Linear and Non-linear Regression Methods to Study the Adsorption of Cr(VI) from an Aqueous Solution Using Pomegranate Peel


  • Salah M. Abdullah Polymer Research Unit, College of Science, Mustansiriyah University, 10052 Baghdad, IRAQ.
  • Aseel F. Alwan Polymer Research Unit, College of Science, Mustansiriyah University, 10052 Baghdad, IRAQ.
  • Atheer M. Majeed Department of Media, College of Art, Mustansiriyah University, 10052 Baghdad, IRAQ.
  • Enageh T. A. Abdalgader Department of Chemistry, College of Education Janzour, University of Tripoli, Janzour, Libya.



Chromium (VI), pomegranate peel, linear regression, non-linear regression, error functions, adsorption


In this study, the previous data of the adsorption of Chromium (VI) ions on the pomegranate peels (MPGP) as adsorbents were used. linear and non-linear equations for Langmuir, Freundlich, Dubinin-Radushkevich, Tempkin, Redlich-Peterson, Sips, and Toth adsorption isotherm models were applied. The five error functions ERRSQ, HYBRD, MPSD, ARE, and EABS were analyzed for non-linear isotherm equations and in each case a set of isotherm parameters were determined. The algorithms for the simulation of linear and non-linear isotherm models using error functions were achieved with the aid of Microsoft Excel solver Add-Ins for minimizing the respective error function across the concentration range studied. Linear and non-linear methods show comparable data for two-parameter models, also high R2 values were obtained for Langmuir, Freundlich, and Temkin models while the Dubinin-Radushkevich model reveals low R2 values, on the contrary, three-parameter models show different data between linear and non-linear methods with high R2 value for all. Which indicates that the error does not obey the Gaussian distribution.


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Y.S. Ho, G. McKay, "The kinetics of sorption of basic dyes from aqueous solutions by sphagnum moss peat", J. Chem. Eng. vol. 76, pp. 822-826,1998.


G. Walker, L. Hansen, J. Hanna, "Kinetics of a Reactive Dye Adsorption onto Dolomitic Sorbents", Water Res, vol.37,pp. 2081-2089, 2003.

CrossRef | PubMed

G. McKay, S. Allen, I. McConvey, "Transport processes in the sorption of colored ions by peat particles," Journal of Colloid Interface Science. vol.80,pp.323-339,1981.


S.J. Allen, G. McKay, "Surface mass transfer processes using peat as an adsorbent for dyestuffs," Journal of Chemical Engineering, vol.58, pp.521-526,1980.


S. Ismadji, S.K. Bhatia, "Adsorption of flavour esters on granular activated Carbon," Journal of Chemical Engineering, vol. 78, pp. 892-901, 2000.


K. V. Kumar, S. Sivanesan, "Pseudo second order kinetics and pseudo isotherms for malachite green onto activated carbon: Comparison of linear and non-linear regression methods," Journal of Hazardous Material, vol. 136, pp.721-726, 2006.

CrossRef | PubMed

K. V.Kumar, "Optimum Sorption Isotherm by Linear and Non- Linear Methods for Malachite Green onto Lemon Peel,'' Dyes and Pigments, vol. 74, pp.595-597,2007.


D. W. Marquardt, "An algorithm for least-squares estimation of nonlinear parameters," Journal of Society for industrial and applied. Mathimatics," vol. 11, pp. 431-44, 1963.


A.Kapoor, R.T. Yang,"Correlation of equilibrium adsortpion data of condensible vapours on porous adsorbents,"Gas Separation and Purification," vol.3, pp.187-192,1989.


T.S.Najim, S. Yasin, "Removal of Chromium from Aqueous Solution Using Modified Pomegranate Peel: Mechanistic Thermodynamic Studies," E-Journal of Chemistry, (S1), vol. 6, S153-S158 ,2009.


Y. S. Ho, J. F. Porter, and G. Macay," Equilibrium isotherm studies for the sorption of divalent metal ions Onto peat : Copper, Nickel and Lead single component systems," Water,Air&Soil Pollution," vol. 141, pp.1-33, 2002.

J. Wang, X. Guo "Adsorption isotherm models: Classification, physical meaning, application and solving Method," Chemosphere, vol.258, 127279, 2020.

CrossRef | PubMed

L. T. Popoola, A. S. Yusuff, O. A. Adesina and M. A. Lala," Brilliant Green Dye Sorption onto Snail Shell-rice Husk: Statisticaland Error Function Models as Parametric Isotherm Predictors," Journal of Environmental Science and Technology, vol.12, pp.65-80, 2019.


M. A. Al-Ghouti, D. A. Da'ana, "Guidelines for the use and interpretation of adsorption isotherm models: A review," Journal of Hazardous Material, vol.393, 12238, 2020.

CrossRef | PubMed

M.R. Kooh,. M. K. Dahri. L. B. Lim, "The removal of rhodamine B dye from aqueous solution using Casuarina equisetifolia needles as adsorbent," Cogent Environmental Science,vol. 2,pp.1-14,2016.




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How to Cite

S. M. Abdullah, A. F. . Alwan, A. M. . Majeed, and E. T. A. . Abdalgader, “Linear and Non-linear Regression Methods to Study the Adsorption of Cr(VI) from an Aqueous Solution Using Pomegranate Peel”, Al-Mustansiriyah Journal of Science, vol. 34, no. 4, pp. 58–65, Dec. 2023.



Chemical Science

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