Hartley–Crank Equations for Coupled Diffusion in Concentrated Mixed Electrolyte Solutions. The CaCl2 + HCl + H2O System

Abstract

Nernst—Planck equations and ionic conductivities are used to calculate accurate limiting interdiffusion coefficients Diko for mixed electrolyte solutions. The electrostatic mechanism for coupled electrolyte diffusion is investigated by calculating the electrostatic contribution to each Diko coefficient to give the flux of each electrolyte driven by the electric field, which is generated by the migration of ions of different mobilities. Ternary diffusion coefficients are measured for dilute aqueous K2SO4 + KOH and Li2SO4 + LiOH solutions. Because of the different mobilities of K+ and Li+ ions relative to SO42− ions, diffusing K2SO4 drives cocurrent flows of KOH, but diffusing Li2SO4 drives counterflows of LiOH. To describe coupled diffusion in concentrated mixed electrolyte solutions, the Hartley–Crank theory is used to correct the limiting Diko coefficients for nonideal solution behavior, viscosity changes, ionic hydration, and the zero-volume flow constraint. Diffusion coefficients predicted for concentrated aqueous CaCl2 + HCl solutions are compared with recently reported data. The large amount of HCl cotransported by the diffusing CaCl2 is attributed to the “salting out” of HCl by CaCl2 and to the migration of H+ ions in the diffusion-induced electric field, which slows down the Cl− ions and speeds up the less-mobile Ca2+ ions to maintain electroneutrality along the CaCl2 gradient.