A comparative study of the linear and non-linear methods for determination of the optimum equilibrium isotherm for adsorption of Pb2+ ions onto Algerian treated clay

Document Type: Research Article


Laboratory of Materials Technology, University of Science and Technology Houari Boumediene, B.P. 32, El-Alia, Bab-Ezzouar, Algiers, Algeria


The adsorption equilibrium isotherms of lead from aqueous solutions onto treated clay were studied and modeled. The ability of clay to remove Pb 2+ ions from aqueous solutions has been studied at different operating conditions: contact time (5-90 min), adsorbent dosage (1-4 g L-1), initial ion concentration (10 - 200 mg L-1) and pH solution (1 - 11) and temperature (298 - 333 K). The maximum uptake (98.%) is obtained under the optimum conditions: pH ∼ 7 and adsorbent dose of 2.5 g L-1 for initial concentration of 10 mg L-1 at 298 K. In order to determine the best fit isotherm, the experimental equilibrium data were analyzed using some adsorption isotherm models with two-parameters as Langmuir, Freundlich, Temkin, Elovich and Dubinin-Radushkevich, and three-parameters as Langmuir-Freundlich, Redlich-Peterson, Sips, Fritz-Schlender and Toth. Models with four-parameters as Fritz-Schlunder and Baudu and with five-parameters as Fritz-Schlunder were also used. A comparison of linear and non-linear regression method for predicting the optimum isotherms were made using the experimental adsorption equilibrium data of Pb2+ ions onto treated clay. The following error analysis methods were used, the coefficient of determination R2, the sum of the squares of the errors, the sum of the absolute errors, the average relative error, the Mean Square Error and the Root Mean Square Error. The error values indicated that non-linear method is a better way to obtain the isotherm parameters describing the Pb2+ ions adsorption onto clay. The comparison between different models shows that Fritz-Schlünder model with five-parameters was more suitable to describe the equilibrium data. The kinetics data of batch interaction was also analyzed with various kinetic models. It was found that the pseudo-second order model using the non-linear regression method predicted best the experimental data.


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