On the Theoretical Development and the Applicability of the Lagergren Equation for the Kinetics of Adsorption at the Solid/Solution Interfaces

It is shown that the Lagergren equation is obtained as the simplest form of a Taylor’s expansion of the general Statistical Rate Theory expression for adsorption kinetics. The parameter of this expansion is the difference between the chemical potential of the adsorbed solute molecules and those in the free bulk phase. Retaining only the first term of this expansion and assuming a constant bulk solute concentration leads to the Lagergren equation. Then, it is shown that retaining higher terms of this Taylor’s expansion leads to more essential improvement of the obtained kinetic equation, than taking into account the changing concentration of the solute in the bulk phase.