Nonosmotic Membrane Equilibrium

Two cases should be considered (i) nonosmotic membrane equilibrium (ii) osmotic membrane equilibrium. In the latter case, where solvent molecules can enter the surface layer or the membrane, the situation is more complicated since mechanical equilibria are also involved. We will start by considering nonosmotic equilibrium. 

For the sake of simplicity, we will consider a negatively charged polymer film (negative sites are formed as a result of a reduction process) in contact with a K+A electrolyte. The concentration of the negatively charged sites (X ) is Cx, the value of which depends on the potential according to the Nemst equation. At fixed potential and a concentration of crx, the partitioning equilibrium (y is taken to be 1) is 

The dependence of the Donnan potential on the electrolyte concentration can be obtained by combining Eqs. 5.20 and 5.22 and taking the value of the activity coefficient of K+ to be 1 or. In fact, the terms containing the activity 

In the true membrane arrangement, when the conducting ion-exchange polymer is situated between two solutions (1 and 11) of different concentrations, a Donnan potential also arises at the other membrane-solution interface, which can be expressed similarly however, no equilibrium exists in this case. 

A diffusion potential (A0diff) arises within the membrane which depends on the concentrations and mobilities of the ions within the membrane. For a perfectly se- 

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An electrochemical system, important particularly in biological systems, is one in which the species are ions and the system is separated into two parts by a rigid membrane that is permeable to some but not all of the species. We are interested in the conditions attained at equilibrium, the Donnan equilibrium. Two cases, one in which the membrane is not permeable to the solvent (nonosmotic equilibrium) and the other in which the membrane is permeable to the solvent (osmotic equilibrium), are considered. The system is at constant temperature and, for the purposes of discussion, we take sodium chloride, some salt NaR, and water as the components. The membrane is assumed to be permeable to the sodium and chloride ions, but not to the R-ions. We designate the quantities pertinent to the solution on one side of the membrane by primes and those pertinent to the solution on the other side by double primes. 

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