Page:Elementary Text-book of Physics (Anthony, 1897).djvu/342

338 an equivalent mass of the other ion, in which is included the heat equivalent of the mechanical work done if the state of aggregation change. Then $$I$$ will represent the number of electro-chemical equivalents evolved in unit time, and $$Ie\theta t$$ will represent the energy expended in the time $$t,$$ which appears as chemical separation and mechanical work. This is equal to $$IA;$$ whence $$A = e\theta t.$$ All these quantities are measured in absolute units. The quantity $$e \theta$$ represents the energy required to separate the quantity $$e$$ of the ion considered from the equivalent quantity of the other ion, and to bring both constituents to their normal condition. Now, $$\frac{A}{t}$$ represents the counter electromotive force set up in the circuit by electrolysis. Hence the electromotive force set up in the electrolytic process may be measured in terms of heat units.

It often is the case that the two ions which appear at the electrodes are not capable of direct recombination, as has been tacitly assumed in the definition of $$\theta.$$ A series of chemical exchanges is always possible, however, which will restore the ions as constituents of the electrolyte, and the total heat evolved for a unit mass of one ion during the process is the quantity $$\theta.$$

The theory here presented is abundantly verified by the experiments of Joule, Favre and Silbermann, Wright, and others. The extension of the theory to cases in which the electromotive force varies with the temperature was made by Helmholtz.

283. Positive and Negative Ions.—Experiment shows that certain of the bodies which act as ions usually appear at the cathode, and certain others at the anode. The former are called electro-positive elements; the latter, electro-negative elements. Faraday divided all the ions into these two classes, and thought that every compound capable of electrolysis was made up of one electro-positive and one electro-negative ion. But the distinction is not absolute. Some ions are electro-positive in one combination and electro-negative in another. Berzelius made an attempt to arrange the ions in a series, such that any one ion should be electro-positive to all those above it and electro-negative to all those below it. There