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 2 SO 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 2 O. 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.

[1]  John H. Weare,et al.  The prediction of borate mineral equilibria in natural waters: Application to Searles Lake, California , 1986 .

[2]  Donald G. Miller.  Application of irreversible thermodynamics to electrolyte solutions. III. Equations for isothermal vector transport processes in n-component systems , 1967 .

[3]  N. Møller,et al.  The prediction of mineral solubilities in natural waters: The Na-K-Mg-Ca-H-Cl-SO4-OH-HCO3-CO3-CO2-H2O system to high ionic strengths at 25°C , 1984 .

[4]  J. A. Rard,et al.  The mutual diffusion coefficients of NaCl−H2O and CaCl2−H2O at 25°C from Rayleigh interferometry , 1979 .

[5]  K. Johnson.  The calculation of ion pair diffusion coefficients: A comment , 1981 .

[6]  Donald G. Miller.  Application of Irreversible Thermodynamics to Electrolyte Solutions. I. Determination of Ionic Transport Coefficients lij for Isothermal Vector Transport Processes in Binary Electrolyte Systems1,2 , 1966 .

[7]  H. S. Harned,et al.  The Diffusion Coefficient of Cesium Chloride in Dilute Aqueous Solution at 25 , 1951 .

[8]  S. Gottlieb,et al.  Occurrence of d-Pinitol in Red Spruce (Picea rubra) , 1951 .

[9]  S. Ben-Yaakov,et al.  Diffusion of seawater ions. Part II. The role of activity coefficients and ion pairing , 1980 .

[10]  J. A. Rard,et al.  Ternary diffusion coefficients of the brine systems NaCl (0.5 M)-Na2SO4 (0.5 M)-H2O and NaCl (0.489 M)-MgCl2 (0.051 M)-H2O (seawater composition) at 25°C , 1986 .

[11]  H. Eugster,et al.  Thermodynamic modeling of geological materials : minerals, fluids and melts , 1987 .

[12]  Lars Onsager,et al.  Irreversible Processes in Electrolytes. Diffusion, Conductance and Viscous Flow in Arbitrary Mixtures of Strong Electrolytes , 1931 .

[13]  John H. Weare,et al.  Calculation of multicomponent ionic diffusion from zero to high concentration: I. The system Na-K-Ca-Mg-Cl-SO4-H2O at 25°C , 1991 .

[14]  K. Pitzer.  Thermodynamic properties of aqueous solutions of bivalent sulphates , 1972 .

[15]  Donald G. Miller.  Application of irreversible thermodynamics to electiolyte solutions. II. Ionic coefficients for isothermal vector transport processes in ternary systems , 1967 .

[16]  J. A. Rard,et al.  Mutual diffusion coefficients and ionic transport coefficients lij of magnesium chloride-water at 25.degree.C , 1984 .

[17]  A. Lasaga,et al.  The treatment of multi-component diffusion and ion pairs in diagenetic fluxes , 1979 .

[18]  Robert L. Baldwin,et al.  Flow Equations and Frames of Reference for Isothermal Diffusion in Liquids , 1960 .

[19]  H. S. Harned,et al.  The Differential Diffusion Coefficients of Magnesium and Barium Chlorides in Dilute Aqueous Solutions at 25 , 1951 .

[20]  P. Mazur,et al.  Non-equilibrium thermodynamics, , 1963 .

[21]  A. Lasaga,et al.  The determination of SO42-, NaSO4-, and MgSO40 tracer diffusion coefficients and their application to diagenetic flux calculations , 1984 .

[22]  M. Pikal.  Theory of the Onsager transport coefficients lij and Rij for electrolyte solutions , 1971 .

[23]  R. Wendt,et al.  The Estimation of Diffusion Coefficients for Ternary Systems of Strong and Weak Electrolytes , 1965 .

[24]  J. A. Rard,et al.  Mutual diffusion coefficients of barium chloride-water and potassium chloride-water at 25 .degree. from Rayleigh interferometry , 1980 .