Kinetics of ion exchange in a stirred-flow cell

Abstract

The kinetics of ion exchange in a stirred-flow cell have been investigated experimentally and theoretically in the concentration range where film diffusion is the rate-determining step. To obtain detailed information, the ratio of the two counterions A and B in the inflow solution, as well as that of the ions initially in the ion exchanger, was selected in such a way that the ion exchanger was converted in successive steps from the pure A form to the pure B form, and back to the A form. The kinetics of the total conversion of the ion exchanger from the pure A form to the pure B form in one step were also determined. The experiments (exchange Cs⁺–H⁺) show that: (i) for partial conversions and for the forward reaction (uptake of the preferred ion, here Cs⁺), the half-life, t_1/2, of the ion exchange decreases considerably if the initial fraction of the preferred ion in the ion exchanger is increased; (ii) at a given initial ionic composition of the ion exchanger, the half-life is shorter when the preferred ion is taken up rather than released; (iii) compared with a process where the ion exchanger is converted only partially from the H⁺ form to the Cs⁺ form, the half-life for the total conversion of the ion exchanger from the H⁺ to the Cs⁺ form in one step is much shorter. The theory describes all observations quantitatively, with only two adjustable parameters (rate coefficient, R, and the ratio of the diffusion coefficients D_A/D_B) for the whole set of experiments. The calculations reveal that the strong dependence of t_1/2 on the initial ionic composition of the ion exchanger is only to a small extent due to the kinetic properties of the ion exchanger, but is rather a result of its selectivity (i.e. non-linearity of the ion-exchange isotherm). This restricts the usefulness of the stirred-flow technique for investigating the kinetics of ion exchange.