A Comment on the Derivation of the Langmuir Isotherm for the Adsorption Kinetics

The justification for the use of the Langmuir isotherm, basically an equilibrium relation, to relate the subsurface concentration Ct at time t to the adsorbed surface concentration Gamma t depends, in many adsorption kinetics models, on the presence of two very different time scales. Though this was implicit in the recent derivation in 1, it was not specifically pointed out. The second long time scale is particularly important because it governs the time evolution of Ct, the subsurface concentration, and helps to determine when the Langmuir isotherm approximation is valid. Here the Langmuir isotherm is derived mathematically from the adsorption kinetics equations governing the surface concentration, the subsurface concentration and the bulk phase adjacent to the surface.