Determination of Intraparticle Diffusivities of Na<SUP>+</SUP>/K<SUP>+</SUP> in Water and Water/Alcohol Mixed Solvents on a Strong Acid Cation Exchanger

A perfectly mixed batch reactor was used for the determination of the intraparticle diffusivities of Na⁺ and K⁺ on commercial Amberlite IR-120 resin in different solvents:  water and solvents composed of different percentages of water and methanol, water and ethanol, and water and 2-propanol. A theoretical model was developed to describe the response of the system that includes the resistance to mass transfer inside the particle and the effect of the electric field (Nernst−Planck approximation). Equilibria were described using a homogeneous model based on the mass action law in which nonideal behavior for both the solution and the solid phase was taken into account. Simulations were performed to analyze the effect of the model parameters on the response curves. The values of intraparticle diffusivities of Na⁺ and K⁺ were obtained by nonlinear regression. Both the regression and the parameters were highly meaningful from the statistical point of view. A simple dimensionless relationship that relates diffusivity (through the Schmidt number) to different physical properties of solvents (namely, viscosity, dipolar moment, and density) and resin swelling was found.