Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/406

 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 is very large (so that the solution is very dilute),  is very large compared with ; that is to say, the salt tends towards a state of complete dissociation.

The ideas of Arrhenius contributed to the success of Walther Nernst 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, and that of the anions be , so that the fraction of the current is transported by the cations, and the fraction  by the anions. If the concentration of the solution be at one electrode, and, 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  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 ; to concentration 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 of the ions, and the work furnished is proportional to the product of this charge and the electro-