Sorption of Non-exchange Electrolyte and the Donnan Equilibrium

When two coexisting phases are subjected to the condition that one or several of the ionic components cannot pass from one phase to the other, a particular type of equilibrium is set up, called a Dorman equilibrium. This type of ionic equilibrium is unique for ionic absorbents containing a fixed ion, and the isotherm describing such equilibria differs from the established Langmuir Freundlich and Bru-nauer, Emmett, and Teller types which are found for neutral species. 

for example, a cation exchanger in the form coexists with a solution of a strong electrolyte no net ion exchange 

Using equation 5.2 to equate the electrochemical potentials of the co-ion in both phases and equation 5.3, the following general equation 

Fig[ure 5.4 Non-exchange electrolyte sorption of NaCl and HCl by styrenk anion and cation exchange resins respectively against external concentration [m = internal molality A = macroporous SB A (low capacity) B = macroporous SBA (conventional) C = isoporous SBA (gel) D = macroporous SAC E = gel SAC] 

If swelling effects are ignored, the usual simplified Donnan equation for co-ion uptake from dilute solutions is obtained namely  

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