In studies of bi-ionic cells containing strontium and potassium chlorides separated by a cation exchange membrane, the water transference was found to have a non linear dependence on ion transference numbers. This finding suggested the existence of local pressure gradients within the membrane during irreversible flow. In order to evaluate this possibility, we developed a method to obtain the concentration profile in a cation exchange membrane from measured fluxes. This permits the calculation of local transport coefficients for the coupled transport of mass and charge by two salts and water within the membrane. The observed variations in transport coefficients across the membrane are used to calculate the hydrostatic pressure profile inside the membrane. The results show that the postulated pressure gradient does exist, but that it has a negligible effect on the chemical potentials. This means that cell potentials can be calculated using the concentration dependent terms of the change in Gibbs free energy.