An Expression for the Diffusion Potential

The expression for the diffusion potential can be obtained in a straightforward though hardly brief manner by using the Onsager phenomenological equations to describe the interaction flows. Consido an electrolytic solution consisting of the ionic species and A and the solvent. When a transport process involves the ions in the system, there are two ionic fluxes,/ and J. Since, however, the ions are solvated, the solvent also participates in the motion of ions and hence there is also a solvent flux Jq. 

however, the solvent is considered fixed, i.e., the solvent is taken as the coordinate system or the frame of reference, then one can consider ionic fluxes relative to the solvent. Under this condition, Jq = 0, and one has only two ionic fluxes. Thus, one can describe the interacting and independent ionic drifts by the following 

The straight coefficients and L represent the independent flows, and the cross coefficients L and the coupling between the flows. 

The important step in the derivation of the diffusion potential is the statement that under conditions of steady state, the electroneutrality field sees to it that the quantity of positive charge flowing into a volume element is equal in magnitude but opposite in sign to the quantity of negative charge flowing in (Fig. 4.82). That is. 

What are the driving forces F and F for the independent flows of the positive and negative ions They are the gradients of electrochemical potential (see Section 4.4.15) 

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An expression for the diffusion potential can also be obtained by integration of the Nemst-Planck flux equations. This integration is generally very complicated, so that further approximations must be introduced. 

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