Ionic diffusion in naturally-occurring aqueous solutions: transition-state models that use either empirical expressions or statistically-derived relationships to predict mutual diffusion coefficients in the concentrated-solution regions of 8 binary systems
Mutual diffusion coefficients for the systems NaCl-H 2O, KCl-H 2O, CaCl 2-H 2O, SrCl 2-H 2O, BaCl 2-H 2O, MgCl 2-H 2O, Na 2SO 4-H 2O, and MgSO 4-H 2O are computed using a model that postulates exchanges between ions and water molecules. Limiting ionic equivalent conductances, a solution-density function, and a mean ionic activity-coefficient function are required as input. A region of changing solution structure extends up to concentrations ranging from about 0.01 molar in MgCl 2-H 2O to about 0.2 molar in KCl-H 2O. In the remaining concentration range to saturation, a single expression in each system containing one variable parameter can be fitted empirically to reproduce selected sets of experimentally measured Dv12 with maximum errors for individual compositions ranging from about 0.25% in KCl-H 2O and Na 2SO 4-H 2O to about 4% in MgCl 2-H 2O. The experimentally measured Dv12 can be reproduced with errors comparable to those of the empirical fits by further postulating that individual ion-water molecule exchanges are coupled to yield hydrated neutral exchange complexes (the activated complexes), and defining probability expressions that describe the following exchanges: Ba2+ + 2 Cl- for 3H 2O, 2 Ca2+ + 4 Cl- for 6H 2O, 2 Sr2+ + 4 Cl- for 6H 2O, Na+ + Cl- for 3H 2O, 2 K+ + 2 Cl- for 5H 2O, NaSO-4 + Na+ for 5H 2O, Mg2+ + SO2-4 (+MgSO 04) for 4H 2O, and MgCl+ + Cl- for 2H 2O. This calculation also contains one variable parameter. Solute transport between exchange sites is by movement of ions, except for the ion-pair contribution indicated in parentheses.