A comparative study of Box-Behnken, central composite, and Doehlert matrix was performed on the adsorption of Pb (II) by Robinia tree leaves in a batch system. As a case study, uptake capacity (q) and removal efficiency (R) of Pb (II) biosorption have been evaluated with all theses approaches. The advantages and limitations of these different response surface techniques have been experimentally considered. The results show the different statistical predictability of Doehlert matrix and Box-Behnken design at 95% confidence level comparable with some extent with that of central composite design at some extreme conditions. An environmental and economical comparison was also carried out between individual and simultaneous optimization of removal efficiency (R) and uptake capacity (q) using desirability function. Optimization of q proves only to have advantages over R or simultaneous optimization of R and q in this particular biosorption process.
Statistical experimental design was utilized to optimize removal of aqueous Hg(II) by Fraxinus tree leaves through a batch biosorption process. Sorbent−sorbate behavior was evaluated by fitting equilibrium data by nonlinear and transformed linear forms of the Langmuir, Freundlich, and Redlich−Peterson isotherms. The comparative study showed that nonlinear regression is a better way to model equilibrium data. A 23 full factorial design was used to identify significant factors and interactions. The pH, Hg(II) initial concentration, and sorbent mass were examined as major factors. The contact time was fixed at 30 min. All of the factors were significant at the 95 % confidence level. The amount of Hg(II) was determined by cold vapor atomic absorption spectrophotometry. A regression model was derived by using a response surface methodology through performing central composite design (CCD). Model adequacy was checked by such diagnostic tests as analysis of variance (ANOVA), lack of fit test, residuals distribution, and over-fitting test. On the other hand a residuals distribution was evaluated for normality according to the Ryan−Joiner test. As a result, the optimized condition for Hg(II) biosorption was calculated to be pH = 4.4, s = 0.25 g, and m = 50 mg·L−1, which corresponds to 92.25 % removal efficiency. The biosorption process was kinetically fast and followed a pseudosecond order kinetic model. Fourier transform infrared (FT-IR) and X-ray diffraction (XRD) spectra were used to find more about the biosorption mechanism.
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