Calculation of multicomponent ionic diffusion from zero to high concentration: II. Inclusion of associated ion species

Abstract

This paper presents a theoretical model of multicomponent ionic diffusion which is valid to high concentration for systems which show ion association. The development is completely general for species which do not react with the solvent. It is demonstrated that the Onsager phenomenological coefficients for associated ion species can be unambiguously determined only in solutions where the concentration of these species can be independently measured. In all other instances, only combinations of the Onsager coefficients for the bare ions and the ion pairs can be experimentally determined. The results of our formulations are contrasted with those of more simplified models for systems containing Na 2SO 4 and MgSO 4, as well as for multicomponent natural seawater. The differences between our model and simplified models are significant, especially at high concentration. Inconsistencies which may develop with the use of the simplified approaches are demonstrated. Our approach requires considerable data which are not available at temperatures other than 25°C. Therefore, other approaches which are based only on data at infinite dilution are of great interest. We show here that, if chemical potential derivatives are included in the infinite dilution model of Nernst and Hartley which uses only infinite dilution mobilities, the model can be extended to slightly concentrated solutions. This extended Nernst-Hartley model gives good agreement with all of the existing experimental mutual diffusion coefficient data at concentrations below about 0.2 M in the six component system Na-K-Ca-Mg-Cl-SO 4-H 2O. This may be the most reliable way to extend infinite dilution data into more concentrated regions. In the systems we have studied, the inclusion of ion-association species for weakly interacting species does not appear to provide significant improvement over our generalized Nernst-Hartley model.