On the quasi‐thermodynamic treatment of diffusion potentials
Authors: Wiebenga E. H. 
Published: September 2010

An expression for the diffusion potential between two electrolytic solutions can be found either by kinetic or by quasi‐thermodynamic reasoning.

The first treatment, more justified in principle, follows the mechanism of diffusion in detail and must restrict itself to simple cases: that of ideal solutions or that of solutions obeying the limiting (√c) laws. The second treatment is based upon a thermodynamic condition of equilibrium and leads in all cases to a result which is useful

See for instance a determination of mean ion activities from the e.m.f. of cells with liquid‐liquid junction by A. S. Brown and D. A. Mc Innes, J. Am. Chem. Soc. 57, 1356 (1935). Th. Shedlowsky and D. A. Mc Innes, J. Am. Chem. Soc. 58, 1970 (1936).

in electrochemistry, viz. an expression of the diffusion potential in terms of transference numbers and ion activities. This will be the reason why the quasi‐thermodynamic method is found in most modern books on electrochemistry.

However, it is generally understood that the quasi‐thermodynamic procedure cannot be justified from the point of view of thermodynamics itself, since a condition of equilibrium is here applied to a system not in equilibrium. This situation has been analysed once more in § 1. Starting from a model of the diffusion layer, the quasi‐thermodynamic method has been critisized by Hermans and Oosterhoff

J. J. Hermans and L. J. Oosterhoff, Phil. Mag. (7) 24, 304 (1937).

, who state that its result is incorrect for non‐ideal solutions. In § 4 we will show that this statement is not justified, not even from their own point of view. Conversely, neither is it possible to prove the correctness of the thermodynamic result on the basis of their model, the model not being general enough for this purpose. As already stated in 1932 by Onsager

L. Onsager, Phys. Rev. 37, 405 (1931); 38, 2265 (1931).

L. Onsager and R. M. Fuoss, J. Phys. Chem. 36, 2689 (1932).

a general proof is possible based on the principle of microscopic reversibility. It appears that the correctness of the quasi‐thermodynamic expression for the diffusion potential is a consequence of the “symmetry in past and future” of the equations of motion of mechanics, i.e. that property that makes a system retrace its former configurations in reversed succession, if the velocities of all the particles present are reversed simultaneously. Onsager's symmetry relations, which can be derived from the principle of microscopic reversibility, are important not only for the problem in hand (diffusion), but are of general importance for many other irreversible processes, e. g. the symmetry of heat conduction in crystals and the correctness of Kelvin's — quasi‐thermodynamic — relations between the thermoelectric quantities.

As the application of Onsager's relations to the diffusion potential of electrolytes seems to be little known, perhaps because Onsager only briefly indicated its possibility, the application of the symmetry relations concerned will be given in detail in § 2 and § 3.

It may be remarked that the problem is of both theoretical and practical importance, since it follows from the quasi‐thermodynamic expression for the e.m.f. of a cell with liquid—liquid junction that it is essentially impossible to deduce single ion activities from measurements of the e.m.f. of such cells

P. B. Taylor, J. Phys. Chem. 31, 1478 (1927). E. A. Guggenheim, J. Phys. Chem. 33, 842 (1929)

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