Optimum isotherm by linear and nonlinear regression methods for lead (II) ions adsorption from aqueous solutions using synthesized coconut shell–activated carbon (SCSAC)

Batch experiment was carried out to determine the optimum isotherm suitable to model the adsorption of Pb(II) ions onto synthesized coconut shell–activated carbon (SCSAC). In order to estimate the equilibrium parameters, the equilibrium adsorption data were analyzed using the following two-parameter isotherms: Langmuir, Freundlich, Temkin and Harkins–Jura by applying linear and nonlinear regression methods. In addition, seven linearized isotherm models (including four linearized Langmuir models) and four nonlinear isotherm models were discussed in this study. The specific surface areas of both nonsynthesized CSAC and synthesized SCSAC-activated carbon were estimated by Sears Method to be 650 m2g−1 and 768 m2g−1, respectively. Likewise other properties like bulk density, particle density, porosity, ash content, Scanning Electron Micrographs (SEM) analysis and Fourier Transform Infrared (FTIR) spectroscopy were also estimated. The error functions which includes the Sum of the Squares of the Errors (SSE), root mean square error (RMSE), Average relative error (ARE), Chi-square (X2), Marquardt’s Percent Standard Deviation (MPSD) and the correlation coefficient (R2) between the calculated and experimental data were also used to compare the suitability of different linearized and nonlinearized model parameters. In conclusion, Freundlich nonlinear isotherm was found to be in better agreement with optimum parameters having generated the maximum adsorption capacity Kf (110.10 Lmg−1), highest coefficient of determination R2 (0.9847) and lowest error functions. Hence, nonlinear isotherms of Freundlich and Harkin–Jura exibited greater performance than linear counterparts in the following order: Freundlich (nonlinear) > Harkin–Jura (nonlinear) > Freundlich (linear) > Harkins–Jura (linear) > Temkin (linear) > Temkin (nonlinear) isotherm models. This shows that transformation of nonlinear isotherm equations to linear forms implicitly alter their error structure.