Silver ion in methanol was exchanged with sodium ion using Dowex 50 cross-linked with 8% divinylbenzene by Gable and Stroebel [J. Phys. Chem., 60, 513–517 (1956)]. The molar selectivity coefficient was found to vary somewhat with the equivalent fraction of Na⁺ in the resin as follows:

If the wet capacity of the resin is 2.5 eq/L and the resin is initially saturated with Na⁺, calculate the equilibrium equivalent fractions if 50 L of 0.05-M Ag⁺ in methanol is treated with 1 L of wet resin.

XNa+ KAg+, Na+ 0.1 0.3 11.2 11.9 0.5 12.3 0.7 14.1 0.9 17.0