Since in a neutral solution the number of anions is equal to the number of cations, this equation may be written
;
it shows that when V is very large (so that the solution is very dilute), n2 is very large compared with n1; that is to say, the salt tends towards a state of complete dissociation.
The ideas of Arrhenius contributed to the success of Walther Nernst[1] in perfecting Helmholtz theory of concentration-cells, and representing their mechanism in a much more definite fashion than had been done heretofore.
In an electrolytic solution let the drift-velocity of the cations under unit electric force be u, and that of the anions be v, so that the fraction u/(u + v) of the current is transported by the cations, and the fraction v/(u + v) by the anions. If the concentration of the solution be c1 at one electrode, and c2, at the other, it follows from the formula previously found for the available energy that one gramme-ion of cations, in moving from one electrode to the other, is capable of yielding up an amount[2] RT log (c2/c1) of energy; while one gramme-ion of anions going in the opposite direction must absorb the same amount of energy. The total quantity of work furnished when one gramme-molecule of salt is transferred from concentration c2; to concentration c1 is therefore
The quantity of electric charge which passes in the circuit when one gramne-molecule of the salt is transferred is proportional to the valency ν of the ions, and the work furnished is proportional to the product of this charge and the electro-
- ↑ Zeitschr. für phys. Chem. ii (1888), p. 613; iv (1889), p. 129; Berlin Sitzungsberichte, 1889, p. 83; Ann. d. Phys. xlv (1892), p. 360. Cf. also Max Planck, Ann. d. Phys. xxxix (1890), p. 161; xl (1890), p. 561.
- ↑ The correct law of dependence of the available energy on the temperature was by this time known.
