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

Main Article Content

Christian Sadeu Ngakou
Gabche Solomon Anagho
Horace Manga Ngomo


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.

Activated carbon, mixture of precursor, non-linear kinetics, non-linear isotherms, SEM, XRD

Article Details

How to Cite
Ngakou, C. S., Anagho, G. S., & Ngomo, H. M. (2019). Non-linear Regression Analysis for the Adsorption Kinetics and Equilibrium Isotherm of Phenacetin onto Activated Carbons. Current Journal of Applied Science and Technology, 36(4), 1-18.
Original Research Article


Kolpin DW, Furlong ET, Meyer M, Thurman EM, Zaugg SD, Barber LB, Buxton HAT. Pharmaceuticals, hormones and other organic wastewater conta-minants in US streams, 1999-2000: A national reconnaissance. Environmental Science and Technology. 2002;36:1202-1211.

Ternes TA. Occurrence of drugs in German sewage treatment plants and rivers. Water Research. 1998;32:3245-3260.

Caturla F, Sabio MM, Ranoso FR. Preparation of activated carbon by chemical activation with ZnCl2. Carbon. 1991;29:999-1007.

Zuccato E, Calamari D, Natangelo M, Fanelli R. Presence of therapeutic drugs in the environment. The Lancet. 2000;355: 1789-1790.

Anwar El-S, Nagwa A. El-M, El-Hawary HH. Averting cancer effect of paracetamol and phenacetin by N-Acetylcystine. International Journal of Pharmacy and Pharmaceutical Sciences. 2014;6(5):383-390.

Brune K, Renner B, Tiegs G. Acetamino-phen/paracetamol: A history of errors, failures and false decisions. European Journal of Pain. 2014;1-3.

Langmuir I. The constitution and funda-mental properties of solids and liquids. Journal of American Chemical Society. 1916;38:2221-2295.

Freundlich HMF. Over the adsorption in solution. Zeitschrift fur Physikalische Chmie. 1906;57A:385-470.

Eun WS, Rowell RM. Cadmium ion sorption onto lignocellulosic biosorbent modified by sulfonation: The origin of sorption improvement. Chemosphere. 2005;60:1054-1061.

Rangabhashiyam S, Anu N, Giri Nandagopal MS, Selvaraju N. Relevance of isotherm models in biosorption of pollutants by agricultural by products. Journal of Environmental Chemical Engineering. 2014;6(5):2398-2414.

Redlich O, Peterson DL. A useful adsorption isotherm. Journal of Physical Chemistry. 1959;63:1024.

Tseng RL, Wu FC, Juang RS. Liquid-phase adsorption of dyes and phenols using pinewood-based activated carbons. Carbon. 2003;41:487–495.

Anagho SG, Ketcha JM, Tchuifon TDR,Ndi JN. Kinetic and equilibrium studies of the adsorption of mercury (II) ions from aqueous solution using kaolinite and metakaolinite clays from Southern Cameroon. International Journal of Research in Chemistry and Environment. 2013;3:1-11.

Ho YS, McKay G. The kinetics of sorption of basic dyes from aqueous solution by sphagnum moss peat. The Canadian Journal of Chemical Engineering. 1998; 76(4):822-827.

Elovich SY, Larinov OG. Theory of Adsorption from Solutions of none lectrolytes on solid (I) equation adsorption from solutions and the analysis of its simplest form (II), verification of the equation of adsorption isotherm from solutions. Izv. Akad. Nauk. SSSR, Otd. Khim. Nauk. 1962;2:209–216.

Weber WJ, Morris JC. Kinetic of adsorption of carbon from solution. Journal of Sanitary Engineering Division-American Society Civil Engineer. 1963; 89, 31-63.

Amrhar O, Nassali H, Elyoubi MS. Application of nonlinear regression analysis to select the optimum absorption isotherm for Methylene Blue adsorption onto Natural Illitic Clay. Bulletin de la Société Royale des Sciences de Liège. 2015;84:116–130.

Yuh-Shan H. Selection of optimum sorp-tion isotherm. Carbon. 2004;42:2113–2130.

Tran HN, You SJ, Hosseini-Bandegharaei A, Chao HP. Mistakes and inconsistencies regarding adsorption of contaminantsfrom aqueous solutions: A critical review. Water Research. 2017;120:88 -116.

Hossain MA, Ngo HH, Guo W. Introduction of Microsoft excel SOLVER function-spreadsheet method for isotherm and kinetic modeling of metals biosorption in water and wastewater. Journal of Water Sustainability. 2013;3(4):223- 237.

Boldizsar N, Carmen M, Andrada M, Cerasella I, Barbu-Tudoran L, Cornelia M. Linear and nonlinea r regression analysis for heavy metals removal using Agaricus bisporusmacrofungus. Arabian Journal of Chemistry. 2017;10:S3569–S3579.

Otheman A, Hakima N, Mohamed SE. Two and three-parameter isothermal modeling for adsorption of Crystal Violet dye onto Natural Illitic Clay: Nonlinear regression analysis. Journal of Chemical and Pharmaceutical Research. 2015;7(9):892-903.

Hamid RG, Hasan P, Abdolhamid T, Kavoos D, Babak G, Vali A, Amin G. Linear and nonlinear two-parameter adsorption isotherm modeling: A case-study. The International Journal of Engineering and Science; 2017.

[ISSN (e): 2319 – 1813]

[ISSN (p): 2319 – 1805]

Can M. Studies of the kinetics for rhodium asorption onto Gallic Acid Derived Polymer: The application of nonlinear regression analysis. Acta Physica Polonica A. 2015;127:1308- 1310.

Goharrizi AS, Rahbari M, Torkzadeh M. the study of lead adsorption from aqueous solution by carbon nanotubes (CNTs): Adsorption equilibrium and kinetics. Environmental Science and Indian Journal. 2009;4(1):36–44.

Chen C. Evaluation of equilibrium sorption isotherm equations. The Open Chemical Engineering Journal. 2013;7:24–44.

Eren E. Removal of copper ions by modified Unye clay, Turkey. Journal of Hazardous Materials. 2008;159:235-244.

Freundlich HMF. Über die adsorption in lösungen, Zeitschrift für Physikalische. Chemie (Leipzig). 1906;57A:385–470.

Koble RA, Corrigan TE. Adsorption isotherms for pure hydrocarbons. Industrial and Engineering Chemistry. 1952;44(2):383- 387.

Brouers F, Al-Musawi JT. On the optimal use of isotherm models for the characteri-zation of biosorption of lead onto algea. Journal of Molecular Liquids. 2012;212: 46-51.

Subramanyan B, Ashutosh D. Adsorption isotherm modelling of phenol onto natural soils-applicability of various isotherm models. International Journal of Environ-mental Research. 2012;6(1):256-276.

Ngakou SC, Ngomo HM, Anagho SG. Batch equilibrium and effects of ionic strength on kinetic study of adsorption of phenacetin from aqueous solution using activated carbon derived from a mixture of ayous sawdust and cucurbitaceae peelings. Current Journal of Applied Science and Technology. 2018;26(2):1- 24.

Rawlings O, Pentula SG, Dickey, DA. Applied regression analysis: A research tool. Second Edition, Springer. 1998;671.

[ISBN 0-387-98454-2]

Wu FC, Tseng RL, Juang RS. Preparation of highly microporous carbons from fir wood by KOH activation for adsorption of dyes and phenols from water. Separation and Purification Technology. 2005;47:10-19.

Kavitha D, Namasivayam C. Experimental and kinetic studies on methylene blue adsorption by coir pith carbon. Bio-resources Technologies. 2007;97:14-21.