Non-linear Regression Analysis for the Adsorption Kinetics and Equilibrium Isotherm of Phenacetin onto Activated Carbons

Activated carbon obtained from ayous sawdust, Cucurbitaceae (egussi) peelings and the mixture of the two were studied for the adsorption of phenacetin. Characterisation of activated carbon by SEM and XRD analysis shows that the mixture of precursors combine the properties of activated carbon obtained separately. The well-knownbatch sorption models– Langmuir (one and two sites), Freudlich, Tempkin, Elovich, Langmuir-Freudlich, Redlich Peterson, Radke-Prausnitz, Fritz Shlunder)—were tested with experimental data for the adsorption of phenacetin to estimate adsorption equilibrium parameters—rate constantsand adsorption capacities. The model with the best fit was identified from extensive statistical analysis of the results of nonlinear regression of the experimental data. Comparison of the statistical errors in parameter estimation between linear and non-linear isotherm models shows that transformation of non-linear isotherm equations to linear forms implicitly alter their error structure. The much smaller size of the various error indicators —Determination Coefficient, R2; Sum of Square Errors, SSE; Chi Test, χ2; Average Relative Errors, ARE—, calculated for the case of non linearization when compared to linearization, indicate the greater accuracy in the application of non linearization. The Langmuir model (one site) gave the best fit and thus the values of adsorption capacity for each activated carbon were calculated from it. Kinetic models show that weak and strong interactions are involved in the adsorption process and that the controlling mechanism may not be limited to intra particle diffusion. The lower value of the boundary layer thickness in the case of activated carbon obtained from the mixture, justified the higher adsorbed quantity of this activated carbon compared to those of activated carbon from each precursor.