Salt (Electrolytes) Sorption By Membranes And/Or Ion-Exchange Resins: Donnan Or Partition Equilibrium?

The sorption equilibrium of salts (electrolytes) between aqueous solutions and ionexchanging phases (membranes, resins, and/or gels) is analysed. Classically this equilibrium had been treated as Donnan equilibrium with unitary constants (Teorell (1953), Schloegl (1964)). However, as phases of different structure and different thermodynamic standard states are involved a partition equilibrium with non-unitary constants is the correct thermodynamic description, as it is used, p.ex. in the solubility-diffusion theory of membrane processes. Surprisingly a complete thermodynamic description of such equilibrium has not been given. Stating the thermodynamic phase equilibrium conditions directly for the salts (not for ions) and taking into account the molarity (X) of fixed ions in the ion exchanging phase (accountable of the characteristic ion exclusion effect) a limiting sorption law for a binary salt of type M ν1Yν2 is obtained (indices: 1 = counter-ion, 2 = co-ion within the sorbing phase): , (qs = ν2 |z2| cs/X; cs = salt molarity in the membrane; external molal salt activity) law which depends on the salt formula (relation ν1/ ν2) and the membrane characteristics. Experimental sorption data of different salt/membrane systems (NaBr/NaR; CsBr/CsR; SrBr2 /SrR; MgCl2 /RCl; MgCl2 /MgR; LaCl3 /LaR; Na2SO4 /NaR) follow this law. In log-log graphs of qs vs. the experimental exponent ns coincides with its theoretical values (1+ ν1/ ν2). The partition constants are also obtained as well as the activity coefficient of the salt within the sorbing phase. It is found that this coefficient (>1) is logarithmically linear in √(Is), the ionic strength of the salt in this phase. Finally the complete sorption equations for qs are solved, i.e. eqs. of 2nd. degree (symmetric electrolytes) and of 3rd. degree (1:2 electrolytes), the latter being treated in detail. The expressions of the partition factors of the counter-ion and of the co-ion are also obtained as well as their limiting expressions.