A mathematical model based on a generalized Maxwell–Stefan equation has been developed to describe multicomponent ion and water transport inside a cation-exchange membrane. This model has been validated using experimental data and has been used to predict concentration profiles, membrane potential drop, and transport numbers of ions and water for the chlor-alkali process at increased current densities. Several improvements have been made to previously developed Maxwell–Stefan models. In our model, the generalized Maxwell–Stefan equation is written in terms of concentration instead of mole fraction and the fixed group (membrane) concentration is assumed to be constant. We have adapted the Augmented matrix method using the built-in partial differential equation parabolic elliptic (pdepe) solver in Matlab®, and both the concentration and the electrical potential gradients have been solved simultaneously. The boundary conditions are determined with the Donnan equilibrium at the membrane–solution interface. We have also employed semi-empirical correlations to define the Maxwell–Stefan diffusivities inside the membrane. For the bulk diffusivities, we applied the correlations for the concentrated solution instead of the values at infinite dilution. With the diffusivities presented in this work, the model shows a better fit to the experimental data than with previously reported fitted diffusivities. Prediction of the sodium transport number and water transport number is generally good, whereas the deviations with regard to membrane potential might also be related to issues with the experimental data. The model predicts an increase in both sodium and water transport numbers at increased current density operation of chlor-alkali production. Graphical abstract