Sorption of Congo Red onto Bentonite: An Isothermal Remodelling Exercise

Abstract

The error distortion caused by the linearized plots of isotherm was avoided by re-analysis of the equilibrium data previously reported for the adsorption of Congo Red onto bentonite by direct nonlinear regression. The data were digitized from the published equilibrium curve and fitted to 19 one-, two- and three-parameter models. The root-mean-square error, the adjusted coefficient of determination, the bias and the accuracy factors, and three information criteria were used to evaluate the model performance. Ranking was based on the diagnostic used: Moreau resulted in the lowest RMSE (0.339 mg g-1) and Hannan-Quinn value, Vieth-Sladek gave the lowest reported BIC, and Freundlich gave the lowest corrected Akaike value. This dependence on the criterion and the small number of equilibrium observations do not justify selection on the basis of goodness of fit alone. The two-parameter Freundlich model provided a close empirical description (RMSE 0.658 mg g⁻¹; adjustedR² 0.99). The Langmuir fit estimated a monolayer capacity of 37.38 mg g⁻¹ (95% confidence interval 24.367-50.393 mg g⁻¹) and an affinity constant of 0.17 L mg⁻¹ (95% confidence interval 0.036-0.310 L mg⁻¹). A Halsey rearrangement of the Freundlich relation gave 26.52 mg g⁻¹, close to the maximum loading observed. These results show that nonlinear fitting improves interpretation of parameters, but mechanistic conclusions remain limited due to sparse data and the uncertainty of parameters.