The Onsager thermodynamics of irreversible processes provides a unified approach to the study of electrolytic systems out of equilibrium, such as concentration cells with transference, the initial and final emf's of thermal cells, and thermal diffusion (Soret effect) of ions. For concentration cells, the method justifies the classical results obtained by Nernst from equilibrium considerations. For nonisothermal systems, the product is the thermodynamic driving force of a process, where is the entropy transported reversibly from the “hot” to the “cold” heat reservoir (in the limiting case of equal temperatures) by the occurrence of a reversible process in the system. The emf of a concentration cell, the initial emf of a thermal cell, and the Soret coefficient, all properties of systems out of equilibrium, are determined, according to the Onsager relations, by the ratios of the reversible fluxes of matter to electricity, of entropy to electricity, and of entropy to matter, respectively, as they occur in systems completely at equilibrium.The transport entropy can become, according to circumstances, the entropy of electrical transport, or the entropy of diffusion transport. in turn involves the entropies of electrochemical transport (for the electrode reactions) and of migration transport (for the thermal liquid junction). The contribution of an ion (or electron) to and to gives rise to the ionic entropies of electrochemical transport and of migration transport , respectively. The latter contributes also to . The sum is known as the entropy of the moving ion and is measurable for a single ionic species. The initial thermal emf involves the transport entropy , the Soret coefficient involves , while the final thermal emf involves where is the transference number of the ion to which the electrodes are not reversible.For the hydrogen ion, , if is taken as zero in a saturated potassium chloride salt bridge. For other ions, , and the mass action dependence is normal. For most ions, appears to be small, i.e., about 0–3 cal/deg, and the mass action dependence is abnormal and low. In dilute solutions, shows a Debye dependence on concentration. These facts are consistent with the electrostatic interpretation of as the entropy of depolarization of the solvent dielectric when the ion moves away. For ions transferred by a chain mechanism (H+ and OH−), is significantly larger. The transport of ions across biological membranes plays an important role in life processes. Since living systems are not necessarily uniform in temperature, ionic transport entropies may have a role to play in the function of the biological cell.
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