Analytical treatment of ion-exchange permselectivity and transport number measurements for high accuracy

We analyse electromotive force measurements of concentration cells using non-equilibrium thermodynamics, and determine the transference coefficients of ion-exchange membranes in aqueous KCl solutions. By taking advantage of the analytical expression for the permselectivity, we extract transport coefficients with high accuracy. The transport number of K+ and the transference coefficient of water in the Selemion CMVN cation-exchange membrane are found to be 100tK+=99.59±0.56 and tw=3.69±0.40 respectively, while for the Selemion AMVN anion-exchange membrane they are 100tCl−=100.21±0.37 and tw=−3.75±0.27. These results suggest that the membranes are perfectly selective to the target ion, and that each ion carries 3-4 water molecules through the membrane, which reduces the membrane permselectivity. In these concentration cells, the electrical potential contribution of the membrane alone was more easily isolated with bare Ag/AgCl electrodes without reference solutions and liquid junction plugs. Additionally, we find a large contribution to the measured concentration cell voltage from concentration gradients across the porous plug of the reference electrode, which cannot be explained by Henderson's equation alone. For most of the concentration range, the transport number of the porous plug is determined to be 100tK+=49.43±0.78 with negligible water transport, similar to literature values for bulk electrolyte. In dilute electrolyte solutions with concentrations below 0.1 mol kg−1, the plug shows anomalous behaviour consistent with an increase in K+ selectivity and water co-transport.