The Conservation of Energy in Electrolysis

187.] Consider an electric current flowing in a circuit consisting partly of metals and partly of electrolytes placed in series.

During the passage of one unit of electricity through any section of the circuit one electrochemical equivalent of each of the electrolytes is electrol- ysed. There is therefore a definite amount of chemical action corresponding to a definite quantity of electricity passed through the circuit. The energy equivalent to any chemical process can be ascertained either directly or indi- rectly. When the process is such that it will go on of itself, and if the only effect external to the system is the giving off of heat generated during the process, then the intrinsic energy of the system must be diminished during the process by a quantity of energy equivalent to the heat given out. If a ma- terial system consisting of definite quantities of so many chemical substances is capable of existing in several different states, and if the system will not of

∗ [See Art. 192 and last two paragraphs of note, starting on p. 167.]JOULE’S EXPERIMENTS. 165 itself pass from one of these states (A) to another (B) we can still find the relative energy of the state (A) with respect to the state (B) provided we can cause both the state (A) and the state (B) to pass into the state (C) which we may suppose to be the state in which all the energies of combination of the system have been exhausted.

Thus if the substances in the system are oxygen, hydrogen and carbon, and if the states (A) and (B) consist of two different hydrocarbons with free hydrogen and oxygen, we cannot in general cause the state (A) to pass into the state (B), but we can cause either (A) or (B) to pass into the state (C) in which all the hydrogen is combined with oxygen as water and all the carbon is combined with oxygen as carbonic acid. In this way the energy of the state (A) relatively to the state (B) can be determined by measurements of heat. 188.] It has been proved experimentally by Joule that the heat developed throughout the whole electric circuit is the same for the same amount of chemical action whatever be the resistance of the circuit provided no other form of energy than heat is given off by the system.

Thus in a battery the electrodes of which are connected by a short thick wire the current is very strong and the heat is generated principally in the cells of the battery and to a much smaller extent in the wire; but if the wire is long and thin, the heat generated in the wire is far greater than that generated in the cells, but if we take into account the heat generated in the wire as well as that generated in the cells, we find that the whole heat generated for each grain of zinc dissolved is the same in both cases.

189.] If, however, the circuit includes a cell in which dilute acid is elec- trolysed into oxygen and hydrogen the heat generated in the circuit, per grain of zinc dissolved, is less than before, by the quantity of heat which would be generated if the oxygen and hydrogen evolved in the electrolytic cell were made to combine.

Or if the circuit includes an electromagnetic engine which is employed to do work, the heat generated in the circuit is less than that corresponding to the zinc consumed by an amount equal to the heat which would be generated if the work done by the engine were entirely expended in friction. 190.] If the arrangement is such that the amount of chemical action de- pends entirely on the quantity of electricity transmitted we can determineE. M. F. IN A VOLTAIC CIRCUIT.

the electromotive force of the circuit by the following method, first given by Thomson (Phil. Mag., Dec. 1851). Let the resistance of the circuit be made so great that the heat generated by the current in the electrolytes may be ne- glected. Let E be the electromotive force of the circuit; then the work done in driving one unit of electricity through the circuit is numerically equal to E. But during this process one electrochemical equivalent of the electrolyte undergoes the chemical process which goes on in the cell. Hence, if the en- ergy given out during this process is entirely expended in maintaining the current, the dynamical value of the process must be numerically equal to E, the electromotive force of the circuit, or, as Thomson stated it, ‘The electromotive force of an electrochemical apparatus is in absolute measure equal to the mechanical equivalent of the chemical action on one electrochemical equivalent of the substance.’

Examples. 191.] If the action in the cell consists in part of irreversible processes, such as

1. The frictional generation of heat by resistance in the electrolyte,
2. Diffusion of the primary or secondary products of electrolysis through the electrolyte, or,
3. Any other action which is not reversed when the direction of the cur- rent is reversed, there will be a certain amount of dissipation of energy and the electromotive force of the circuit will be less than the loss of intrinsic energy corresponding to the electrolysis of one electrochemical equivalent. It is only the strictly reversible processes that must be taken into account in calculating the electromotive force of the circuit. 192.] The determination of the total electromotive force in an electrochem- ical circuit is therefore always possible. If, however, we wish to determine the precise points in the circuit where the different portions of this electro- motive force are exerted, we find the investigation much more difficult than in the case of a purely metallic circuit.

For the chemical action at the junction of a metal with an electrolyte isE. M. F. IN A VOLTAIC CIRCUIT. 167 generally of such a kind that it cannot take place by itself, that is to say, without an action equivalent to that which takes place at the other electrode. Thus, when a current passes between silver electrodes through fused chlo- ride of silver, chlorine is liberated at the anode which immediately acts on the electrode so as to form chloride of silver and silver is deposited on the cathode.

Now we know the amount of heat given out when an equivalent of free chlorine combines with an equivalent of silver, and this is equivalent to the energy which must be spent in electrolysing chloride of silver into free chlo- rine and free silver, but the process that takes place at the anode is the com- bination of silver, not with free chlorine, but with chlorine in the act of being electrolysed out of chloride of silver∗ .

[The following note is an extract from Professor Maxwell’s letter on Potential published in the Electrician, April 26th, 1879.]

In a voltaic circuit the sum of the electromotive forces from zinc to the electrolyte, from the electrolyte to copper, and from copper to zinc, is not zero but is what is called the electromotive force of the circuit—a measurable quantity. Of these three electromotive forces only one can be separately measured by a legitimate process, that, namely, from copper to zinc. Now it is found by thermoelectric experiments that this electromotive force is exceedingly small at ordinary temperatures, being less than a microvolt, and that it is from zinc to copper. Hence the statement deduced from experiments in which air is the third medium, that the electromotive force from copper to zinc is .75 volts, cannot be correct. In fact, what is really measured is the difference between the potential in air near the surface of copper, and the po- tential in air near the surface of zinc, the zinc and copper being in contact. The number .75 is therefore the electromotive force, in volts of the circuit copper, zinc, air, copper, and is the sum of three electromotive forces, only one of which has as yet been measured. Mr. J. Brown has shown (Phil. Mag., Aug. 1878, p. 142), by the divided ring method of Sir W. Thomson, that whereas copper is negative with respect to iron in air it is positive with respect to iron in hydrogen sulphide.

It would appear, therefore, that the reason why the results of the comparison of metals by the ordinary ‘contact force’ experiments harmonise so well with the comparison by dipping both metals in water or an oxidizing electrolyte is not because the electromotive force between a metal and a gas or an electrolyte is small, but because the properties of air agree, to a certain extent, with those of oxidising electrolytes. For, if the active component of the electrolyte is sulphur, the results are quite different, and the same kind of difference occurs when hydrogen sulphide is substituted for air. We know so little about the nature of the ions as they exist in an electrolyte that, even if weCONSTANT BATTERIES. 168