 Solution

Suppose initially $c_1>c_2$. Positive ions initially move by diffusion from side 1 to side 2. Since negative counterions cannot cross, side 1 acquires a negative interfacial charge and side 2 a positive one. The resulting electrical force opposes further positive-ion transfer. The two contributions balance when the electrochemical potentials are equal; individual ions still cross in both directions, but there is no net electric current of the permeant chemical species.

A simple capacitor model makes the feedback quantitative. If $n$ moles of monovalent positive ions move from initially neutral side 1 to side 2, the charge on side 1 is $-Fn$, hence $V=-Fn/C$. The free-energy stationarity condition isAs $n$ increases, both the concentration imbalance and the voltage drive toward reversal diminish the original diffusion tendency. The equilibrium lies before the bulk concentrations become equal. This demonstrates why a nonzero Nernst potential can coexist with very little change in bulk composition and approximate bulk electroneutrality. A concentration difference alone does not maintain an electrical voltage if both counterions can freely follow each other; selective permeability is essential to this model.