# The Diffusion Role in Adsorption of Hexavalent Chromium on Solid Olive Mill Waste
## 4 Results and Discussion
### Spectral Characterization of Cr(VI) Aqueous Solutions  
In aqueous solutions, Cr(VI) gives rise to different chemical equilibria involving various ionic species (_speciation_) [8,21]. In Figure 2a, the absorption spectra of K\({}_{2}\)CrO\({}_{4}\), at 25 \({}^{\circ}\)C, for 0.96, 1.92, 3.85, 7.69, 9.61, 19.6, 50.0, 76.9 \(\upmu\)M concentrations, were collected. It was immediately seen that, for each concentration investigated, the spectrum exhibited two distinct bands. Since at pH = 7.6, CrO\({}_{4}\)\({}^{2-}\) and HCrO\({}_{4}\)\({}^{-}\) are the predominant species, the following equilibrium:  
\[\text{CrO}_{4}\text{${}^{-2}$}+\text{H}_{2}\text{O}\ \raisebox{-1.72 pt}{ $\stackrel{{\longleftrightarrow}}{{\longleftrightarrow}}$} \text{HCrO}_{4}\text{${}^{-}$}+\text{OH}\text{${}^{-}$}\]  
can be considered as largely responsible for the spectra displayed in Figure 2a [8,21]. Indeed, the electronic configuration of Cr(VI) is 3d\({}^{5}\)4s\({}^{1}\) corresponding to a state \(d^{0}\), then the probability of d-d transitions is negligibly small. In addition, the formal charge on Cr atom (+6) is very high so that electrons flow from O atoms to the Cr atom. In other words, both bands shown in the spectra of Figure 2a are the result of the charge transfer. If the molecular structure of the CrO\({}_{4}\)\({}^{-2}\) ion is analyzed, one finds that it is perfectly symmetrical since the metal is surrounded by four perfectly equivalent O atoms. Hence, the representative band II is wide and centered in the range of 360-373 nm. On the contrary, in the HCrO\({}_{4}\)\({}^{-}\) molecule, the neutralization of an O atom reduces the symmetry and makes the charge transfer more energetic. As a result, the representative band I shifts to lower  
Figure 1: (**a**) TG and DTG curves of biomass WP. Measurements were performed under N\({}_{2}\) stream (100 cm\({}^{3}\) min\({}^{-1}\)) and at a heating rate of 10 \({}^{\circ}\)C min\({}^{-1}\); (**b**) the DSC profiles of biomass WP were obtained by measurements performed under N\({}_{2}\) stream (100 cm\({}^{3}\) min\({}^{-1}\)) and a heating rate of 10 \({}^{\circ}\)C min\({}^{-1}\). Figure 2: Results of the spectrophotometric measurements on aqueous solutions of K\({}_{2}\)CrO\({}_{4}\) at different concentrations in the range of 0.960–76.9 \(\upmu\)M. (**a**) The absorption spectra show two distinct bands whose intensity increases with increasing Cr(VI) concentration; (**b**) the integral absorbance of the individual samples is a linear function of Cr(VI) concentration and can be used as a calibration line; (**c**) increasing Cr(VI) concentration of \(\lambda_{max}\) of band II shifts to longer wavelengths and reaches a plateau. wavelengths and is displayed at 262 nm. A careful inspection of Figure 2a reveals that increasing the Cr(VI) concentration, band I remains practically fixed while band II shifts to longer wavelengths. Whilst it can be seen that only the peak wavelength, \(\lambda_{max}\) can hardly capture information about the molecular structure and it is convenient to refer to integral absorbance, this allows us to generalize [PERSON]'s law [22]. Mathematically, it assumes the following form:  
\[\bar{A}(C)=\int_{\lambda_{1}}^{\lambda_{2}}A(C,\lambda)d\lambda \tag{20}\]  
where \(\lambda\) is a wavelength (in nm) within the experimental interval \([\lambda_{1},\lambda_{2}]\) and \(C\) is the Cr(VI) molar concentration. In Figure 2b, \(\bar{A}(C)\) is plotted as a function of Cr(VI) concentration (\(\upmu\)M). The relationship between \(\bar{A}\) and \(C\) is established by fitting the first-degree polynomial, \(\bar{A}=p_{1}C+p_{2}\), to experimental data. A linear least square method is used for determining the parameters \(p_{1}\) and \(p_{2}\) and the goodness of the fit is confirmed by a high correlation coefficient \(R^{2}=0.99\). Accordingly, this polynomial is used as a calibration line to convert the integral absorbance into Cr(VI) concentration.