equivalent conductivity reaches a limiting value indicating that | § II., "Nature of Electrolytes "). It is probable that the complete ionization is reached as dilution is increased. With electrical effects constitute the strongest arguments in favour such salts alone is a valid comparison possible.

sharp contrast with the difficulty experienced in the case of non-electrolytes. Moreover, a study of the chemical relations of electrolytes indicates that it is always the electrolytic ions that are concerned in their reactions. The tests for a salt, potassium nitrate, for example, are the tests not for KNO1, but for its ions K and NO,, and in cases of double decomposition it is always these ions that are exchanged for those of other substances. If an element be present in a compound otherwise than as an ion, it is not interchangeable, and cannot be recognized by the usual tests. Thus neither a chlorate, which contains the ion CIO3, nor monochloracetic acid, shows the reactions of chlorine, though it is, of course, present in both substances; again, the sulphates do not answer to the usual tests which indicate the presence of sulphur as sulphide. The chemical activity of a substance is a quantity which may be measured by different methods. For some substances it has been shown to be independent of the particular reaction used. It is then possible to assign to each body a specific coefficient of affinity. Arrhenius has pointed out that the coefficient of affinity of an acid is proportional to its electrolytic ionization.

The affinities of acids have been compared in several ways. W.Ostwald (Lehrbuch der allg. Chemie, vol. ii., Leipzig, 1893) investigated the relative affinities of acids for potash, soda and ammonia, and proved them to be independent of the base used. The method employed was to measure the changes in volume caused by the action. His results are given in column I. of the following table, the affinity of hydrochloric acid being taken as one hundred. Another method is to allow an acid to act on an insoluble salt, and to measure the quantity which goes into solution. Determinations have been made with calcium oxalate, CaCO,+H2O, which is easily decomposed by acids, oxalic acid and a soluble calcium salt being formed. The affinities of acids relative to that of oxalic acid are thus found, so that the acids can be compared among themselves (column. II.). If an aqueous solution of methyl acetate be allowed to stand, a slow decomposition goes on. This is much quickened by the presence of a little dilute acid, though the acid itself remains unchanged. It is found that the influence of different acids on this action is proportional to their specific coefficients of affinity. The results of this method are given in column III. Finally, in column IV. the electrical conductivities of normal solutions of the acids have been tabulated. A better basis of comparison would be the ratio of the actual to the limiting conductivity, but since the conductivity of acids is chiefly due to the mobility of the hydrogen ions, its limiting value is nearly the same for all, and the general result of the comparison would be unchanged.

It must be remembered that, the solutions not being of quite the same strength, these numbers are not strictly comparable, and that the experimental difficulties involved in the chemical measurements are considerable. Nevertheless, the remarkable general agreement of the numbers in the four columns is quite enough to show the intimate connexion between chemical activity and electrical conductivity. We may take it, then, that only that portion of these bodies is chemically active which is electrolytically active-that ionization is necessary for such chemical activity as we are dealing with here, just as it is necessary for electrolytic conductivity.

The ordinary laws of chemical equilibrium have been applied to the case of the dissociation of a substance into its ions. Let x be the number of molecules which dissociate per second when the number of undissociated molecules in unit volume is unity, then in a dilute solution where the molecules do not interfere with each other, xp is the number when the concentration is p. Recombination can only occur when two ions meet, and since the frequency with which this will happen is, in dilute solution, proportional to the square of the ionic concentration, we shall get for the number of molecules re-formed in one second y where q is the number of dissociated molecules in one cubic centimetre. When there is equilibrium, xp=yq2. If u be the molecular conductivity, and its value at infinite dilution, the fractional number of molecules dissociated is

/o, which we may write as a. The number of undissociated mole
cules is then 1-a, so that if V be the volume of the solution containing
I gramme-molecule of the dissolved substance, we get
q= a/V and p= (1−a)/V,

hence

and

@=

This constant k gives a numerical value for the chemical affinity and the equation should represent the effect of dilution on the molecular conductivity of binary electrolytes. In the case of substances like ammonia and acetic acid, where the dissociation is very small, 1-a is nearly equal to unity, and only varies slowly with dilution. The equation then becomes a2/V = k, or Vk, so that the molecular conductivity is proportional to the square root of the dilution. Ostwald has confirmed the equation by observation on an enormous number of weak acids (Zeits. physikal. Chemie, 1888, ii. p. 278; 1889. iii. pp. 170, 241, 369). Thus in the case of cyanacetic acid, while the volume V changed by doubling from 16 to 1024 litres, the values of k were 0.00 (376, 373, 374. 361, 362, 361, 368). The mean values of k for other common acids were-formic, 0.0000214; acetic, 0.0000180; monochloracetic, 0-00155: dichloracetic, 0-051; trichloracetic, 1-21; propionic, 0.0000134. From these numbers we can, by help of the equation, calculate the conductivity of the acids for any dilution. The value of k, however, does not keep constant so satisfactorily in the case of highly dissociated substances, and empirical formulae have been constructed to represent the effect of dilution on them. Thus the values of the expressions a2/(1-a√V) (Rudolphi, Zeits, physikal. Chemie, 1895, vol. xvii. p. 385) and a/(1-a) V (van 't Hoff, ibid., 1895, vol. xviii. p. 300) are found to keep constant as V changes. Van 't Hoff's formula is equivalent to taking the frequency of dissociation as proportional to the square of the concentration of the molecules, and the frequency of recombination as proportional to the cube of the concentration of the ions. An explanation of the failure of the usual dilution law in these cases may be given if we remember that, while the electric forces between bodies like undissociated molecules, each associated with equal and opposite charges, will vary inversely as the fourth power of the distance, the forces between dissociated ions, each carrying one charge only, will be inversely proportional to the square of the distance. The forces between the ions of a strongly dissociated solution will thus be considerable at a dilution which makes forces between undissociated molecules quite insensible, and at the concentrations necessary to test Ostwald's formula an electrolyte will be far from dilute in the thermodynamic sense of the term, which implies no appreciable intermolecular or interionic forces.

When the solutions of two substances are mixed, similar considerations to those given above enable us to calculate the resultant changes in dissociation. (See Arrhenius, loc. cit.) The simplest and most important case is that of two electrolytes having one ion in common, such as two acids. It is evident that the undissociated part of cach acid must eventually be in equilibrium with the free hydrogen ions, and, if the concentrations are not such as to secure this condition, readjustment must occur. In order that there should be no change in the states of dissociation on mixing, it is necessary, therefore, that the concentration of the hydrogen ions should be the same in each separate solution. Such solutions were called by Arrhenius isohydric." The two solutions, then, will so act on each other when mixed that they become isohydric. Let us suppose that we have one very active acid like hydrochloric, in which dissociation is nearly complete, another like acetic, in which it is very small. In order that the solutions of these should be isohydric and the concentrations of the hydrogen ions the same, we must have a very large quantity of the feebly dissociated acetic acid, and a very small quantity of the strongly dissociated hydrochloric, and in such proportions alone will equilibrium be possible. This explains the action of a strong acid on the salt of a weak acid. Let us allow dilute sodium acetate to react with dilute hydrochloric acid. Some acetic acid is formed, and this process will go on till the solutions of the two acids are isohydric: that is, till the dissociated hydrogen ions are in equilibrium with both. In order that this should hold, we have seen that a considerable quantity of acetic acid must be present, so that a corresponding amount of the salt will be decomposed, the quantity being greater the less the acid is dissociated. This " replacement" of a "weak" acid by a "strong "one is a matter of common observation in the chemical laboratory. Similar investigations applied to the general case of chemical equilibrium lead to an expression of exactly the same form as that given by C. M. Guldberg and P.Waage, which is universally accepted as an accurate representation of the facts.

The temperature coefficient of conductivity has approximately the same value for most aqueous salt solutions. It decreases both as the temperature is raised and as the concentration is increased, ranging from about 3.5% per degree for extremely dilute solutions (i.e. practically pure water) at o° to about 1.5

for concentrated solutions at 18°. For acids its value is usually | portions of the electrolyte which surround them. A current rather less than for salts at equivalent concentrations. The influence of temperature on the conductivity of solutions depends on (1) the ionization, and (2) the frictional resistance of the liquid to the passage of the ions, the reciprocal of which is called the ionic fluidity. At extreme dilution, when the ionization is complete, a variation in temperature cannot change its amount. The rise of conductivity with temperature, therefore, shows that the fluidity becomes greater when the solution is heated. As the concentration is increased and un-ionized molecules are formed, a change in temperature begins to affect the ionization as well as the fluidity. But the temperature coefficient of conductivity is now generally less than before; thus the effect of temperature on ionization must be of opposite sign to its effect on fluidity. The ionization of a solution, then, is usually diminished by raising the temperature, the rise in conductivity being due to the greater increase in fluidity. Nevertheless, in certain cases, the temperature coefficient of conductivity becomes negative at high temperatures, a solution of phosphoric acid, for example, reaching a maximum conductivity at 75° C. The dissociation theory gives an immediate explanation of the fact that, in general, no heat-change occurs when two neutral salt solutions are mixed. Since the salts, both before and after mixture, exist mainly as dissociated ions, it is obvious that large thermal effects can only appear when the state of dissociation of the products is very different from that of the reagents. Let us consider the case of the neutralization of a base by an acid in the light of the dissociation theory. In dilute solution such substances as hydrochloric acid and potash are almost completely dissociated, so that, instead of representing the reaction as HCI+KOH= KCl+H2O, we must write

can be obtained by the combination of two metals in the same
electrolyte, of two metals in different electrolytes, of the same
metal in different electrolytes, or of the same metal in solutions
of the same electrolyte at different concentrations. In accord-
ance with the principles of energetics (q.v.), any change which
involves a decrease in the total available energy of the system
will tend to occur, and thus the necessary and sufficient condition
for the production of electromotive force is that the available
energy of the system should decrease when the current flows.
In order that the current should be maintained, and the
electromotive force of the cell remain constant during action, it
is necessary to ensure that the changes in the cell, chemical or
other, which produce the current, should neither destroy the
difference between the electrodes, nor coat either electrode
with a non-conducting layer through which the current cannot
pass. As an example of a fairly constant cell we may take that
of Daniell, which consists of the electrical arrangement-zinc |
zinc sulphate solution copper sulphate solution | copper,-the
two solutions being usually separated by a pot of porous earthen-
ware. When the zinc and copper plates are connected through
a wire, a current flows, the conventionally positive electricity
passing from copper to zinc in the wire and from zinc to copper
in the cell. Zinc dissolves at the anode, an equal amount of
zinc replaces an equivalent amount of copper on the other side
of the porous partition, and the same amount of copper is
deposited on the cathode. This process involves a decrease in
the available energy of the system, for the dissolution of zinc
gives out more energy than the separation of copper absorbs.
But the internal rearrangements which accompany the produc-
tion of a current do not cause any change in the original nature
of the electrodes, fresh zinc being exposed at the anode, and
copper being deposited on copper at the cathode. Thus as long
as a moderate current flows, the only variation in the cell is the
appearance of zinc sulphate in the liquid on the copper side of the
porous wall. In spite of this appearance, however, while the
supply of copper is maintained, copper, being more easily
separated from the solution than zinc, is deposited alone at the
cathode, and the cell remains constant.

The ions K and Cl suffer no change, but the hydrogen of the acid and the hydroxyl (OH) of the potash unite to form water, which is only very slightly dissociated. The heat liberated, then, is almost exclusively that produced by the formation of water from its ions. An exactly similar process occurs when any strongly dissociated acid acts on any strongly dissociated base, It is necessary to observe that the condition for change in so that in all such cases the heat evolution should be approxi- a system is that the total available energy of the whole system mately the same. This is fully borne out by the experiments of should be decreased by the change. We must consider what Julius Thomsen, who found that the heat of neutralization of one change is allowed by the mechanism of the system, and deal with gramme-molecule of a strong base by an equivalent quantity of a the sum of all the alterations in energy. Thus in the Daniell cell strong acid was nearly constant, and equal to 13,700 or 13,800 the dissolution of copper as well as of zinc would increase the calories. In the case of weaker acids, the dissociation of which loss in available energy. But when zinc dissolves, the zinc is less complete, divergences from this constant value will occur, ions carry their electric charges with them, and the liquid tends for some of the molecules have to be separated into their ions. to become positively electrified. The electric forces then soon For instance, sulphuric acid, which in the fairly strong solutions stop further action unless an equivalent quantity of positive used by Thomsen is only about half dissociated, gives a higher ions are removed from the solution. Hence zinc can only dissolve value for the heat of neutralization, so that heat must be evolved when some more easily separable substance is present in solution when it is ionized. The heat of formation of a substance froin to be removed pari passu with the dissolution of zinc. The its ions is, of course, very different from that evolved when it is mechanism of such systems is well illustrated by an experiment formed from its elements in the usual way, since the energy devised by W. Ostwald. Plates of platinum and pure or amalassociated with an ion is different from that possessed by the gamated zinc are separated by a porous pot, and each suratoms of the element in their normal state. We can calculate rounded by some of the same solution of a salt of a metal the heat of formation from its ions for any substance dissolved more oxidizable than zinc, such as potassium. When the plates in a given liquid, from a knowledge of the temperature coefficient are connected together by means of a wire, no current flows, of ionization, by means of an application of the well-known and no appreciable amount of zinc dissolves, for the dissolution thermodynamical process, which also gives the latent heat of of zinc would involve the separation of potassium and a gain evaporation of a liquid when the temperature coefficient of its in available energy. If sulphuric acid be added to the vessel vapour pressure is known. The heats of formation thus obtained containing the zinc, these conditions are unaltered and still no may be either positive or negative, and by using them to supple-zinc is dissolved. But, on the other hand, if a few drops of acid ment the heat of formation of water, Arrhenius calculated the be placed in the vessel with the platinum, bubbles of hydrogen total heats of neutralization of soda by different acids, some of appear, and a current flows, zinc dissolving at the anode, and them only slightly dissociated, and found values agreeing well hydrogen being liberated at the cathode. In order that positively with observation (Zeits. physikal. Chemie, 1889, 4, p. 96; and electrified ions may enter a solution, an equivalent amount of 1892, 9, p. 339). other positive ions must be removed or negative ions be added, and, for the process to occur spontaneously, the possible action at the two electrodes must involve a decrease in the total available energy of the system.

Voltaic Cells. When two metallic conductors are placed in an electrolyte, a current will flow through a wire connecting them provided that a difference of any kind exists between the two conductors in the nature either of the metals or of the

Considered thermodynamically, voltaic cells must be divided

into reversible and non-reversible systems. If the slow pro- | stronger solution by the separation of metal from it. We may cesses of diffusion be ignored, the Daniell cell already described may be taken as a type of a reversible cell. Let an electromotive force exactly equal to that of the cell be applied to it in the reverse direction. When the applied electromotive force is diminished by an infinitesimal amount, the cell produces a current in the usual direction, and the ordinary chemical changes occur. If the external electromotive force exceed that of the cell by ever so little, a current flows in the opposite direction, and all the former chemical changes are reversed, copper dissolving from the copper plate, while zinc is deposited on the zinc plate. The cell, together with this balancing electromotive force, is thus a reversible system in true equilibrium, and the thermodynamical reasoning applicable to such systems can be used to examine its properties.

The effective electromotive force of the common lead accumu- | of the zinc as it is at the surface of the copper. Since zinc goes lator (q..) is less than that required to charge it. This drop in the electromotive force has led to the belief that the cell is not reversible. F. Dolezalek, however, has attributed the difference to mechanical hindrances, which prevent the equalization of acid concentration in the neighbourhood of the electrodes, rather than to any essentially irreversible chemical action. The fact that the Gibbs-Helmholtz equation is found to apply also indicates that the lead accumulator is approximately reversible in the thermodynamic sense of the term.

Polarization and Contact Difference of Potential.-If we connect together in series a single Daniell's cell, a galvanometer, and two platinum electrodes dipping into acidulated water, no visible chemical decomposition ensues. At first a considerable current is indicated by the galvanometer; the deflexion soon diminishes, however, and finally becomes very small. If, instead of using a single Daniell's cell, we employ some source of electromotive force which can be varied as we please, and gradually raise its intensity, we shall find that, when it exceeds a certain value, about 1.7 volt, a permanent current of considerable strength flows through the solution, and, after the initial period, shows no signs of decrease. This current is accompanied by chemical decomposition. Now let us disconnect the platinum plates from the battery and join them directly with the galvanometer. A current will flow for a while in the reverse direction; the system of plates and acidulated water through which a current has been passed, acts as an accumulator, and will itself yield a current in return. These phenomena are explained by the existence of a reverse electromotive force at the surface of the platinum plates. Only when the applied electromotive force exceeds this reverse force of polarization, will a permanent steady current pass through the liquid, and visible chemical decomposition proceed. | It seems that this reverse electromotive force of polarization is due to the deposit on the electrodes of minute quantities of the products of chemical decomposition. Differences between the two electrodes are thus set up, and, as we have seen above, an electromotive force will therefore exist between them. To pass a steady current in the direction opposite to this electromotive force of polarization, the applied clectromotive force E must exceed that of polarization E', and the excess E- E' is the effective electromotive force of the circuit, the current being, in accordance with Ohm's law, proportional to the applied electromotive force and represented by (E- E')/R, where R is a constant called the resistance of the circuit.

into solution and copper comes out, the electromotive force of the cell will be the difference between the two effects. On the other hand, it is commonly thought that the single potentialdifferences at the surface of metals and electrolytes have been determined by methods based on the use of the capillary electrometer and on others depending on what is called a dropping electrode, that is, mercury dropping rapidly into an electrolyte and forming a cell with the mercury at rest in the bottom of the vessel. By both these methods the single potential-differences found at the surfaces of the zinc and copper have opposite signs, and the effective electromotive force of a Daniell's cell is the sum of the two effects. Which of these conflicting views represents the truth still remains uncertain.

Diffusion of Electrolytes and Contact Difference of Potential between Liquids.—An application of the theory of ionic velocity due to W. Nernst and M. Planck enables us to calculate the diffusion constant of dissolved electrolytes. According to the molecular theory, diffusion is due to the motion of the molecules of the dissolved substance through the liquid. When the dissolved molecules are uniformly distributed, the osmotic pressure will be the same everywhere throughout the solution, but, if the concentration vary from point to point, the pressure will vary also. There must, then, be a relation between the rate of change of the concentration and the osmotic pressure gradient, and thus we may consider the osmotic pressure gradient as a force driving the solute through a viscous medium. In the case of nonelectrolytes and of all non-ionized molecules this analogy completely represents the facts, and the phenomena of diffusion can be deduced from it alone. But the ions of an electrolytic solution can move independently through the liquid, even when no current flows, as the consequences of Ohm's law indicate. The ions will therefore diffuse independently, and the faster ion will travel quicker into pure water in contact with a solution. The ions carry their charges with them, and, as a matter of fact, it is found that water in contact with a solution takes with respect to it a positive or negative potential, according as the positive or negative ion travels the faster. This process will go on until the simultaneous separation of electric charges produces an electrostatic force strong enough to prevent further separation of ions. We can therefore calculate the rate at which the salt as a whole will diffuse by examining the conditions for a steady transfer, in which the ions diffuse at an equal rate, the faster one being restrained and the slower one urged forward by the electric forces. In this manner the diffusion constant can be calculated in absolute units (HCl=2·49, HNO3=2·27, NaCl-1.12), the unit of time being the day. By experiments on diffusion this constant has been found by Scheffer, and the numbers observed agree with those calculated (HCl=2·30, HNO3=2·22, NaCl = 1·11).

As we have seen above, when a solution is placed in contact with water the water will take a positive or negative potential with regard to the solution, according as the cation or anion has the greater specific velocity, and therefore the greater initial rate of diffusion. The difference of potential between two solutions of a substance at different concentrations can be calcu

When we use platinum electrodes in acidulated water, hydrogen and oxygen are evolved. The opposing force of polarization is about 1.7 volt, but, when the plates are disconnected and used as a source of current, the electromotive force they give is only about 1-07 volt. This irreversibility is due to the work required to evolve bubbles of gas at the surface of bright platinum plates. If the plates be covered with a deposit of platinum black, in which the gases are absorbed as fast as they are produced, the minimum decomposition point is 1.07 volt, and the process is reversible. If secondary effects are eliminated, the deposition of metals also is a reversible process; the decomposition voltage is equal to the electromotive force which the metal itself gives when going into solution. The phenomena of polariza-lated from the equations used to give the diffusion constants. tion are thus seen to be due to the changes of surface produced, and are correlated with the differences of potential which exist at any surface of separation between a metal and an electrolyte. Many experiments have been made with a view of separating the two potential-differences which must exist in any cell made of two metals and a liquid, and of determining each one individually. If we regard the thermal effect at each junction as a measure of the potential-difference there, as the total thermal effect in the cell undoubtedly is of the sum of its potentialdifferences, in cases where the temperature coefficient is negligible, the heat evolved on solution of a metal should give the electrical potential-difference at its surface. Hence, if we assume that, in the Daniell's cell, the temperature coefficients are negligible at the individual contacts as well as in the cell as a whole, the sign of the potential-difference ought to be the same at the surface

The results give equations of the same logarithmic form as those obtained in a somewhat different manner in the theory of concentration cells described above, and have been verified by experiment.

The contact differences of potential at the interfaces of metals and electrolytes have been co-ordinated by Nernst with those at the surfaces of separation between different liquids. In contact with a solvent a metal is supposed to possess a definite solution pressure, analogous to the vapour pressure of a liquid. Metal goes into solution in the form of electrified ions. The liquid thus acquires a positive charge, and the metal a negative charge. The electric forces set up tend to prevent further separation, and finally a state of equilibrium is reached, when no 1 Zeits. physikal. Chem. 2, p. 613. Wied. Ann., 1890, 40, p. 561.