A transport model is developed for the selective extraction of a solute from a binary solute mixture using a dense polymeric sorbent in a batch process. The effects of unequal solute transport rates and molecular solvation between solutes in the polymer phase are considered. In the absence of intersolute solvation, the model reduces to the analytical solution for mass uptake from a finite volume. The inclusion of intersolute solvation requires a numerical solution owing to the coupled nature of the species continuity equations. The model is solved numerically using the method of finite differences and compared to the analytical solution in the absence of solvation for verification. Results from the model indicate that separation factors significantly higher than the equilibrium value can be obtained at intermediate times and at high levels of extraction when the diffusion coefficient of the desired solute is greater than that of the undesired one. Intersolute solvation in the polymer can enhance this effect under certain conditions by retarding the transport of the undesired solute to a greater degree than that of the desired solute, The magnitude and range of diffusion coefficients in polymers allows for the practical application of such an approach to improve a selective extraction process based on nonporous polymeric sorbents. The measurement of solvated and unsolvated diffusion coefficients in a dense polymer film using FTIR-ATR spectroscopy is demonstrated.