Determining rate coefficients for ion adsorption at the solid/water interface: better from desorption rate than from adsorption rate

One of the most common approaches in the adsorption kinetics literature is to compare the fitting performance of several empirical or non-empirical equations (pseudo-first order, pseudo-second order, Elovich, parabolic diffusion, etc.) with the aim of selecting the equation that best describes the experimental data. This is normally a futile fitting exercise that leads to the determination of ambiguous rate parameters, without providing insights into the behaviour of the studied system. A more realistic approach is to treat it as a combination of mass transport and chemical reaction under controlled conditions, and thus actual adsorption-desorption rate parameters are readily estimated. This article applies a simple and realistic physicochemical model to describe and understand the adsorption-desorption kinetics of ions at the solid/water interface. The model is applied to an ATR-FTIR study of phosphate adsorption-desorption on goethite, which is a very well-known and reference system, ideal for testing the performance of a physicochemical treatment that combines transport and reaction. Always the same phosphate species (monodentate mononuclear protonated) was present at the goethite surface during adsorption-desorption. There was an excellent agreement between theory and experiments at a variety of phosphate concentrations and surface coverages for adsorption kinetics, desorption kinetics and equilibrium situations, employing just one set of rate coefficients. The use of rate vs. adsorption curves permitted easy detection of conditions of transport- and reaction-controlled kinetics. The phosphate-goethite system is a fast-adsorbing/slow-desorbing system, with an adsorption rate constant k = 1.26 × 10³ s^-1 and a desorption rate constant k_d = 1.66 × 10^-5 s^-1. Therefore, adsorption was transport-controlled and desorption was reaction-controlled. The half-life of the desorption reaction is 41 700 s (11.6 h) but for adsorption it would take only a few seconds in the absence of transport control. For this kind of system, which is ubiquitous in nature and technological processes, it is easier to determine rate constants from desorption than from adsorption experiments.