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As a result of extensive development of experimental techniques and equipment, highly precise limiting ionic conductances with their temperature and pressure dependences have been available for some time. This has resulted in several attempts to provide a theoretical basis to account for the deviations reported from Stokes’ behavior. These deviations in the conductancevisocsity product include a maximum in the ion size dependence, positive and negative temperature dependencies and different size dependencies for cations and anions as well as for large and small ions. Furthermore, specific solvent effects must be accounted for. In this article an attempt is made to evaluate several theories as to their ability to account for these deviations. INTRODUCTION During the first sixty years of th is century little progress was made in explaining the magnitude of limiting conductances. Some of the more important factors affecting their magnitude had not been recognized but discussions generally were limited to a consideration of Stokes’ law and to various solvation schemes. Although the data available were voluminous, few systematic precise studies, with some notable exceptions,’l) had been carried out in any solvent except water and temperature and pressure dependencies were for the most part unknown. Inspite of the fact that some early workers had developed the experimental techniques required for precise work(a33’ the methods were time consuming, tedious and required considerable skill. Furthermore, the general lack of transference data required a consideration of the salt conductances which are dependent on the properties of two entirely different ions. In the past thirty years the situation has changed dramatically. Modem equipment and techniques(45) have produced a wealth of highly precise ionic conductance data for a broad cross section of solvents.(6) Temperature and pressure coefficients have been established for several systems. Advances in conductance theory“ produced a reliable extrapolation procedure when coupled with least squares computer programs.’*) Transference data, including temperature and pressure dependencies, are available for several of the more common solvents. The net effect has been a clear picture of how ionic mobilities were affected by the more important variables and the response from the theorists was considerable. In this review an attempt will be made to illustrate how well the various theoretical models actually reflect the experimental facts. It is not possible to document even a small portion of the experimental data. The actual data can be traced in the references given. Several systems such as surfactants, protonic conductance and ionic melts are not included. The temperature range considered is that in which the mobilities are not affected by small changes in solvent density. For the most part computer simulations are a separate subject and only special cases are considered here. STOKE‘S LAW Most discussions of limiting ionic conductances k,, commence with a discussion of Stokes’ law which assumes non interacting spherical ions of radius R, (generally set equal to the crystallographic radius r,) and charge zie in a solvent continuum of viscosity q. The boundary factorfvaries between 6 for perfect stick conditions and 4 for perfect slip. A comparison of the predictions of Eq. (1) with experimental data(g) at 25OC can be found in the Walden product plot in Fig. 1. It is clear that Stokes’ law does not reproduce the size dependence of typical ions except for large ions for which there is the uncertainty as to whether the f = 4 or 6 condition holds. An appeal to solvation to form a large moving entity qualitatively could explain the values of k,,V below either of the Stokes’ lines but not those points above. Perhaps the most serious problem for theories that treat the solvent as a continuum is the fact that cations and anions lie on two distinct curves. Also, for the higher alcohols (1-PrOH and 2-BuOH) it is not possible to join the large RJV and alkali-metal ions by a simple curve without introducing maxima and minima. Such behavior suggests either a serious restriction of Stokes’ law or a different mechanism of conductance for small and large ions in these solvents. Stokes’s law also predicts that the Walden product should be independent of temperature and pressure. Although the temperature coefficient of k , , ~ is small, amounting to less than 1%, for ions in most organic solvents, its magnitude is considerable for aqueous solutions‘”) as shown in Fig. 2 where both positive and negative temperature coefficients of k , , ~ are evident. The pressure coefficients‘”) of k,,q on the other hand are substantial in all solvents and show complicated behaviour. Data for aqueous solutions are shown in Fig. 3a, and for methanol solutions in Fig. 3b. G U RN EY -FRAN K-W EN MODEL was the first to offer a model that provided a reasonable, explanation for the size and temperature dependence of ionic mobilities in aqueous solutions. He introduced the concept of an ionic cosphere, that part of the solvent surrounding an ion whose physical properties differ from the bulk solvent properties due to the presence of the ion. His ideas can best be demonstrated by what has become known as the Frank-Wen model(13) which is shown in Fig. 4. 1393

The current state of our understanding of ionic mobilities