Isotherms for the adsorption of Cu(II) onto lignin: Comparison of linear and non-linear methods

Abstract

Equilibrium studies were carried out for the adsorption of Cu(II) onto Kraft lignin as an adsorbent. The experimental data were fitted to the Freundlich, Langmuir and Redlich-Peterson isotherms by linear and non-linear method. Comparison of linear and non-linear regression method was given in selecting the optimum isotherm for the experimental data. The coefficient of correlation r2 and Chi-square test χ2 was used to select the best linear theoretical isotherm. The best linear model is Redlich-Peterson isotherm model, where r2=0,985 and χ2=0,02. In order to predict the error ERRSQ, HYBRD, MPSD, ARE and EABS were used. Moreover, by minimizing these error functions the optimal values of parameters and also the optimum isotherm was found. The Redlich-Peterson isotherm was found to be the best representative for adsorption of Cu(II) on the adsorbent in the cases when ERRSQ, HYBRD, MPSD functions were used. There coefficients of determination are 0.986, 0.985, 0.984, respectively and Chi-square is 0.02 in all cases. Freundlich isotherms which were obtained by minimization of the ERRSQ, HYBRD, MPSD, ARE and EABS function showed very good agreement with experimental data. In all cases the coefficients of determination are greater than 0.91. Besides, it was observed that non-linear isotherm models were better for representation of equilibrium data than linearized models

Removal of Cadmium(II) and Lead(II) from Water by Chemically Treated Citrullus lanatus Peels as Biosorbent in Cost Effective Way

“…1/qe = 1/bqmCe + 1/qm (1) logq = logKF + (1/n)logCe (2) In case of Langmuir model, on the basis of R 2 values given in (table 1), it was presumed that Langmuir isotherm could explain the sorption process in good way. Maximum sorption capacity 'qm' for Cd(II) and Pb(II) was 19.310 mg and 25.775 mg, respectively [21]. It was compared with other adsorbents as reported [22,23] various agro-waste materials.…”

Removal of Acidic Dyes from Aqueous Media Using Citrullus Lanatus Peels: An Agrowaste-Based Adsorbent for Environmental Safety

“…On the basis of R values, it was assumed that the Langmuir isotherm could describe the sorption process in good way. Moreover, the maximum sorption capacity "q m " was highest for it [13].…”

Elucidation of Sorption Mechanism of R. arrhizus for Reactive Blue 222 using Equilibrium and Kinetic Studies

“…In this regard, equilibrium relationships, known as adsorption isotherms, describe how pollutants interact with the adsorbents [22,23]. In addition, the quality of the fit of the experimental results indicates whether adsorption is monolayer or multilayer, on a homogeneous or a heterogeneous surface [24].…”

“…Due to the inherent bias from linearization, alternative isotherm parameter sets were determined by non-linear regression. This provides a mathematically meticulous method for determining the isotherm parameters by using the original form of the isotherm equation [24]. In all of the error analysis methods it is assumed that both the liquid-phase concentration and the solid-phase concentration contribute equally to weighting the error criterion for the model solution procedure.…”

“…The average relative error (ARE) (Equation18) function attempts to minimize the fractional error distribution across the entire concentration range. 19), a composite fractional error function was developed in order to improve the fit of the SAE method at low concentration values [24]. In this method each SAE value is divided by the experimental solid-phase concentration value q.…”