Diffusion coefficients of ions through ion excange membrane in Donnan dialysis using ions of different valence

Abstract

Donnan dialysis with an ion exchange membrane was investigated for ions of different valence. The effective diffusion coefficients ( D e) of various kinds of ions in the membrane were obtained by fitting of the equation derived from the Nernst–Planck equation to three or more sets of experimental data for Donnan dialysis. It became apparent that the value of D e/ D s of monovalent ions (e.g., K + or Na + ions) at z A=1 and z B=2 (feed ions are monovalent ones and driving ions are bivalent ones) remained constant at ca. 1/210 and that of bivalent ions (e.g., Ca 2+, Cu 2+, or Mg 2+ ions) remained constant at ca. 1/526 where D s denotes the diffusion coefficient of ions at infinite dilution in water calculated from the Nernst–Einstein equation, and z A and z B represent the valences of the feed and driving ions, respectively. D e/ D s of monovalent ions (e.g., H +, K +, or Na + ions) at z A=2 and z B=1 (feed ions are bivalent ones and driving ions are monovalent ones) was constant at ca. 1/23.3 and that of bivalent ions remained constant at ca. 1/58.4. It was proved that D e/ D using D e at z A=1 and z B=2 was constant at 1/3.0 and that at z A=2 and z B=1 remained constant at 3.0 where D represents the diffusion coefficient of ions in the membrane at z A= z B (the valences of both feed and driving ions are equal). Therefore, it was found that a large flux of ions could be obtained using the monovalent driving ions in Donnan dialysis. On the other hand, the small flux can be obtained using bi- or higher-valent driving ions.