Kinetic Models of Batch Sorption in a Limited Volume

The batch sorption kinetics described by a nonlinear equation with a variable equilibrium parameter for the interface was considered. It was shown that a difference equation of this type can be reduced, with a certain approximation, to the pseudo first- and pseudo second-order kinetic equations with constant parameters that are convenient for processing the experimental data. The errors of this approximation are smaller than the characteristic experimental errors in constructing the kinetic curves. For the linear sorption isotherm and Langmuir isotherm, the sorption kinetics can be approximated by the pseudo first-order equation. In addition, for the Langmuir isotherm and BET isotherm of polymolecular sorption, the kinetics can be described by the sum of the pseudo first- and pseudo second-order equations, or only by the pseudo second-order equation. For all these cases, it was shown how the parameters of kinetic equations are related with the equilibrium characteristics of sorbents. Our analysis shows that the possibility of describing the experimental data obtained in batch kinetic experiments using pseudo first- or pseudo second-order models is related to the possibility of mathematical approximations and transformations and cannot be used to characterize the kinetic mechanisms.