The Ionization and Activity of Largely Ionized Substances.

In applications of the ionic theory of solutions it is customary to employ, in accordance with the original hypothesis of Arrhenius, as a measure of the degree of ionization of salts, acids, and bases, the ratio of the equivalent conductance of the substance at any given concentration to the limiting value of the equivalent conductance as the concentration approaches zero, where the ionization may be assumed to be complete. This assumption, however, is not a necessary conclusion from the fundamental theory of ionic conduction. According to this theory, the equivalent conductance A (which is by definition the quantity of electricity which under a potential-difference of one volt passes per second between electrodes of indefinite extent 1 cm. apart, between which is placed that quantity of solution which contains one equivalent weight of the ionizing substance) is for a uniunivalent substance given by the expression A = -yr(u+ + u-), in which y is the fraction of the substance ionized (equal in this case to the number of equivalents of each ion present in the solution), F the quantity of electricity (96,500 coulombs) associated with each equivalent of ion, and u+ and uthe mobilities of the positive and negative ions (that is, their velocities through the solution under a potential-gradient of one volt per centimeter). For the equivalent conductance A. at zero concentration, where the ionization becomes complete, we have the corresponding expression A. = F(U.+ + u0 . Combining these two equations we get