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Investigating the Reaction and Transport Controlled Mechanism for the Sorption of Cr(III) and Mn(II) Ions onto Acid Activated Shale using Non-Linear Error Functions

Time dependent adsorption study on the sorption of Cr(III) and Mn(II) ions onto acid activated shale was conducted using batch adsorption techniques to investigate the effect of initial metal ion concentration on the process of adsorption. Experimental data obtained were fitted into different kinetic models to analyze the mechanism of adsorption in terms of reaction controlled and transport controlled mechanism. Some of the selected kinetic models include; Pseudo-first order, Pseudo-second order, Elovich, Film diffusion, Parabolic diffusion and Intra-particle diffusion model. From the result, it was observed based on the linear coefficient of determination (r2) that the experimental data fitted well into the various kinetic model tested. Application of non-linear error function such as error sum of square (SSE), root mean square error (RMSE) and residual average (RA) revealed that the rate limiting step for the adsorption of Cr3+ and Mn2+ ions on acid activated shale was chemical attachment (chemisorption) and the reaction mechanism follows the Pseudo-second order kinetic model.