extent. In this case, then, there is an apparent departure from Faraday's laws, the production of gas being considerably less than that calculated from the quantity of electricity flowing.

An extreme instance of residual current is to be found in the Nernst lamp. Large quantities of electricity are passed through the white-hot metallic oxides of which this is made, without any visible decomposition taking place; yet there is, according to Nernst,1 evidence to show that the conduction is electrolytic, and so presumably follows Faraday's laws but all the products of decomposition diffuse and recombine. The whole current is therefore, if this view be correct, a "residual current."

Returning to the electrolysis of dilute acid, if the applied electromotive force be raised say from half a volt to a volt, a fresh quantity of electricity will flow momentarily through the cell, increasing the quantity of oxygen and hydrogen on the plates till the polarisation is raised to one volt; it will then stop, leaving only the residual current, which will be somewhat larger than before.

When the applied electromotive force is again raised, to about III volt, the electrodes become saturated with oxygen and hydrogen, and any further electrolysis will be without effect in this direction. They have then become effectively converted into oxygen and hydrogen electrodes, with the potentials due to those substances, and no further back electromotive force of polarisation is to be obtained. Hence if the applied E.M.F. be made still greater, the excess over I'II volts will be continuously available for production of current, in accordance with Ohm's law; gas will then be continuously evolved.

A peculiar consequence of the law of mass action should here be noted. By adding an acid to water we can increase the concentration of H ions in it; by adding an alkali, the OH' ions; but in neither case is the potential difference required for decomposition affected. For equilibrium must subsist between the concentration of the hydrogen ions (CH), of the hydroxyl ions (Con), and of the water (CH20); and,

1 Zeitschr. f. Elektroch., 6. 41-43.

according to the law of mass action, the condition of equilibrium is

CHX COн = const. X CH20

But the concentration of the water, which is overwhelmingly greater than that of the ions, is practically constant; therefore

i.e. if by any means the logarithm of the concentration of the hydrogen ions is increased, that of the hydroxyl ions is necessarily decreased by the same amount. Now, according to Nernst's law, the potential of the H electrode increases in proportion to increase of log CH; that of the OH' electrode increases in proportion to decrease of log Coн; hence the potentials of the two always rise or fall together, and the difference of potential between the two is fixed, amounting to about 1'11 volts.

Still another complicating circumstance has to be taken into account, however. The potential difference I'II volt is that found to exist between electrodes saturated with oxygen and hydrogen, when these are used to form a voltaic cell; it is that which corresponds to the energy change in the reaction H• + OH' = H2O, and may be described as the theoretical, or reversible electromotive force of this combination. But when the action is reversed, i.e. when water is electrolysed, the voltage required to separate visible quantities of gas is always greater than this, and varies according to the metal used for electrode. There is a specific "excess voltage" required, which may perhaps be regarded as corresponding to a state of supersaturation of the gases. The supersaturation most readily occurs when the absorptive power of the metal for the gas is slight; it is least, therefore, in the case of well-platinised platinum plates, and much less for hydrogen than for oxygen.

The phenomenon was studied by Caspari,1 whose arrangement of apparatus is shown in Fig. 36. C is a platinised

1 Zeitschr. f. phys. Chem., 30. 89.

platinum electrode kept saturated with hydrogen; this served as a standard (see p. 238). B was another large platinised electrode, A, a small electrode of the metal to be studied. Connection between the electrodes was made by a narrow tube, and the electrolyte used, normal sulphuric acid. A polarising voltage of variable amount was applied from the battery E, to electrodes A and B; these, therefore, with the liquid between them, constituted the electrolytic cell. The difference of potential between

C and A or B was then measured by the potentiometer F. If the process at the electrodes were exactly reversible, the cathode of the electrolytic cell ought to exhibit no difference of potential from the standard hydrogen electrode, while the anode should be positive to it by by 1'11 volt (Caspari gives 1'08 in accordance with the data then available; hence his values of the excess voltage at the anode have been reduced by o‘03). The results obtained were these:

The excess voltage varies but slightly with the mechanical

condition of the metallic surface.

From the table it appears that to produce visible decomposition with platinised platinum electrodes requires

while with polished platinums it takes

I'II + 0·09 + 0°59 = 1'79 volt.

The latter number is about what is usually quoted as the practical decomposition potential.

As an extreme instance, it appears that by using a bright platinum anode and a mercury cathode it is possible to apply

I'II + 0'59 + 0·78 = 2'48 volts

to an aqueous solution before producing any visible evolution

of gas.

§ 7.

THERMODYNAMIC THEORY. (i)

The attempt made in § 2 to calculate the electromotive force of a voltaic cell led only to approximate results, and did not afford any means even of estimating the degree of approximation. The reason of this is in the assumption that the chemical energy spent by the materials of the cell is all converted into electrical energy; and as we then saw, this assumption is by no means always justified by the facts.

The complete theory of the energy transformations of the voltaic cell was given, independently, by Willard Gibbs1 and

1 Trans. Connecticut Acad., 3. 108-248, 343-524 (1875); German translation in Ostwald's Klassiker (Engelmann: Leipzig).

T. P. C.

N

by Helmholtz; their method of treatment is that of thermodynamics, so that the results arrived at may be regarded as forming a branch of that science. An outline of the results is given below; for complete mathematical treatment we may refer to treatises on thermodynamics and in particular to the volume in this series by F. G. Donnan.

When the chemical energy lost by the materials of a cell in their action ("heat of reaction") is not all converted into electrical energy, the remainder of it appears as heat in the cell; hence the energy equation should run

Heat of reaction = electrical work done + heat evolved

There are, however, cases in which the electrical work done exceeds the chemical energy spent: this, we saw, is true both for the Daniell cell and for the accumulator; the "heat evolved" is then negative, i.e. heat is absorbed. These voltaic combinations, in fact, serve as means of converting some of the heat stored up in their own materials into a useful form. Their action may be compared to that of a cylinder of compressed air if the air is allowed to flow out and work an air-motor, it cools in doing so, and the work is done-partly at least- -at the expense of surrounding heat. The immediate effect of the inequality between heat of reaction and electrical work is that the cell either rises or falls in temperature during action; it will afterwards, of course, give out the excess to, or absorb the deficiency of heat from, surrounding bodies; and for reasoning about the energy changes it is more convenient to suppose the action to take place slowly, so that the cell is always at the same temperature as its surroundings.

It is then natural tó describe the last term in the equation as latent heat of action of the cell; or rather, that term may be applied to the heat absorbed. For by "latent heat of evaporation" of liquid we mean the heat which must be supplied from surrounding sources when the transformation of liquid into vapour takes place, in order to keep the temperature

constant.

We may therefore rewrite the energy equation as―

1 Berl. Sitzber., 22-39 (1882).