A Full Analytical Solution for the Sorption−Desorption Kinetic Process Related to Langmuir Equilibrium Conditions

A full analytical solution for the kinetics of an adsorption−desorption reaction is presented. The proposed solution is made by solving the differential equation which describes the accumulation rate of the sorbed complex, based on a site specific, single layer adsorption mechanism. Two important features of the presented solution are as follows: (a) Unlike previously presented analytical solutions, this equation does not impose any initial conditions and is also applicable for nonzero initial sorbed concentrations. Thus, the proposed equation might be used for modeling desorption as well as adsorption or as a part of a model that describes solute transport through an adsorptive medium in nonequilibrium conditions. (b) It converges with the Langmuir/Scatchard equations at infinite time (i.e., chemical equilibrium).