Potentiometric determination of transport numbers of ternary electrolyte systems in charged membranes

The potentiometric determination of transport numbers in charged membranes for the case of ternary systems is critically analyzed, and expressions are derived to evaluate these transport numbers close to equilibrium conditions. The apparent potentiometric transport number (i.e., that obtained by assuming that the ternary system behaves as a binary system) is also studied and the conditions that make it reliable for the estimation of the membrane fixed charge concentration are given. Particular attention is paid to the case of amphoteric membranes where the pH adjustment is necessary and the bathing solutions are often ternary systems. However, our theoretical study is general, and can also be applied to estimate the effect of any impurity ion present in the bathing solution. The main conclusion is that the interpretation of ion transport data in terms of the binary system equations can be an erroneous procedure even when the third ion present has a relatively low concentration.