A Revised Pseudo-Second Order Kinetic Model for Adsorption, Sensitive to Changes in Sorbate and Sorbent Concentrations

Much contemporary research considers the development of novel sorbents for the removal of toxic contaminants. Whilst these studies often include experimental adsorption kinetics, modelling is normally limited to application of the pseudo-second order (PSO) rate equation, which provides no sensitivity towards changes in experimental conditions and thus no predictive capability. We demonstrate a relatively simple modification of the PSO model, with the final form dqt/dt = k’C_t(1-(q_t/q_e))^2 where k’=k₂*(q_e*^2)/C₀*. We demonstrate that unlike the PSO model, this new rate equation provides first-order dependence upon initial sorbate concentration (observed experimentally as x̄=0.829±0.417), whilst rate constant k’ is significantly less sensitive to changes in C₀ and C_s than PSO rate constant k₂. We demonstrate that this model improves predictive capacity towards changes in C₀ and C_s, particularly when q_e is calculated using the Langmuir or Freundlich adsorption isotherm. Finally, we explore how the new rate constant, k’, responds to changes in sorbent morphology, identifying that particle radius is a better constraining parameter than surface area. In this new equation, the conditionality of the rate constant upon experimental conditions is significantly decreased, facilitating better comparison of new results with the literature.