book II. 1 1 4 ELEC TROCHE MIS TR Y. when a substance whose dielectric constant is DC is used. According to the theory of electric vibrations the velocity with which electric waves travel along wires varies inversely as the square root of the dielectric constant of the surrounding medium. The methods of measuring the dielectric constant are founded on these two laws. The quantity of electricity is measured which is necessary to charge a given con- denser; this is best done by the use of the Wheatstone bridge. Or the deflection of the needle of a quadrant electrometer is observed once in air and again in the medium in question, and thus the difference in the force of attraction between the needle and the quadrants is directly determined for the two media. Another method, worked out by Drude, depends on the determination of the length of electric waves along wires surrounded by different media. A table of the values of the dielectric constants of a number of substances which can be used as solvents for electrolytes will be given in Book II, and also a more complete description of the methods of measure- ment. CHAPTER V. ELECTROMOTIVE FORCE AND THE GALVANIC CURRENT. To aid in forming a clear idea of the relations between current and voltage we will make use of an illustration, although this illustration, like all comparisons, does not hold at all points. Suppose we have an air-tight ring-shaped tube filled with air. At a point A in Fig. 9 we place a pumping arrangement which draws in air on one side and expels it on the other. As a result a partial vacuum is created to the right of the pump and the pressure of the air on the other side is raised. The air seeks to equalize this difference in pressure by flowing around through the tube from left to right, and the pump strives to keep up the difference in pressure. As a result a stationary condition is arrived "5 FIG. 9. n6 ELECTROCHEMISTRY. at when the quantity of air flowing around through the tube from left to right is the same as that brought over by the pump- from right to left. From right to left along the tube the difference in pressure gradually falls off, as is indicated in the figure by the different lengths of the arrows. In the narrow part of the tube where the air finds the greatest resistance the pressure falls off most rapidly. If the tube is closed at any point the pump continues working for a short time and forces air over till the difference in pressure between the ends of the tub e is the same as the pressure which the pump can exert. Let us now take, in place of the tube, a wire through which electricity can flow, and replace the air-pump by an electricity pump which takes in positive electricity on one side and gives it out on the other (or what amounts to the same thing, gives out positive electricity on one side and negative on the other). For this purpose we may use a battery or a dynamo. In the first illustration the air pressure on the left was raised and on the right lowered; in this case also the electric pressure, or " potential," is raised on the left and lowered on the right. The electricity seeks to equalize this difference of potential by flowing around through the wire, while the battery strives to maintain the constant difference of potential. The potential falls off along the wire from the left pole around to the right, and it decreases most rapidly at those points where the electricity finds the greatest friction, i.e., where the resistance of the circuit is highest. If we cut the wire at any point so that elec- tricity can no longer flow, the battery still continues to work for an instant, but only until the difference of potential between the ends of the wire is the same as the ELECTROMOTIVE FORCE AND GALVANIC CURRENT, electromotive force of the battery. The amount of electricity which is necessary to bring the ends of the wire up to this potential is known as the capacity of the wire; the capacity is equal to one, when i coulomb is required to give a difference of potential of i volt. If the circuit is closed so that a current can pass, Ohm's law applies to every portion of the circuit (cf. p. 78). If s is the difference of potential between any two points, w the resistance, and i the quantity of electricity passing per second, then e = iw. If, in Fig. 10, P and P_ e represent the poten- tials on the left- and right-hand sides of the battery when the circuit is open, so that P -P_ e represents the electromotive force of the battery, then the potential will gradually fall off along the wire from P e to P_ when the circuit is closed. Let the potential at different points along the wire be FIG. 10. and let the value of each be indicated 'by the length of the arrow. PQ represents the original potential of the wire before the battery was attached and the direc- tion of the arrows shows whether the potential at any point is higher( \ ) or lower ( j ) than at P . If the electromotive force at the terminals of the battery (represented by P and P_4 in Fig. 10) is measured while the battery is in action we no longer 1 1 8 ELECTROCHEM1STR Y. obtain the true electromotive force of the cell P P- e , since part of the voltage is used in sending current through the cell itself. This loss of voltage in the battery is given by i=iwi, where w\ is the internal resistance. If the measurement is made when the circuit is open, when i = o then 1 is also zero and we obtain the true electromotive force P e -P_ of the battery. In measuring the electromotive force of a cell, then, we obtain the true value only when no current is flow- ing. A value slightly smaller is obtained when the current is very low, and for this reason all voltmeters are made with a high resistance. If any appreciable current is taken from the cell the voltage measured at the terminals may be much lower than the true voltage of the cell, and the error will be larger the greater the internal resistance of the cell. Contact Electricity. A difference of potential is always present when two different substances are brought in contact and the surface of contact is the seat of the electromotive force. Positive electricity is taken from one substance and collected on the other, or, what amounts to the same thing, one substance becomes charged positively, the other negatively. Chemical reactions are undoubt- edly the cause of this contact electricity, but their nature has not been determined in all cases. The amounts of substance which enter into chemical reactions under these circumstances are so excessively small that the quantity of electricity produced is also very small. It is a well-known fact that when one substance is rubbed with another, both become electrified (frictional ELECTROMOTIVE FORCE AND GALVANIC CURRENT. 119 electricity). When sealing-wax is rubbed with a piece of wool the wool becomes positively electrified ; when glass is rubbed with silk, the silk becomes negatively charged. No simple law without any exceptions has yet been discovered with regard to contact electricity. Sub- stances may, however, be arranged in a series so that a body rubbed with any of those following it in the series becomes positively charged; the charges so pro- duced are larger the farther apart the substances stand. Such a series is the following: glass, wool, silk, wood, .metal, amber, hard rubber, sulphur, shellac, sealing- wax. Coehn has discovered a law which seems to have pretty general application: When two substances are brought in contact, the one whose dielectric constant is higher becomes positively electrified. Since contact and frictional electricity are of very little importance in chemistry on account of the very small amounts of electricity concerned, we will only mention one fact in this connection, which has lately become of technical importance. If we suspend in water some very finely divided material such as powdered glass, precipitates, dyes, peat, etc., and introduce two electrodes which are connected with a source of elec- tricity, we find that the particles which become nega- tively charged are attracted to the cathode and deposited there. This movement of the suspended particles is called " Endosmosis " or " Cataphosesis." If an electric current is sent through peat mud, the positively charged water moves to the negative pole, and this fact may be used for expelling water from peat. On the other hand, water when pressed through a porous diaphragm carries positive electricity with it, and so gives rise to a current. I2O ELEC TROCHE MIS TR Y. Galvanic Production of Current. If we wish to obtain larger quantities of electricity (without using a dynamo) we must use some arrange- ment in which the chemical energy of large quantities of material is converted into electric energy. This can be done by using a galvanic cell. The early experiments of Galvani on the twitching of a frog's nerve under the influence of electric-spark discharges showed that those same movements also occurred when two metals touched each other and also the nerve. Galvani wrongly attributed this to an electric force in the nerve itself. Volta found, how- ever, that the twitching did not occur when the same metal touched the nerve at two points, but that two different metals were necessary. His classic experi- + Cu , , Zn Cu u z - ; 1 ** Zn Cu FIG. ii. ments showed further that two metals and a simple salt solution are sufficient to produce a current. He believed that the force producing the current lay at the junction of the two metals, but found further that a series of metals connected one with another could give no current in the absence of moisture, although they became electrically charged. On the basis of his discoerievs ELECTROMOTIVE FORCE AND GALVANIC CURRENT, 121 Volta built his well-known Voltaic Pile, which consisted of a number of pairs of Zn and Cu plates having between each pair a pad soaked in ordinary salt solution. One end of this arrangement he found was strongly charged with positive electricity and the other end with an equal amount of negative. The production of electricity is due to a reaction between the solution and the zinc, which becomes oxidized. This " pile," like the battery shown in Fig. n, rapidly loses its electromotive force when current is taken from it. Volta placed in each of a number of beakers a strip of copper and one of zinc, filled the beakers with dilute sulphuric acid and connected each copper with a zinc pole as shown in Fig. ii. The electromotive force of this battery falls off rapid- ly, since hydrogen is evolved on the copper. The reaction which furnished the current is In order to avoid the evolution of hydrogen Daniell used a com- bination of two metals and two solutions, forming the well-known Daniell element. A porous porce- lain cell is filled with a solu- tion of copper sulphate and in this is placed a rod of copper; FlG - I2 - this cell is then placed in a solu- tion of ZnSO 4 contained in a glass jar and a zinc rod is 122 ELECTROCHEMISTRY. placed in the ZnSO 4 .* When the two metals are con- nected by a wire electricity flows through the wire from the copper to the zinc. The reaction which occurs in the Daniell cell is or written in the ionic form, Zn+.Cu" -Cu+Zn". Copper is displaced from its salt by zinc; the zinc passes over from the metallic state into the state of ions, and copper passes from ions into the metallic state. The arrangement of the above cell Zn/ZnSO 4 - CuSO 4 /Cu shows that at the left position ions go into solution and at the right position ions are precipitated, and thereby just as much positive electricity is taken away from the zinc electrode as is given up to the copper electrode. This process goes on, before the circuit is closed, until the electrostatic attraction or repulsion between the electrodes and ions prevents any more ions from enter- ing or leaving the solution. The process* therefore stops as soon as the electromotive force between the electrodes corresponds to the energy of the reaction. In the case of the Daniell cell the difference of potential between the electrodes is about i . i volts. * In Fig. 12 is shown the arrangement of a Bunsen cell, which is similar to the Daniell except that in place of copper in copper sulphate a carbon rod in HNOs is used. A number of other cells, with the reactions taking place in them, will be given in Book II. ELECTROMOTIVE FORCE AND GALVANIC CURRENT. 123 As soon as the electrodes are connected by a wire, the two kinds of electricity flow through the wire and unite. The chemical reaction seeks to maintain the two electrodes at a difference of potential of i.i volts, so that an uninterrupted current flows through the wire from copper to zinc. Calculation of Electromotive Forces. The electromotive force of a chemical reaction can only be calculated in such cases where the process is a reversible one (see p. 12); that is, when the chemical energy is converted entirely and without loss into elec- trical energy. The various formulae no longer hold when insulation is faulty, or when unknown secondary chemical reactions are involved. A chemical reaction is reversible when it can be made to go backward and the system be restored to its original condition by the exact quantity of electrical work which the reaction has furnished. The process at an electrode of Cu in CuSCU is reversible. If we send current through the electrode in one direction, copper is dissolved according to the scheme Cu > Cu". If current is sent in the opposite direction copper is precipitated : Cu " > Cu . The reaction at an aluminium electrode, Al Al"', is not reversible, because the reverse reaction, Al"' >A1, does not take place in a water solution. Aluminium cannot be deposited on an electrode by the electrolysis of a water solution of an Al salt. The H* ions are dis- charged instead.- 1 24 ELECTROCHEMISTRY. We saw on p. 10 that there is a relation between the heat of a reaction and its electromotive force. If the formula which was derived, is true of any given reaction, then we may be sure that our experimental arrangement fulfils the condition of reversibility. In order to use this equation in electrical calculations it must be remembered that the transfor- mation of i gram equivalent of any metal into ions results in the production of 96 540 coulombs of electricity. In the case of the Daniell cell, where the elements Cu and Zn are divalent, 2 Xg6 540 coulombs are produced for every atomic weight in grams of zinc which is dissolved. When 2 X 96 540 coulombs pass through the cell 65.6 grs. of Zn are dissolved and 63.6 grs. of Cu are deposited. The work done by the cell is therefore coulombs X vol- tage E (cf. p. 6), and A =96 540 nE, where n is the valence. Consequently E = ~- + T^ 96540^ dT This is the well-known Gibbs-Helmholtz equation. Another method of calculating the electromotive force of chemical reactions is furnished by van't Hoff's energy equation (p. 31). Copper is precipitated from the solution until equilibrium is reached. If Ci represents the concentration of the Zn ions, c^ that of the Cu ions ELECTROMOTIVE FORCE AND GALVANIC CURRENT. 125 in the cell at the start, and if the concentrations of Zn" and Cu" are c 0l and c 0z after equilibrium is reached when practically all the Cu has been removed from solution, then van't Hoff's equation gives If n is the valence of the reaction (in this case 2) we obtain #96 I Substituting the value of R in watt-seconds, = 8.3 167 (cf. p. 5), and changing the natural to the Briggs logarithm by multiplying by 2-3026 we have n 96 5403 = 8.3167 X2.3026T log a .22S23 r i og For the ordinary temperature of 18 (T = 273 + 18) we have The values of c 0l and c 0z are called the equilibrium concentrations of the ions. They may be determined if we allow the reaction to continue till it stops of itself, and then measure the different concentrations. In most cases, however, our chemical methods are not delicate 126 ELECTROCHEMIS TR Y. enough, for many reactions go on until one of the sub- stances seems to entirely disappear. The ratio of the two concentrations J2i, however, may > a often be determined by electrical methods; for example, by measuring the electromotive force when the con- centrations c\ and 2 are known. ILLUSTRATION: If the concentrations of Zn and Cu ions are made equal to i, or if they are simply made equal whatever their values, then c\ and c 2 cancel in the equation and we have 1 b c 02 E has been found to be i.i volts, so that log -^- =38 c C z or -^- = io 38 ; that is, when we put zinc into a solution of CuSO 4 the copper will be precipitated until the concentration of the zinc ion is io 38 times that of the remaining copper ions. For all analytical purposes this precipitation is absolutely quantitative; but theoretically this small remainder is of very great importance, since otherwise the energy of this reaction would be infinite. As a second example we will calculate the electro- motive force of a Daniell cell in which c\ = i and c% = o.ooi ; then we have = 0.02-9 lg Io38 > or 12= i.i +0.029 log o.ooi = 1.013 volts. In a similar way, if we know the electromotive force ELECTROMOTIVE FORCE AND GALYANIC CURRENT. 127 for some particular concentration we can calculate it for any concentration. Nernst has given the name " electrolytic solution pressure " to the values c 0l and c 02 . The meaning of this term will be considered in the next section. Nernst's Formula. Every substance has a certain tendency to change over fro" i the condition in which it happens to be to some of er. This tendency has been given the name of " fugacity." For instance, liquid water has a tendency to pass over into water vapor, and water vapor, on the other hand, strives to condense and reform liquid water. If the first tendency prevails evaporation actually takes place. The fugacity is dependent on the temperature, but at constant temperature is higher the higher the concentration, or in the case of condensation, the higher the vapor density. When a 'solid soluble salt is brought in contact with water it strives to pass over into the dissolved condition. The concentration of the solid salt is constant and con- sequently the fugacity of a solid salt is constant. On the other hand the salt which has already dissolved has a tendency to leave the solution and go back to the solid state, and this tendency is greater the higher the concentration of the solution is. The actual force which causes the salt to dissolve is equal to the difference be- tween the two fugacities and is therefore smaller the more concentrated the solution is. Finally the concentration of the solution reaches a value where the two fugacities balance, then no more salt dissolves and the solution is 128 ELECTROCHEMIS TR Y. saturated. If the concentration is too high, i.e., if the solution is supersaturated, the tendency to take the solid form overcomes the tendency to dissolve and the re- action goes in the reverse direction. Very similar relations hold for the metals. They all have a tendency to pass over into the form of ions, and this tendency is constant as long as solid metal is present, for the active mass of a metal is constant. On the other hand, the ions strive to pass back into the metallic con- dition, and their tendency to do so varies according to their concentration. We represent the first value by P, the solution pressure, as P Zn , PCW PA S , etc.; the deionizing tendency will be represented by p, and is nothing less than the osmotic pressure of the ions. The osmotic pressure and deionizing tendency both strive to make the solution more dilute. As in the reaction of a salt going into solution, a precipitation of the metals actually takes place, according as P or p has the higher value, but the one essential point of difference lies in the fact that the* metals can only go into solution in the form of positively charged ions and thus carry positive electricity with them. Con- sequently the passage of the metal from the solid to the dissolved state leaves the remaining metal negatively charged (or if p > P, the resulting solid metal is positively charged) and the electrostatic attraction (or repulsion) thus produced soon puts a stop to any further solution (or deposition). The following three cases are possible, illustrated by Figs. 13, 14, and 15. IiP>p traces of metal will go into solution and the metal takes on a negative charge. If P

. ^y i contains the electrolytic potentials of the different ele- ments; the second column contains the same values all shifted 0.277 v lt m order to refer them to another standard proposed by Ostwald.* We can obtain from this table the electromotive force of any cell of the Daniell type. For instance, a copper- nickel element, in which the concentration of the metallic * According to a theory of Helmholtz, the surface tension of polarized mercury has a maximum value when there is no difference between its potential and that of the solution. This theory, however, has not been satisfactorily proven; it appears that the surface-tension phenomena of polarized mercury are more complicated than Helmholtz supposed. 1 3 6 ELECTROCHEMISTRY. ions of each salt is equal, has an electromotive force of + 0.288 ( 0.329) = 0.557 volt. A Zn-Pb cell has a voltage of 0.619, Zn Cu, i.e., the Daniell cell, has 1.099 volts, Cu Ag 0.442 volt, etc. Gas Electrodes. If we take an electrode of platinum which has had deposited on it a coating of finely divided platinum and allow bubbles of hydrogen to pass up over it, some of the gas dissolves in the platinum and the electrode behaves electrochemically as if it were composed of the metal hydrogen. Every chemist knows that most gases, hydrogen particularly, are chemically much more active in the presence of finely divided platinum (Pt " sponge "). This is probably due to the fact that hydrogen dissolved in Pt is partially dissociated into atoms, H 2 = H + H, and the atoms enter into reaction much more readily than the H 2 molecules. The quantity of hydrogen which dissolves in the Pt, i.e., its concen- tration or active mass, is dependent on the pressure which is exerted on the hydrogen above the solution. This follows from Henry's absorption law, which states that the solubility of a gas in a liquid or solid is pro- portional to the concentration of the gas, and this in turn, according to Boyle's law, is directly proportional to the pressure on the gas. To calculate the electromotive force of gas electrodes we again make use of van't Hoff's equation, but we must remember that in previous cases the active mass of the metals were constants and therefore cancelled out in the fraction after the log. In the case of gases, however, the active masses do not thus disappear; they are not constants, but are dependent on the pressure. Let us consider two hydrogen electrodes at atmospheric ELECTROMOTIVE FORCE AND GALVANIC CURRENT. 137 pressure in a solution whose H* ion concentration is ci, then RT C A RT C A E = - In - In = o. 2 C\ 2 Ci CA is the active mass of the hydrogen dissolved in the Pt at atmospheric pressure P. The 2 in the denominator is due to the fact that H 2 has a valence of 2. If we combine an electrode under atmospheric pressure with another under the pressure p, in which the active mass of the hydrogen is C PJ we have RT C p RT C A E = - In 2 - In , 2 Ci 2 Ci or since C P :C A = If p>P the current in the solution goes from the p electrode to the P electrode ; if p < P it goes in the opposite direction, that is, the electrode which has less hydrogen gets more from the passage of the current, and this will continue till the pressure at both electrodes becomes the same. If the pressures p and P are kept constant the cell Pt with H 2 under pressure P\ solution |Pt with H 2 under pressure p will furnish a steady current. The reactions at the elec- trodes are H 2 -> 2 H- or 2 H-^H 2 according to the direction of the current. This is a 13& ELECTROCHEMISTRY. " concentration cell " in which the current is due to a dif- ference in concentration of the substances forming the electrodes. If the pressure is changed by a power of . 0.058 10 the potential is changed = 0.029 vo ^- Other gases when dissolved in Pt act similarly to hydrogen in their electrochemical relations. A platinum electrode saturated with chlorine behaves like an electrode of the element chlorine, and its potential, which is 1.35 at atmospheric pressure, changes with the pressure in the same way as that of the hydrogen electrode. The oxygen electrode also changes its potential with the pressure, but we must remember that in this case the molecule O2 has a valence of four. From the values for the potentials of the metalloids as given in the table on p. 135 we can derive the electro- motive force of any cell ; for instance, the cell Zn|ZnCl 2 |Pt C i 2 has an electromotive force of 2.12 volts; the voltage with which chlorine displaces iodine from a solution of an iodide is 1.35 0.52=0.83 volt when the concentration of chlorine and iodine ions is normal. The Grove gas-cell, O 2 1 solution |H 2 , has a voltage of 1.12. This value for the potential of O 2 refers to a solution when the concentration of H* ions is normal. We cannot calculate the true potential of oxygen in a solution which is normal with respect ELECTROMOTIVE FORCE AMD GALVANIC CURRENT. 139 the O" ions, for at present we do not know the con- centration of the O" ions in any solution with any degree of certainty. Potential of Alloys. The dependence of the electro- motive force on the concentration of the substances forming the electrodes is also seen in the case of metals which form alloys. Suppose we have a cell whose electrodes are composed of dilute zinc amalgams whose zinc concentrations are different, and in which the electrolyte is a solution of ZnSO 4 ; the electromotive force of such a cell is, as above, Here P 2 and PI are the solution pressures of the zinc in the amalgams, and since, as in the case of Pt and H 2 , we may consider zinc as the dissolved substance and mercury as the solvent, we have P^'-Pi^c^Ci, where 2 and Ci are the zinc concentrations in the amalgams. We have therefore This formula has been verified experimentally. We have assumed in the above formula that the molecules of the dissolved zinc are composed of single atoms. If this were not the case, and the molecules were composed, say, of two zinc atoms, Zn 2 , then we would have to divide R T by 4 to get the electromotive force. But since the formula as written represents the experimental facts, this in itself furnishes a proof that the zinc molecules when dissolved in mercury are composed of single atoms. HO ELECTROCHEMISTRY. The amalgams, or in general the alloys, may be divided into three classes: 1. The metals form a mechanical mixture. Such mixtures have the potential of the " less noble " metal. For instance a mixture of Zn and Fe has the potential of pure zinc. 2. The metals form a solution (amalgam or alloy). A metal solution is always " nobler," i.e., has a potential nearer that of- oxygen, than its least noble component, and the greater the amount of work which results from the formation of the alloy the nearer will its potential approach that of oxygen. 3. The metals form a chemical compound. In this case the electrode has its own particular solution pres- sure, and the ions it sends into solution are formed in the same proportion as the elements exist in the elec- trodes. These various conditions have to be considered in the electrolytic solution of impure metals; for instance, in the refining of crude copper, silver, and gold. Details concerning the solution of alloys and the refining of the metals will be given in Books II and III. Potential of Compounds. Case 3, mentioned above, has a very general application. Every element when entering a compound attains an entirely different potential. For instance, chlorine has a very different potential, according as it is present as the free element, or a as solution in platinum, or as a chloride, and its potential is changed to a larger degree according to the amount of free energy developed in the formation of the compound. As may be seen from the table on p. 135, AgCl has a lower potential of formation than CuCl, i.e., its chlorine ELECTROMOTIVE FORCE AND GALVANIC CURRENT. 141 potential is higher than that of CuCl. This will be clearer when we remember that the reaction like all reactions, goes on only till a certain state of equi- librium is reached. All the chlorine does not enter into combination, but an excessively small quantity of Ag and Cl2 remains free. This small remainder may react like chlorine at an exceedingly low concentration, and silver chloride will have a chlorine potential correspond- ing to this concentration of C\2, i.e., its electromotive force will be that of a chlorine electrode at very low pressures. The more stable a compound is, i.e., the higher the voltage of the cell Metal j solution of the chloride of the metal | chlorine is, the more complete is the reaction and the lower the chlorine pressure and chlorine potential. An electrode made of a metal covered with its solid chloride has a perfectly definite potential and is re- versible with respect to chlorine. For instance, the electrode Hg/HgCl + wKCl has a potential of 0.283 volt. If current passes from left to right HgCl is formed; if in the reverse direction, chlorine goes into solution and HgCl disappears. Elec- trodes like this which are reversible with respect to the anion are called electrodes of the second kind, while those reversible with respect to the metal are called electrodes of the first kind. Electrodes of the second 142 ELECTROCHEMIS TR Y. kind are very often employed in potential measurements on account of their constancy. The calomel electrode is the one most used. The potential varies with the concentration of the CY ions in the solution according to the same formula as for the metals, n D c where - log P is the potential of the electrode when ti the concentration of the CF ions in the solution is i. Reversible electrodes for other metalloids or radicals can be made in the same way ; for instance, Ag/Agl + KI or Hg/Hg 2 SO 4 +H 2 SO 4 , etc. Salts which are the least soluble in water are naturally chosen for use in normal electrodes. The following table gives the potentials of some electrodes of this sort: Hydrogen Electrode = Calomel Electrode = 0.56 Pb/PbSO + 1 O4wH 2 SO 0.284 o 007 Hg/Hg 2 SO 4 + 1 .owK 2 SO 4 Hg/Hg 2 Cl 2 + 1 owKCl -0.644 o 283 0.921 o 560 Hg/Hg 2 Cl 2 +o. iwKCl Ag/AgCl +i owKCl -0.338 O 2OO 0.614 o 483 Ag/AgCl +o iwKCl o. 263 o. 540 The values given in this table are to be used in the same way as those given on p. 135, so that a cell con- sisting of Zn in ZnSC>4 combined with a mercurous sulphate electrode will have a voltage of 0.77+0.644 = 1.414 volts. ELECTROMOTIVE FORCE AND GALVANIC CURRENT. 143 The so-called oxidation and reduction potentials are to be considered in a similar way. A Pt electrode cov- ered with potassium chlorate (KC1O 3 ) has a perfectly definite potential, for the chlorate has a definite oxygen pressure, due to the incompleteness of the reaction which has produced the chlorate. The Pt electrode becomes charged with oxygen at this pressure and thus becomes an oxygen electrode, which can bring about reactions of oxidation. The potential of such a secondary oxygen electrode corresponds to the pressure with which the oxidizing agent tends to give up oxygen. The potential of a Pt electrode in a solution of an oxidizing agent, therefore, is due simply to a charge of gaseous oxygen furnished by the oxidizing agent, as Nernst has proven experimentally. The reduction potential of reducing agents is due to exactly similar causes. Reducing agents give up H2 to a Pt electrode, or, what amounts to the same thing, they abstract oxygen, until the gas concentration, and consequently the potential, reaches a value corresponding to the reducing power of the substance. If we bring together on a Pt electrode an oxidizing agent, such as KMnC>4 and a reducing agent, such as FeC^, the per- manganate gives up oxygen to the electrode and the FeCl 2 takes it away; that is, the second substance becomes oxidized by the first. The potential with which this reaction takes place is simply the difference between the oxidation potentials of the two substances. These potentials are dependent on the concentrations of the oxidizing and reducing agents and may be calculated by Nernst's equation. Data and information concerning the use of a number of oxidation and reduction electrodes 1 44 ELE C TROCH^ MIS TR Y. will be given in Book II. The Grove gas-cell, for instance, is an oxidation-reduction cell, consisting of the oxidizing agent oxygen and the reducing agent hydrogen. Concentration Cells. A kind of concentration cell differing from that on p. 139 is the following: Ag|A g N03-AgN0 3 |A g , ci 2 i.e., electrodes of the same metal dipping into solutions of a salt of the metal having different concentrations. The current through the solution flows from the less concentrated to the more concentrated solution. On one side silver is dissolved, on the other precipitated, until the concentration on both sides is the same. If we neglect on account of its smallness the difference of potential at the point of contact of the two solutions as we have always done hitherto the electromotive force at 18 is given by E = RTln = 0.0577 log . C-2 2 The solution pressure of the metal, being the same at each electrode, does not appear in the formula. In many cases the electromotive force at the junction of the two solutions may be neglected, but not always. The following consideration will show the cause of this electromotive force and how to calculate it. Two so- lutions of different concentration always strive to dif- fuse into each other till the concentration is the same at all points. When a dissolved salt diffuses the ion having the highest velocity tends to move on ahead of ELECTROMOTIVE FORCE AND GALVANIC CURRENT. MS the other. In the case of acids this is the hydrogen ion which has the highest velocity of any of the ions. This partial separation of the ions can only take place to an immeasurable extent, for since the more dilute solution has an excess of H' ions, the electrostatic attraction of the ions gives rise to a force which compels the two kinds of ions to remain together. As a result, in the diffusion of a salt the more rapid ion is held back and the slower is accelerated. This tendency of one ion to hurry on ahead of the other gives rise to an electromotive force which, as Nernst has shown, can be calculated from the velocity of the ions. If u represents the velocity of the cation and v that of the anion, then C 2 e being the difference of potential at the junction of two solutions whose concentrations are c\ and c< 2 ; the salt in each solution is supposed to be completely dissociated and the ions all univalent. This formula holds only for 1:1 salts (cf. p. 96); the formulae for others are more com- plicated, and most of them have not been derived.* From the theory of the diffusion of electrolytes it follows that this electromotive force at the junction of two solutions of different concentration practically disappears when each solution contains equal amounts of another salt whose concentration is much higher. To avoid this somewhat uncertain contact-electromotive * For further particulars see the list of text-books named at the close of this volume: in particular Nernst, Theoretische Chemie, 4th edition, p. 699. 146 ELECTROCHEMIS TR Y. force a large excess of some indifferent salt is often added. Applications of Nernst's Formula. The formula on p. 144 has been experimentally verified in a great number of cases, and may be used to determine the solubility of certain difficultly soluble salts in cases where the solubility is too small to be measured by chemical means. We find, for instance, that the electromotive force of the cell Ag|o.ooi n AgNO 3 + i.owKNO 3 -i.o n KNO 3 +AgI|Ag is 0.22 volt. The concentration of the silver ions on the left is o.ooi ; let that on the right be c where c is the value sought. From the formula o.ooi 0.22 =0.0577 log we find that c = i.6Xio~ 8 , i.e., a litre of a saturated Agl solution contains 1.6 X i o~ 8 mols of Agl = 0.000003 5 gr. Agl. This agrees very well with the value i.5Xio~ 8 obtained from conductivity measurements. Another very important application of the measure- ment of concentration cells is in determining the disso- ciation constant of water, a method already mentioned on p. 72. The cell Pt H2 |NaOH-HCl|Pt H2 is called the " neutralization cell " because the reaction of neutralization is the one which furnishes the current NaOH + HC1 = NaCl + H 2 O, or more correctly, as we saw on p. 66, ELECTROMOTIVE FORCE AND GALVANIC CURRENT, 14? The voltage of this cell with o.i n solutions is 0.6460 at 25 To this 0.0468 volt must be added, because at the contact of the two solutions there is an opposing electro- motive force of this value. The voltage of the cell without this " diffusion " voltage would therefore be 0.6928. The concentration of the H' ions in a o.i n solution of HC1 is 0.0924, that of the OH' ions in a o.i n solution of NaOH is 0.0847, as found from conductivity measurements. The cell is to be considered as a concentration cell with respect to the H* ions, and therefore follows the formula on p. 144. Introducing the different values we have o 0024. 0.6928 = 0.05898 log - , c where c is the concentration of the H' ions in the NaOH solution, c is found to be i.66Xio~ 13 . Therefore [H'][OH']=i.4o6Xio- 14 and c = i.i87Xio- 7 , which is in excellent agreement with the values obtained by other methods (cf. p. 65 and also p. 91). Secondary Elements and the Accumulator. The secondary elements do not differ in principle nor in the calculation of their electromotive forces from the primary elements which we have just studied. They are nominally distinguished from the first, however, because after they are once used up they may be revived or recharged by sending a reverse current of electricity through them, and it is not necessary to rebuild them of 1 4 8 ELEC TROCHE MIS TR Y. fresh material as in the case of primary cells. The oxygen-hydrogen cell Pto 2 |solution|Pt Ha may be considered as a secondary cell if the gases re- sulting from the electrolysis are collected at the electrodes and then used to produce a current. The most important of the secondary elements is the lead accumulator or storage battery. If we put two lead electrodes in a solution of sulphuric acid a small amount of PbSCU is formed by chemical action on the surface of the electrodes. If we pass a current through the solution, the PbSC>4 on the cathode becomes reduced to metallic lead, and at the anode is oxidized to lead peroxide (PbO2), so that we now have a polarization element (cf. p. 152) of the form Pb|H 2 SO 4 |PbO 2 . This can furnish a current and has an electromotive force of about 2 volts. Since the formation of PbSC>4 was very slight, very little Pb and PbO 2 was formed and the cell can only furnish a small amount of electricity. To increase the capacity, i.e., to allow of the formation of large amounts of PbO 2 , the electrodes should expose as large a surface as possible. This may be accomplished, according to Plante*, by electrolyzing first in one direction and then in the other, which causes the electrodes to become somewhat porous; or, according to Faure, a paste of lead oxide and red lead is spread on a grating of lead and when this is electrolyzed we obtain spongy ELECTROMOTIVE FORCE AND GALVANIC CURRENT. 149 lead at the cathode and lead peroxide at the anode. When such an element furnishes a current PbSO 4 is formed -at both electrodes. In "Charging," the PbSO 4 on the cathode, or " nega- tive pole," is reduced to Pb, and the following reaction occurs : * This is an electrode of the second -kind, which sends SO 4" ions into solution (cf. p. 141). At the anode or " positive pole " SO 4 " ions are set free, which through the agency of water ,act on the PbSO 4 , forming PbO 2 and H 2 SO 4 : In " Discharging," SO 4 " is liberated at the anode (now the lead pole): Pb + S0 4 " + 2=PbS0 4 . At the cathode (now the PbO 2 pole) H' ions are dis- charged and with the help of the H 2 SO 4 act on the PbO 2 and convert it into PbSO 4 : PbO 2 + 2 H" + H 2 SO 4 + 2 = PbSO 4 + 2 H 2 O. Summing up these equations we obtain as the chemical process which produces the current the equation PbO 2 + Pb + 2 H 2 SO 4 <= 2 PbSO 4 + 2 H 2 O. * In equations the symbol represents 96 540 coulombs of positive electricity, the same quantity of negative 1 5 ELECTROCHEMIS TR Y. Read from right to left this represents the reaction on charging, from left to right the reaction on discharging. In charging 2PbSO 4 and 2H 2 O disappear and TbO 2 , Pb, and 2H 2 SO4 are formed; the reverse is true on dis- charging.* * On the application of the different thermodynamical and electro- chemical theories to the lead accumulator, see Book II, and also the excellent work of F. Dolezalek, " The Theory of the Lead Accumula- or," Wiley & Sons. CHAPTER VI. POLARIZATION AND ELECTROLYSIS. IN this chapter we will discuss briefly a number of facts which are of the greatest importance to the ex- perimental and technical side of electrochemistry and which will be easily understood from what has been said in the previous chapters. The way in which a current is conducted through a solution and the part played by the different ions has been discussed in the chapter on conductivity. On arriving at the electrodes the ions give up their charges, and are either precipitated as neutral substances, where they remain in a solid state as in the case of the metals, or, as in the case of the gases, escape into the at- mosphere or dissolve in the solution; on the other hand, they may react at once with the surrounding solution as soon as they are set free, and thus give rise to oxidizing or reducing effects. As a result of electrolysis either the electrode or the solution around the electrode is changed, and conditions are produced which result in an electro- motive force opposed to that which is sending the current through the solution; in other words, the electrolytic cell becomes " polarized." 15* ELECTROCHEMISTRY. Polarization. If we electrolyze a solution of HC1 with an electro- motive force of 0.7 volt, a very small quantity of hydrogen is deposited at the cathode, and a very small quantity of chlorine at the anode, and current will flow until the concentrations of the gases in the cell Pt H2 |HCl|Pt C i 2 is high enough to produce a counter electromotive force just equal to the applied 0.7 volt. A hydrogen-chlorine cell in which the gases have a pressure of i atmosphere has, according to the table on p. 135, a voltage of 1.35. At o. 7 volt we therefore have a H2 Cl2 cell in which the concentration of the gases and therefore their solution pressure is much smaller than at atmospheric pressure (cf. p. 136). These concentrations only become high enough to just balance the applied voltage. In order to produce this formation of H 2 and C1 2 current must flow on applying an electromotive force, but this soon stops on account of the counter electro- motive force of the H 2 -C1 2 cell which is thus formed. If we now increase the applied voltage to i volt a new current appears, the electrodes become charged with more gas, and the chlorine hydrogen cell also soon attains an electromotive lorce of i volt. This goes on until we come to 1.35 volts. At this voltage the electrodes are charged with gas at atmospheric pressure. This counter electromotive force is called " polariza- tion." If we now increase the voltage to 1.5 the polarization is no longer able to bring the current down to zero, and above 1.35 volts we have a perceptible, continuous current. 1.35 is called the decomposition voltage of HC1. Above 1.35 volts the current follows the law, POLARIZATION AND ELECTROLYSIS. 153 E = iw, where E is the applied voltage, e the counter electro- motive force of polarization, and w the resistance of the solution. The polarization increases very slightly above 1.35 as the voltage and current rise, since the gases are evolved under a pressure greater than that of the atmos- phere, but since they are able to escape in gaseous form the polarization will never be as great as the applied electromotive force. Similar conditions also prevail when solid substances are precipitated. For instance when we electrolyze a solution of CuCl 2 between Pt electrodes, chlorine is formed at the anode under a certain pressure, and at the cathode a Cu coating of such a density that the resulting cell has the same electromotive force as the applied voltage. The small amount of electricity which is necessary to bring the electrode into the polarized condition is known as the " polarization capacity " of the electrode. This capacity is naturally dependent on the surface of the electrode and further depends on the nature of the metal of which the electrode is made. For equal surfaces palladium has a higher polarization ^capacity when hy- drogen is discharged on it than platinum, and platinum a higher capacity than iron ; for the solubility of hydrogen is the greatest in palladium, and consequently a larger amount of hydrogen and therefore a larger amount of current is required to bring the hydrogen dissolved in palladium up to the same pressure as that dissolved in platinum or iron. 154 ELECTROCHEMISTRY. If for any reason the substances which cause polar- ization are removed, either by dissolving in the solu- tion and diffusing away, or by chemical actions, we say that " depolarization " occurs. This is the case when we electrolyze a substance which gives soluble gases. Further, polarization is prevented when we have a re- ducing agent, as FeCl2 at the anode, for this prevents the oxygen polarization by combining with oxygen to form a ferric salt (cf. p. 143). Such substances are called " depolarizers." FeCls is a cathodic depolarizer^ since it prevents the hydrogen polarization and is reduced to FeCl 2 . The electrolysis of water furnishes a good illustration of these facts. If we apply i volt to two platinum elec- trodes in water, the cathode becomes charged with hydro- gen and the anode with oxygen until the electromotive force of this gas-cell is i volt, when the current should stop. The two gases C>2 and H 2 , however, are soluble in water, and they consequently diffuse away from their electrodes and either escape into the air or recombine at the electrodes to form water. The electrodes therefore are continually losing gas, and in order to make good this loss and keep up the electromotive force of i volt a small current must continue to flow. This small current is known as the residual current (Reststrom). Such substances as are easily oxidized at the anode and reduced at the cathode may maintain a much larger residual current. For instance if an iron salt gets into the storage battery, it is reduced to ferrous salt at the cathode, diffuses to the anode, and is there oxidized to ferric salt, diffuses back to the cathode, and is again reduced, etc. Iron salts in the storage battery therefore maintain a POLARIZATION AND ELECTROLYSIS. .'55 residual current which is useless for charging purposes and causes a considerable loss. If oxygen or air is passed over the cathode during the electrolysis of water, this removes the hydrogen polarization, and such an electrode is called " unpolar- izable." Those anodes are unpolarizable which are electrolytically dissolved, such as Cu. In general an electrode is unpolarizable when no new substance is formed on it during electrolysis. In order to determine the decomposition voltage of a salt, we put two Pt electrodes in the solution and connect them with a source of electricity whose voltage may be 1.3 l.GT] FIG. 17. varied at will. We then gradually increase the voltage and observe the current at each voltage. The current first rises and then decreases almost to zero every time the voltage is raised, until the decomposition voltage is reached. From this point on the current follows Ohm's law (cf . p. 78) : E w. If the voltage is plotted as abscissa and the current as ordinate we obtain the curves shown in Fig. 17. In 156 ELECTROCHEMISTR Y. the case of AgNO 3 the current below 0.7 volt is prac- tically zero, above this it increases regularly. 0.7 volt is therefore the decomposition voltage of silver nitrate. The values in the following table were obtained by Le Blanc and his students. DECOMPOSITION VOLTAGES. Acids Salts Sulphuric acid, H 2 SO 4 i . 67 Zinc sulphate, ZnSO 4 2 .35 Nitric acid, HNO 3 i . 69 Zinc bromide, ZnBr 2 i . 80 Phosphoric acid, H 3 PO 4 . ... 1.72 Nickel sulphate, NiSO 4 2.09 Malonic acid', CH 2 (COOH) 2 i .69 Nickel chloride, NiCl 2 i .85 Perchloric acid, HC1O 4 i . 65 Lead nitrate, Pb(NO 3 ) 2 1.52 Hydrochloric acid, HC1 i .31 Silver nitrate, AgNOs 0.70 Oxalic acid 95 Cadmium nitrate, Cd(NOs) 2 i . 98 Hydrobromic acid 0.94 Cadmium sulphate, CdSO 4 . 2.03 Hydriodic acid 0.52 Cadmium chloride, CdCl 2 . . . i . 88 Cobalt sulphate, CoSO 4 . ... 1.92 Bases Cobalt chloride, CoCl 2 i . 78 Sodium hydroxide, NaOH . . i . 69 Potassium hydroxide, KOH. i . 67 Ammo'm hydroxide,NH 4 OH. i . 74 Since the polarization is nothing less than a gal- vanic cell resulting from electrolysis, it will follow the same laws and formulae as these cells. Just as the electromotive force of a galvanic cell is made up of two separate potentials (cf. p. 132) so the decomposition voltage of an electrolyte is composed of the two voltages necessary to discharge the ions. Furthermore these "deposition voltages" must be exactly the same as the single potentials of the metals which are being deposited. They also follow Nernst's formula, i.e., the deposition voltage is lower, and precipitation takes place easier when the concentration of the ions which are to be precipi- tated is high. The decomposition voltage of zinc chlo- ride, 2.1 volts, is composed of. the potential of zinc, 0.77, and that of chlorine, 1.35 (cf. table on p. 135). The POLARIZATION AND ELECTROLYSIS. 157 deposition voltages may be measured by combining the electrode in question with one whose potential i ; constant and of known value. If a current is passed through the combination Pt|CuSO 4 H 2 SO4 + Hg2SO 4 |Hg so that Cu is precipitated, it is found that the electro- motive force of the resulting cell, Cu|CuS0 4 H 2 S0 4 + H g2 S0 4 |Hg, is 0.315 volt. Knowing that the single potential of the mercurous sulphate electrode is 0.644 (cf. p. 140) we find that the deposition voltage of Cu is -0.329, which is just the same as the single potential of Cu. There is still another kind of polarization, in which the electrodes are not changed. If we have two silver electrodes in a solution of AgNO 3 , and pass a current, a displacement of the concentration occurs, due to the different velocities with which the anion and cation move (cf. p. 108). Consequently a concentration cell is formed whose electromotive force acts in opposition to the applied voltage. This cell also, like all concentration cells, must follow Nernst's formula. Deposition and solution do not necessarily accompany electrolysis. Other reactions, as oxidation and reduction, may take place, and these obey the laws which have been discussed in the preceding pages. Every reaction taking place at an electrode has its own particular voltage. For instance, it requires a definite potential to reduce FeCl 3 to FeCl 2 . In certain cases the gases do not act in accordance with Nernst's formula. When a gas is evolved at an 158 ELECTROCHEMISTRY. electrode two separate reactions are to be distinguished: first, the discharge of the ions to form atoms, as and secondly, the union of the atoms to form the mole- cules of the gas, as This reaction meets with a different resistance from the different metals used as electrodes, or, more correctly, this reaction has a great chemical resistance which is removed catalytically to a different extent by the different metals. Platinized platinum is the most effective cata- lyzer for this purpose; hydrogen is evolved on platinized platinum at the potential o.o volt. Iron is less effective as a catalyzer and Hg, Pb, and Zn are the least. This phenomenon is called " overvoltage," and we say that hydrogen is evolved on zinc with an overvoltage of 0.7 volt. The following table shows the overvoltages necessary to evolve hydrogen and oxygen on the different metals. OVERVOLTAGE. Hydrogen Deposition Oxygen Deposition Metal Potential Metal Potential Pt platinized Au Fe in NaOH Pt polished As o.oo O.OI 0.08 0.09 0.15 0.21 0.2 3 0.46 o-53 0.64 0.70 0.78 Au Pt polished Pd i-75 1.67 65 65 63 53 .48 47 47 36 35 .28 Cd . . As.. . N!"" Pb Pn Cu Pd Fe Sn . ; Pt platinized. . . . Co Pb Zn Ni polished Ni spongy. He. . POLARIZATION AND ELECTROLYSIS. 159 The recognition of these facts was extremely important, for it explained a number of experimental discoveries which could not be theoretically accounted for. In nearly all solutions there are several different ions which may be. discharged, and consequently several different reactions are possible at the electrodes. The general rule is that that process actually takes place which requires the least expenditure of energy. For instance, if we have a solution containing ZnCl 2 , CuCl2, and HC1 no electrolysis will be effected by any electro- motive force less than i volt, for the decomposition voltage of CuCl2 is i volt. Between i and 1.35 volts the only reaction at the cathode will be the deposition of Cu, since the decomposition voltage of HC1 is 1.35. Above 1.35 volts both Cu and H may be deposited, but in reality that process will take place which requires the lowest voltage, and only Cu will be deposited as long as it is present in sufficient quantity. If the solution is electrolyzed with a high current, however, the Cu in the immediate neighborhood of the cathode soon becomes nearly all used up, its deposition voltage is raised in accordance with Nernst's formula, and finally a condition is reached where hydrogen is more easily discharged than copper. Finally, if the voltage is raised above 2.2 zinc may also be deposited, and this may be brought about by using a high-current density so that the solution around the cathode contains very little copper. By using a high-current density brass may be deposited on the cathode on electrolyzing a mixture of copper and zinc salts. Now, hydrogen ions are always present in some quantity, and the fact that zinc may be deposited from a solution 160 ELECTROCHEMISTRY. containing hydrogen ions can only be explained by the phenomenon of overvoltage. If there were no over- voltage we could no more deposit zinc from a water solution than we can aluminium or sodium. As it is zinc can only be precipitated from a neutral or alkaline solution, and not from one containing acids. The deposition voltage of zinc is 0.77, that of hydrogen from an acid solution, on account of the overvoltage, is raised from o.o to 0.70 as soon as the slightest trace of zinc is deposited. In an acid solution the hydrogen will therefore be deposited before the zinc. In a neutral solution, however, when the concentration of the H- ions is about io~ 7 the deposition voltage of hydrogen is raised, and is 0.0577 log io~ 7 = 0.404 volt higher than in an acid solution ; it is raised still further in an alkaline solution where the H* ion concentration is very much lower. From a neutral solution, therefore, hydrogen can be discharged electrolytically on zinc only at a potential of 0.4 + 0.7 = 1.1 volts, and consequently from such a solution the zinc will be deposited before the hydrogen. What is true of the deposition of ions is true of certain other reactions: that one occurs first which requires the lowest potential. If we have a solution of potassium permanganate and chloric acid, that one of these sub- stances will be first reduced which has the highest ox- idizing potential, for oxidizing potential is nothing less than the effort of the substance to give up oxygen and become reduced. Such processes are really nothing less than a change of the charges on the ions. For instance, the reduction of FeCl 3 to FeCl 2 simply consists in Fe'" >Fe". The reduction of MnC>4 to a manganese salt consists in MnO 4 ' Mn". If we keep in mind this POLARIZATION AND ELECTROLYSIS. 161 transfer of charges, we can derive a formula similar to Nernst's for all such reactions. Using the method explained on p. 155 we can often obtain the deposition voltages of every kind of ion in the solution (Fig. 18). In the anodic curve for H 2 SO4 a slight bend is noticed at 1.12 volts where the oxygen ions are discharged. The change in direction of the curve is slight, as Fig. 18 shows, be- cause the concentration of the O" ions is excessively small, and when used up they are not immediately replaced by of the water. J.1& 1.07 Volt*. FIG. 18. a further dissociation On further raising the voltage another bend is noticed at 1.67 volts which probably corresponds to the discharge of the OH' ions. Under suitable con- ditions two other points are obtained with H 2 SO 4 , at 1.9 where the SO 4 " ions are discharged and at 2.6 where the HSO/ ions are discharged. The following deposition voltages not contained in the other table have been obtained by Nernst and his students : Mg +1.482 SO 4 -1.9 Al +1.276 HS0 4 -2.6 *O -i. 12 NO 3 -1.88 *OH -1.67 * These figures refer to solutions normal with respect to the H' ion; i.ia and 1.67 are the deposition voltages of O" and OH' from a normal acid solu- tion. To discharge OH' or O" ions from a normal alkaline solution requires 0.8 volt less than to discharge them 1 6 2 ELECT ROCHE MIS TR Y. from a normal acid solution; to discharge H from a normal alkaline solution requires 0.8 volt more than from a normal acid solution. Faraday's Law. As we have already shown (pp. 52, 82), equivalent quantities of the ions of different substances are always combined with the same amount of electricity, and this charge is 96 540 coulombs for every equivalent in grams. This amount of electricity is carried by 39.15 grams of the positively charged univalent potassium ion, or by 35.5 grams of negatively charged univalent chlorine ion. In general the ions of any substance carry 96 540 coulombs for every valence. If one equivalent of any substance passes through the cross-section of an electrolytic cell, it carries with it 96 540 coulombs and the current strength is 96 540 ampere-seconds. When 108 grams of silver are de- posited on the cathode, 96 540 coulombs of positive electricity pass from the solution to the electrode. If i coulomb, i.e., i ampere for i second, is passed through an electrolytic cell 0.01036 mg. equivalents are deposited. Faraday's law may therefore be stated: The amount of electricity required to deposit, dissolve, or otherwise bring into chemical action i gram equivalent of any element or compound is always p6 540 coulombs. The weight in grams of the substance which is produced or destroyed may therefore be obtained by dividing the molecular weight (in the case of elements the atomic weight) by the valence, multiplying by the number of ampere-seconds and then by 0.00001036. The following table contains in the first column the elements, in the second the atomic POLARIZATION AND ELECTROLYSIS. 163 weights, in the third the milligrams per ampere-second, and in the fourth the grams per ampere-hour. All the values except those for H', Ag", and Cu" are approxi- mate. Elements Symbol and Valence Atomic Weight Milligrams A pef Ampere- second Grams per Ampere- hour A1-" 27. 1 o . oo ^ <; O 337 Sb- I2O. 2 0.415 1 .494 Sb 120.2 0.25 0.90 Ba" 137.4 0.712 2 .56 Bi- 208.5 1. 08 3.89 Bromine Br' 79.96 0.8 2 .Q4 Cadmium Cd" II2-4 0.58^? 2. IO Calcium Ca" 4O. I o. 207=; 0.75 Carbon C"" 12 .OO o 031 o. 1115 Chlorine ' Cl' 2C AC o. ^677 i 322 Cobalt Co" 4 on a Pt electrode no lead is formed, and we have simply an evolution of hydrogen. The same thing happens when a foreign metal such as copper gets into the storage battery. It is deposited on the cathode, and when we attempt to charge the battery, hydrogen is evolved on the traces of copper and no PbSC>4 is reduced. These facts are important in the analytical determina- tion of the metals by electrolysis (cf. Book II). The metals can only be deposited when their deposition voltage is below that of hydrogen, and we must give the solution such a composition that this 'will be the case. In determining nickel, for instance, we use an ammo- niacal solution. What has been said also applies to the reaction at the anode. An anion will only be discharged when this reaction takes place easier than the discharge of the O" or OH' ions which are always present. We can never 1 6 6 ELECTROCHEM1S TR Y. obtain fluorine by electrolyzing a water solution, but we can obtain bromine and iodine. When we electrolyze a solution of Na 2 SO 4 , the SO 4 " ions are not discharged, but rather the oxygen ions, and gaseous oxygen is evolved. As the oxygen ions disappear hydrogen ions remain in the solution, and since SO 4 " ions are brought up by the current, this results in the formation of sulphuric acid at the anode.* Another class of reactions may occur when the ions which have been brought up to the anode find an oppor- tunity to enter into a reaction which requires a potential lower than that necessary for their discharge. In a strongly acid solution of Na 2 SO4 which contains very few O" ions, the reaction SO 4 + SO 4 = S 2 O 8 can be more easily brought about than the evolution of oxygen, consequently H 2 S 2 Os is formed and little or no oxygen is produced. In an acid solution of Na 2 SO 4 , however, OH' and HSO 4 ' ions are also present, and it is very probable that the formation of persulphuric acid is due to the direct union of two discharged HSO 4 ions. We have still to consider the presence of OH' ions. When we electrolyze a solution with a voltage of about 1. 12 or a little higher, O" ions are discharged, but they soon become so largely removed in the vicinity of the * It should be noticed that many text -books explain these facts in a somewhat different way, by assuming that the SO/' ions are actually discharged and then react with water according to the equation S0 4 + H 2 0=H 2 S0 4 + 0. The formation of NaOH at the cathode is similarly explained on the assumption that Na ions are first discharged and then immediately react with the water, forming H and NaOH. It is evidently unneces- sary to explain the facts in this roundabout way. POLARIZATION AND ELECTROLYSIS. 167 electrode that their deposition voltage is raised above that of the OH' ions. Therefore in the electrolysis of a NaOH solution we have only a very weak current between 1.12 and 1.67 volts. Above this last voltage, which is the deposition potential of the OH' ions, we obtain a much stronger current. The reaction which takes place at the electrodes is OH+OH=H 2 0+O. A reaction of this sort in which the ions are destroyed is evidently not reversible (cf. p. 12 and 123), for the OH ions cannot be restored to the solution by reversing the current. A chemical reaction may be brought about more easily than by direct deposition if the ions have an oppor- tunity to form a compound or alloy. For instance, if we electrolyze a sodium chloride solution, using a mercury cathode, two causes unite to lower the deposition voltage of the Na* ions below that of hydrogen: first, the discharge of Na is facilitated because it may unite with mercury to form an amalgam, and . secondly, the discharge of H on mercury requires a high overvoltage. In this case Na' ions can be discharged before H* ions, and this fact forms the basis of a very important industry: the manu- facture of sodium amalgam and its subsequent conversion into pure sodium hydroxide. These primary reactions of deposition are to be dis- tinguished (Book III) from secondary reactions into which the deposited substances may enter. In the electrolysis of sodium chloride the chlorine set free at the anode dissolves in the solution, diffuses away, and 1 68 ELBCTROCHEM1STR Y. reacts with the NaOH which is formed at the cathode, thus: 2 NaOH + C1 2 = NaOCl + NaCl + H 2 O ; i.e., the hypochlorite is a secondary product of electrolysis. This reaction also has great technical importance, for the electrolytic hypochlorite solutions are largely employed for bleaching purposes. If these bleaching solutions are again electrolyzed the hypochlorite is oxidized to chlorate. CHAPTER VII. THE ELECTRON THEORY. RECENT researches on the chemical effect of the silent electric discharge, on the cathode and X-rays, and es- pecially the discoveries in connection with radioactivity have caused the revival of an old theory, according to which electricity is an actual chemical substance (formerly called the " electric fluid "). We must confine ourselves to a very brief outline of the development of the " electron theory " and its application to electrochemical questions. The cathode rays discovered by Hittorf are rays sent out from the cathode of a vacuum tube under the in- fluence of very high voltages. They consist of negative electricity which is ejected from the cathode at a very high velocity. These particles of electricity must possess a certain weight, since they are capable of exerting a force when in motion. At discharge potentials of 3000 to 14 ooo volts their velocity ranges from 0.3 to o.yXio 10 centimetres per second, i.e., is from T V to J of the velocity of light. When the rays enter an electric or magnetic field, their path becomes changed. From this deviation and from the velocity it has been calculated that the weight of the electric atom or " electron " is about ToW tnat f tne hydrogen atom. 169 170 ELECTROCHEMISTRY. The Becquerel rays emitted by radium and other radioactive substances are very similar to the cathode rays, only their velocity (and consequently, their pene- trating power) is greater, being from 2.5 to 2.8Xio 10 cms. per second, or nearly as high as the velocity of light. If the cathode rays consist of negative electrons, we must assume that the same is true of the radium rays. It therefore follows that negative electrons are capable of existing in a free state and not combined with matter. The same should be true of the positive electrons, although it is doubtful whether they have yet been isolated. When electrons pass through air, they attach themselves to the gas molecules and form air ions, and the gas becomes a conductor of electricity. The velocities of these ions have been measured, and it has also been found that they obey the ordinary laws of diffusion. The diffusion coefficients of the gas ions have been cal- culated on the assumption that they are electrically univalent, i.e., contain only one positive or negative electron, and the calculated and experimental values agree very well. The conductivity imparted to air by the electrons, and also their effect in causing the con- densation of supersaturated vapors (which last may also be brought about by dust particles), forms an important test for the presence of electrons. When an electron moving at a high velocity collides with a " neutron," the latter is broken up and new positive and negative electrons are formed. These may later on recombine and again form neutrons, according to the equation We must assume the existence of these neutrons if THE ELECTRON THEORY. 17* we accept the electron theory. Neutrons must be present everywhere like the ether, and are without mass, non- conducting but capable of being polarized.* The following electrochemical definitions would follow from the theory. The electron acts chemically like an element. It combines with other elements to form saturated compounds, which are the ions. 96 540 coulombs correspond to i mol of a univalent element; the unites with negative elements or radicals to form saturated compounds, as O" = SO 4 ", can replace the metallic element in compounds, while combines with the positive elements and radicals and is capable of replacing the negative elements and radicals: 10 'fa N H 4 +=NH 4 =NH 4 -, etc. If an electron can spring from one atom to another as in the reaction * For further details see Nernst, Theoretische Chemie, 4th edition, D. 389 ff. 172 ELECTROCHEMISTRY. it must be capable of existing in a free state for a certain length of time, a conclusion which we have already drawn from the conduct of the cathode rays. The electrons have a different affinity for the different elements, just as the elements have a different affinity for one another. The positive electrons have a greater affinity for the metals, and the order of this affinity is shown in the table 'of potentials (p. 135); the negative electrons have an affinity for the metalloids and negative radicals. The affinity of the positive electron for any element or radical increases as the affinity of the negative electron decreases, as in the following list: F, S0 4 , Cl, O, Br, I, Ag, Hg, Cu, Fe, Zn, Al, Na, Cs. When two ions unite, as H' + C1'=HC1, the molecule HC1 is to be considered as a double salt of the form HQC1, which decomposes into its components on being dissolved in H 2 O: i.e., it dissociates just as the alums do when dissolved: These " neutron double salts " in no way resemble their components, while the alloys, and compounds like PCla, BrCl, etc., which are not neutron double salts, retain some of the characteristics of the elements from which they are made. LITERATURE. A. BOOKS. W. NERNST. Theoretische Chemie. Verlag von Enke, Stuttgart. 1904. Theoretical Chemistry from the Standpoint of Avogadro's Rule, and Thermodynamics. Revised edition. 1904. W. OSTWALD. Lehrbuch der allgemeinen Chemie. Verlag von En- gelmann, Leipzig 1890-1904. Grundriss der allgemeinen Chemie. Verlag von Engelmann, Leipzig. 1899. The Scientific Foundations of Analytical Chemistry. 1899. Elektrochemie, ihre Geschichte und Lehre. Verlag von Veit & Co., Leipzig. 1896. und R. LUTHER. Physico-chemische Messungen. Verlag von Engelmann, Leipzig. 1902. A Manual of Physical and Chemical Measurements. Macmillan & Co. 1902. J. H. VAN'T HOFF. Vorlesungen iiber theoretische und physikalische Chemie. Verlag von Vieweg & Sohn, Braunschweig. 1904. Lectures on Theoretical and Physical Chemistry. 3 vols. Long- mans, Green & Co. J. WALKER. Introduction to Physical Chemistry. Macmillan & Co., New York. W. RAMSAY. Modern Chemistry. Macmillan & Cc. W. NERNST and A. SCHONFLIES. 2 vols. Einflihrung in die mathe- matische Behandlung der Naturwissenschaften. Verlag von Olden- bourg, Miinchen-Berlin. 1904. F. KOHLRAUSCH. Lehrbuch der praktischen Physik. Verlag von Teubner, Leipzig. 1905. 173 174 LITERATURE. A. A. NOYES. General Principles of Physical Science. Henry Holt & Co., New York. 1902. S. ARRHENIUS. Lehrbuch der Electrochemie. Verlag von Quandt & Handel, Leipzig. 1901. Electrochemistry. Longmans, Green, & Co. M. LE BLANC. Lehrbuch der Electrochemie. Verlag von Leiner, Leipzig. 1903. Elements of Electrochemistry. (A new edition preparing.) Mac- millan & Co. F. HABER . Grundriss der technischen Elektrochemie auf theoretischer Grundlage. Verlag von Oldenbourg, Miinchen. 1898. R. LJBKE. Grundz'jge der Elektrochemie. Verlag von Springer, Berlin. 1903. P. TH. MULLER. Lois fondamentales de Pelectrochimie. Masson & Cie, Paris. 1903. A. HOLLARD. La theorie des ions et Pelectrolyse. Carre & Cie, Paris. 1900. R. ABEGG. Die Theorie der elecktrolytischen Dissociation. Verlag von Enke, Stuttgart. 1903. The Theory of Electrolytic Dissociation. Wiley & Sons. H. C. JONES. Theory of Electrolytic Dissociation. Macmillan & Co., New York. F. B. AHRENS. Handbuch der Elektrochemie. Verlag von Enke, Stuttgart. 1903. W. BORCHERS. Handbuch der Elektrochemie. Verlag von Knapp, Halle. (In preparation.) Elektrometallurgie. Verlag v'on Hirzel, Leipzig. 1905. Electro Smelting. Lippincott Co. H. DANNEEL. Spezielle Elektrochemie. Verlag von Knapp, Halle. (In preparation.) Jahrbuch der Elektrochemie. Verlag von Knapp, Halle. 1902- 1905. F. KOHLRAUSCH und L. HOLBORN. Das Leitvermogen der Elektro- lyte. Verlag von Teubner, Leipzig. 1898. Introduction to Physical Measurements. Macmillan & Co. F. DOLEZALEK. Die Theorie des Bleiakkumulators. Verlag von Knapp, Halle. 1901. The Theory of the Lead Accumulator. Wiley & Sons. F. M. PERKIN. Practical Methods of Electrochemistry. Longmans, Green & Co., New York and London. 1905. R. LORENZ. Elektrochemisches Praktikum. Verlag von Vandenhock und Ruprechht, Gottingen. 1901. LITERATURE. 175 M. ROLOFF und P. BERKITZ. Elektrotechnisches und elektrochemisches Seminar. Verlag von Enke, Stuttgart. 1904. W. NERNST und W. BORCHERS. Jahrbuch der Elektrochemie. Verlag von Knapp, Halle. 1894-1901. B. PERIODICALS. Zeitschrift fiir Elektrochemie. Organ der Bunsengesellschaft, Knapp, Halle. Zeitschrift fur physikalische Chemie. Engelmann, Leipzig. Zeitschrift fur anorganische Chemie. Voss, Hamburg. Journal of Physical Chemistry. Ithaca, N. Y. Journal de chimie physique, Kundig, Genf; Gautiers-Villard, Paris. Transactions of the American Electrochemical Society. Published by the Society, Philadelphia. Electrochemical Industry. Electrochemical Publishing Co., New York. Transactions of the Faraday Society. Published by the Society, London. INDEX. Absolute potential, 135 Absolute temperature, 10 Absolute velocities of the ions, 112 Absorption law, 136 Acceleration, 2 Accumulator, 147 Acetic acid, dissociation of, 100 Acid-alkali cell, 72, 146 Acids and bases, strength of, 97 Active mass, 36, 40 Additive properties of the ions, 74 Affinity of acids, 102 Air pressure, 16 Air ions, 170 Alcohols as solvents, 93 Alloys, potential of, 140 Amalgams, potential of, 14 formation of, 167 Ammonia as a solvent, 93 Ampere, 3, 6 Analysis, electrolytic, 165 and the dissociation theory, 105 Anion, 51 Arrhenius, theory of, 56 Atmosphere, pressure of, 19 Atomic weights, table of, 163 Avogadro's Law, 18 Bases, 64 Bases and acids, strength of, Becquerel rays, 1 70 Berthelot's Principle, 9 Bleaching solutions, 168 97 Boiling-point, rise of, 28, 47 molecular rise of, 47 Carbon monoxide and oxygen, 38, 41 Carbon dioxide, dissociation of, 38, 41 Calcium carbonate, dissociation of, 40 Calomel electrode, 141 Calorie, 4 Capacity, 117 of the storage battery, 148 Capillarity, 75 Catalyzers, 15 Catalysis and dissociation constant, 98 Cataphoresis, 119 Cathode rays, 169 Cation, 51 Cell, galvanic, 120 Chemical energy, 5, 6 Chemical equilibrium, 32 Chemical-force and reaction velocity, 14 Chemcial kinetics and statics, 35, 36 Chemical resistance, 15 Chemical work and osmotic pressure, 29 Chemistry, applications of the disso- ciation theory in, 61 Chlorates, 168 Chlorine electrode, 138 Chlorine-hydrogen cell, 152 177 i 7 8 INDEX. Chlorine potential of chlorides. 141 Clausius, theory of, 55 Complete reactions, 32 Compounds, potential of, 140 Concentration cells with respect to the electrodes, 137, 138 Concentration cells with respect to the electrolyte, 144 Conduction through salts, 45 Conductivity, 77 Conductivity, of acetic acid, 100 metallic and electrolytic, 80 of the metals, 79 of pure substances, 91 of solutions, 8 1 specific, 78 temperature coefficient of, 79, 107 of water, 73 Conservation of energy, 7 Contact electricity, 118 Copper, precipitation of , by zinc, 126 Coulomb, 3, 78 and ion, 52 Current, production of, by chemical means, 115 Daniell cell, n, 121, 126 Decomposition voltage, 152, 155, 156 Depolarization, 154 Deposition voltage of the ions, 156, 160, 161 Dielectric constant, 113 and dissociating power, 93, 94 Diffusion potential 145 Dilution law, Ostwald's, 101 Dissociating power, 92 Dissociation constant, 58, 99 Dissociation constants, table of, 102 Dissociation constant and hydroly- sis, 68 Dissociation, electrolytic, 48 decrease of, 102 degree of, 48, 57, 87 formula of salts, 58 of gases, 38 heat of, 67 pressure, 41 of salts, 96 stepwise, 63, 106 theory of, 45 of water, 73, 147 Dyne, 2 Electric work, 3, 6 Electricity, a chemical substance, 169 quantity of, 3 Electrochemistry, history of, 49 and work obtainable from reac- tions, 12 Electrodes, 51 of first and second kind, 141, 142 Electrolysis, 164 Electrolyte, 51 Electrolytic solution pressure, 127 Electrolytic potential, 130 Electromotive force, calculation of, 123 Electron, velocity and mass of, 169 theory, 169 Element, 120 Endosmosis, 119 Energy, chemical, 5, 6 electric, 3, 6 free, u heat, 4 kinds of, i, 6 kinetic, 7 law of the conservation of, 7 law of the transformation of, 9 mechanical, 2 potential, 8 radiant, 5 table of equivalents, 5 temperature coefficient of, 10 volume, 2 Energy equation of Gibbs-Helm- holtz, 124 of van't Hoff, 31, 124 of Nernst, 127 Equilibrium, chemical, 32 and temperature, 41 Equilibrium, constant, 35 concentration, 125 Equivalent, 83 conductivity, 83, 86, 90 weights table of, 163 Ester formation, 32, 36 Expansion, work done in, 4 Faraday's law, 52, 162 Ferrocyanide of copper membrane, 24 INDEX. 179 Fluid, electric, 169 Force, 5 chemical, and reaction velocity, 14 Free energy, n Freezing-point, lowering of, 27 molecular lowering of, 46 Friction, of the ions, 93 internal, 75 Frictional electricity, 119 Fugacity, 127 Galvani's experiments, 120 Galvanic cell, 120 Gas-constant R, 18 value of, in different units, 5 Gas electrodes, 136 Gas laws, 16 Gas pressure, 16 Gases, dissociation of, 37 expansion of, 2 work obtainable from, 16, 21 overvoltage of, 158 Gay-Lussac's Law, 16 Gibbs-Helmholtz formula, 124 Gram equivalent and molecule. 18, 83 Grottnus, theory of, 53 Grove, theory of, 54 gas cell, 138, 144 Heat energy, 4, 6 Heat, mechanical equivalent of, 4 theory of, 7, 9 Heat and motion, 8 of reaction, 8, 43, 44 of neutralization, 66 Helmholtz's energy equation, 124 Henry's absorption law, 136 Heterogeneous systems, 39 H.ttorf's experiments on the trans- port number, 55 Van't Hoff , energy equation, 31 laws of solutions, 56 laws of dilution, 101 Homogeneous systems, 39 Hydrogen, deposition of, 160 electrode, 133, 137 electrolytic potential, 133 overvoltage of, 158 Hvdroiodic acid, formation of, 37 Hydrolysis, 68 and the dissociation constant, 71 Hydroxyl ions, deposition of, 167 Hypochlorites, 168 I, van't Hoff 's factor, table, 49 Incomplete reactions, 32, 33 Insulators, conductivity of, 79 Inversion of sugar, 98 Ions,. -48, 52 additive properties of, 75 charges on, 49, 52 deposition voltage of, 156, 160, 161 as electron compounds, 171 friction overcome by, 113 reactions of, 61 velocities of, 84 velocities of absolute, 112 Isohydric solutions, 103 Isosmotic and isotomic solutions, 23 Kinetics, law of chemical, 35 Kohlrausch, law of the independent wandering of the ions, 5 5 , 85 , 1 1 1 Lead, deposition of, 165 storage battery, 147 Light, absorption of, 75 Litre atmosphere, 2, 19 Liquids, contact potential of, 145 Mass, 2 Mass action, 36, 40 law of, 35 and dissociation, 57 Maximum work, 6, 8 determination of, 12 Mechanical energy, 2 Mechanicat equivalent of heat, 4 Mercury, potential and surface tension of, 135 normal electrode, 134 Metal solutions, potential of, 140 Metals, specific conductivity of, 79 Mixtures, potential of, 140 Mol, 18 Molecule, gaseous, 18 Molecular concentration, 23 Molecular conductivity of the ions, 85 i8o INDEX. Nernst's formula, 127 applications of, 146 Neutralization, 66 Neutralization cell, 146 Neutralization, heat of, 66 Neutron, 170 Nitrogen, density of, 18 "Nobility" of the metals, 134 Normal electrodes, 134, 142 Ohm's law, 78, 117 Osmotic cells, 25 Osmotic work, 30 Osmotic pressure, 27 of salts, 49 of sugar (table), 26 and solution pressure, 128 and work, 20 Ostwald's dilution law, 101 Oxidation potential, 143 Oxygen electrode, 138 Oxygen, overvoltage of, 158 Oxygen and carbon monoxide, 38, 41 Oxygen-hydrogen cell, 138 Partial pressure, 17 Perpetual motion, 7, 9 Persulphuric acid, 166 Plant cells, osmotic pressure of, 22, 24 Phosphorous chloride, formation of, 3 8 Physiological solutions, 76 Physiology and the theory of elec- trolytic dissociation, 75 Plasmolysis, 23 Platinum as semipermeable mem- brane, 25 Platinum black, catalytic action of, . 136 Poisonous action of the ions, 76 Polarization, 152 capacity, 153 Polymerization and dissociating power, 95 Potential, absolute, 135 of alloys, 140 of compounds, 140 at contact of solutions, 145 difference of, 2, 77, 116 electric, 116 Potential, electrolytic, 130, 134 energy, 7 fall of, 116 of mixtures, 140 of reducing and oxidizing agents 143 Pressure, 2 osmotic, and chemical work, 30 Principe du travail maximum, 9 Principles of thermodynamics, 6, 9, 10 R, the gas-constant, 18 Radium, 170 Reaction, complete and incomplete, 3 2 heat of, 8 reversible, 34 work obtainable from, 12 Reaction velocity, 14, 35 Reduction potential, 143 Residual current, 154 Resistance, chemical, 15 specific, of metals, 79 Reversibility, 12, 123 Saponification, 71, 99 Salt solution, osmotic pressure of, 47 Salts, dissociation of, 58 solution of, 40 Schlieren apparat, 28 Secondary reactions, 167 Secondary elements, 147 Semipermeable membranes, 22 of Cu 2 Fe(CN) c , 24 of air, 28 of ice, 27 of platinum, 25 Series of the elements according to their electrolytic solution pres- sure, 135 Silver analysis, and the dissociation theory, 104 Silver, equivalent of, 3. Cf. also Faraday's law Silver iodide, solubility of, 146 Silver ions, precipitation of, by chlorine ions, 61 Sodium acetate, hydrolysis of, 68 Sodium amalgam, 167 Solids, active mass of, 36, 40 INDEX. 181 Solubility, constant, 40 from electromotive force, 146 Solubility product, 104 Solutions, conductivity of, 81 dilute and the gas laws, 20 isotonic, 23 of salts, osmotic pressure, 47 Solution pressure, electrolytic, 127, 128 Solvent, active mass of, 36 dissociating, 92 Specific conductivity of metals, 79 Statics, law of chemical, 35 Cf. ciation Stepwise dissociation. Cf. Disso- Succinic acid, solution of, 44 Sugar, osmotic pressure of, 25 inversion of, 98 Sulphuric acid, specific conductivity of, 91 decomposition voltages of, 161 Temperature, absolute, 10 and chemical equilibrium, 41 Temperature coefficient of capacity for work, 10 of conductivity, 79, 80, 107 Thomson's Rule, 9 Transformation of energy, 9 Transport number, 108 Valence, variable and dissociating power, 95 Vapor pressure of water, 41 lowering of, 27, 47 Velocity of the ions, 85 Volt, 4 Voltage, 3, 6 measurement of, 118 of decomposition, 152 Voltaic pile, 121 Walls, semipermeable, 22 Wandering of the ions, law of the independent, 85 Water, conductivity of, 90 dissociating power of, 93 dissociation of, 65, 73, 147 electrolysis of, 154 evaporation of, 32 vapor pressure of, 41 Watt second, 3, 6 Weight, 2 Williamson, theory of, 55 Work, chemical, and osmotic pres- sure, 30 from expansion of gases, 16, 19 maximum, 7, 9 from natural processes, 6 osmotic, 19 Zero, absolute, of temperature, 10 Zinc, deposition of, 160 Zinc amalgam, potential of, 139 SHORT-TITLE CATALOGUE OP THE PUBLICATIONS OP JOHN WILEY & SONS, NEW YORK. 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Church's Mechanics of Engineering 8vo, 6 oo- Diagrams of Mean Velocity of Water in Open Channels paper, i 50 Hydraulic Motors 8vo, 2 oo Coffin's Graphical Solution of Hydraulic Problems i6mo, morocco, 2 50 Flather's Dynamometers, and the Measurement of Power I2rco, 3 oo Folwell's Water-supply Engineering : 8vo, 4 oo Frizell's Water-power 8vo, 5 oo 7 Fuertes's Water and Public Health , .121110, i 50 Water-filtration Works i2mo, 2 50 Ganguillet and Kutter's General Formula for the Uniform Flow of Water in Rivers and Other Channels. (Hering and Trau twine.) 8vo, 4 oo Hazen's Filtration of Public Water-supply: 8vo, 3 oo Hazlehurst's Towers and Tanks for Water-works 8vo, 2 50 Herschel's 115 Experiments on the Carrying Capacity of Large, Riveted, Metal Conduits 8vo. 2 oo Mason's Water-supply. 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Andrew's Handbook for Street Railway Engineers. .. .3x5 inches, morocco, i 25 Berg's Buildings and Structures of American Railroads 4to, 5 oo Brook's Handbook of Street Railroad Location i6mo, morocco . i 50 Butt's Civil Engineer's Field-book i6mo, morocco, 2 50 Crandall's Transition Curve i6mo, morocco, i 50 Railway and Other Earthwork Tables 8vo, i 50 Dawson's "Engineering" and Electric Traction Pocket-book i6mo, morocco, 5 oo Dredge's History of the Pennsylvania Railroad: (1870) Paper, 5 oo * Drinker's Tunnelling, Explosive Compounds, and Rock Drills. 4to, half mor., 25 oo Fisher's Table of Cubic Yards Cardboard, 25 Godwin's Railroad Engineers' Field-book and Explorers' Guide. . . i6mo, mor., 2 50 Howard's Transition Curve Field-book i6mo, morocco, i 50 Hudson's Tables for Calculating the Cubic Contents of Excavations and Em- bankments 8vo, i oo Molitor and Beard's Manual for Resident Engineers. s i6mo, i oo Nagle's Field Manual for Railroad Engineers i6mo, morocco, 3 oo Philbrick's Field Manual for Engineers. i6mo, morocco, 3 oo Searles's Field Engineering i6mo, morocco, 3 oo Railroad Spiral i6mo, morocco, i 50 Taylor's Prismoidal Formulae and Earthwork 8vo, i 50 * Trautwine's Method ot Calculating the Cube Contents of Excavations and Embankments by the Aid of Diagrams 8vo, 2 oo The Field Practice of Laying Out Circular Cyrves for Railroads. i2ino, morocco, 2 50 Cross-section Sheet Paper, 25 Webb's Railroad Construction i6mo, morocco, 5 oo Economics of Railroad Construction Large i2tno, 2 50 Wellington's Economic Theory of the Location of Railways Small 8vo- 5 oo DRAWING. 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(Herrmann Klein.). 8vo, 5 oa Machinery of Transmission and Governors. (Herrmann Klein.). .8vo, 5 oo Wolff's Windmill as a Prime Mover 8vo, 3 oo Wood's Turbines 8vo, 2 50 MATERIALS OP ENGINEERING. *,Bovey's Strength of Materials and Theory of Structures 8vo, 7 50 Burr's Elasticity and Resistance of the Materials of Engineering. 6th Edition. Reset 8vo, 7 50 Church's Mechanics of Engineering 8vo, 6 oo * Greene's Structural Mechanics 8vo, 2 50 Johnson's Materials of Construction 8vo, 6 oo Keep's Cast Iron . 8vo, 2 50. Lanza's Applied Mechanics 8vo, 7 50. Martens's Handbook on Testing Materials. (Henning.) 8vo, 7 so> Maurer's Technical Mechanics 8vo, 4 oa Merriman's Mechanics of Materials " 8vo, 5 oo Strength of Materials i2mo, i oa Metcalf's Steel. A manual for Steel-users i2mo, 2 oa Sabin's Industrial and Artistic Technology of Paints and Varnish. 8vo, 3 oa Smith's Materials of Machines i2mo, i oa Thurston's Materials of Engineering 3 vols., 8vo, 8 oa Part II. Iron and Steel 8vo, 3 50 Part III. A Treatise on Brasses, Bronzes, and Other Alloys and their Constituents 8vo, 2 50* Text-book of the Materials of Construction 8vo, 5 oo> Wood's (De V.) Treatise on the Resistance of Materials and an Appendix on the Preservation of Timber Svo, 2 oo- Elements of Analytical Mechanics Svo, 3 oo Wood's (M. P.) Rustless Coatings: Corrosion and Electrolysis of Iron and Steel., 8vo, 400. STEAM-ENGINES AND BOILERS. Berry's Temperature-entropy Diagram i2mo, i 25 Carnot's Reflections on the Motive Power of Heat. 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Design, Construction, and Operation 8vo, 6 oo Handbook of Engine and Boiler Trials, and the Use of the Indicator and the Prony Brake 8vo, 5 oo Stationary Steam-engines 8vo, 2 50 Steam-boiler Explosions in Theory and in Practice I2mo, i 50 Manual of Steam-boilers, their Designs, Construction, and Operation 8vo, 5 oo Wehrenfenning's Analysis and Softening of Boiler Feed-water (Patterson) 8vo, 4 oo Weisbach's Heat, Steam, and Steam-engines. (Du Bois.) 8vo, 5 oo Whitham's Steam-engine Design 8vo, 5 oo Wood's Thermodynamics, Heat Motors, and Refrigerating Machines. . .8vo, 4 oo MECHANICS AND MACHINERY. Barr's Kinematics of Machinery : 8vo, 2 50 * Bovey's Strength of Materials and Theory of Structures 8vo, 7 50 Chase's The Art of Pattern-making i2mo, 2 50 Church's Mechanics of Engineering 8vo, 6 oo Notes and Examples in Mechanics. . , .* 8vo, 2 oo Compton's First Lessons in Metal-working. . . i2mo, 50 Compton and De Groodt's The Speed Lathe i2mo, 50 Cromwell's Treatise on Toothed Gearing. 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