Diffusion of Electrolyte Through Ion Exchange Membranes

When there is concentration difference of solutes across an ion exchange membrane (driving force difference of chemical potential) the solute diffuses through the membrane. Thus, a diffusion potential corresponding to the concentration gradient is generated across the membrane. The flux of i through the membrane, J is expressed by the Nemst-Planck equation as 

Because electrical current does not pass through the membrane, 

In the steady state, because J+, J are constant, the flux of diffusion can be calculated. Considering a 1 1 electrolyte, if y+y. = y 2, the equivalent ionic fraction is defined, 

The flux of electrolyte across the membrane is obtained by integration of Eqn. (2.65)  

Because the ion exchange membrane shows ideal permselectivity at sufficiently low solution concentration, compared with the fixed ion concentration of the membrane, the difiusional flux is expressed as follows, for a cation exchange membrane 

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