The development of new adsorbent materials for the removal of toxic contaminants from drinking water is crucial to achieving the United Nations Sustainable Development Goal 6 (clean water and sanitation). The characterisation of these materials includes fitting models of adsorption kinetics to experimental data, most commonly the pseudo-second order (PSO) model. The PSO model, however, provides no sensitivity to changes in experimental conditions such as adsorbate and adsorbent concentrations (C 0 and C s ) and consequently is not able to predict changes in performance as a function of operating conditions. Furthermore, the experimental conditionality of the PSO rate constant, k 2 , can lead to erroneous conclusions when comparing literature results. In this study, we analyse 108 kinetic experiments from 47 literature sources to develop a relatively simple modification of the PSO rate equation, yielding:Unlike the original PSO model, this revised rate equation (rPSO) demonstrates the first-order and zero-order dependencies upon C 0 and C s that we observe empirically. Our new model reduces the residual sum of squares by 66% when using a single rate constant to model multiple adsorption experiments with varying initial conditions. Furthermore, we highlight how the rPSO rate constant k' is more appropriate for literature comparison, highlighting faster kinetics in the adsorption of arsenic onto alumina versus iron oxides. This revised rate equation should find applications in engineering studies, especially since unlike the PSO rate constant k 2 , the rPSO rate constant k' does not show a counter-intuitive inverse relationship with the increasing reaction rate when C 0 is increased.

<p>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.</p>

<p>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.</p>