No abstract

For practical applications of solid/solution adsorption processes, the kinetics of these processes is at least as much essential as their features at equilibrium. Meanwhile, the general understanding of this kinetics and its corresponding theoretical description are far behind the understanding and the level of theoretical interpretation of adsorption equilibria in these systems. The Lagergren empirical equation proposed at the end of 19th century to describe the kinetics of solute sorption at the solid/solution interfaces has been the most widely used kinetic equation until now. This equation has also been called the pseudo-first order kinetic equation because it was intuitively associated with the model of one-site occupancy adsorption kinetics governed by the rate of surface reaction. More recently, its generalization for the two-sites-occupancy adsorption was proposed and called the pseudo-second-order kinetic equation. However, the general use and the wide applicability of these empirical equations during more than one century have not resulted in a corresponding fundamental search for their theoretical origin. Here the first theoretical development of these equations is proposed, based on applying the new fundamental approach to kinetics of interfacial transport called the Statistical Rate Theory. It is shown that these empirical equations are simplified forms of a more general equation developed here, for the case when the adsorption kinetics is governed by the rate of surface reactions. The features of that general equation are shown by presenting exhaustive model investigations, and the applicability of that equation is tested by presenting a quantitative analysis of some experimental data reported in the literature.

It is shown that the popular pseudo-first-order Lagergren equation can be applied to correlate kinetic adsorption data only in the adsorption systems that are not far from equilibrium. Also, it is shown that the Lagergren equation is then the limiting form of the kinetic equations developed by assuming both diffusional and surface reaction kinetic models. However, the theoretical interpretation of the coefficients in the Lagergren equation is then different for the two different kinetic models. The comparison of the theoretically predicted values of these coefficients with their experimentally determined values creates a chance to conclude whether the diffusional or the surface reaction model should be assumed to represent the kinetics of adsorption in an investigated adsorption system.