## 3 Results and Discussion
### Adsorption Thermodynamic  
The changes in Gibbs free energy (\(\Delta\)G\({}^{\circ}\)), enthalpy (\(\Delta\)H\({}^{\circ}\)), and entropy (\(\Delta\)S\({}^{\circ}\)) for CV and Cr (VI) adsorption process were evaluated using van't Hoff curves (Figure 15). The calculated values of \(\Delta\)G\({}^{\circ}\), \(\Delta\)H\({}^{\circ}\) and \(\Delta\)S\({}^{\circ}\) for CV and Cr (VI) adsorption are collected in Table 7. The negative values of \(\Delta\)G\({}^{\circ}\) for both pollutants indicate that the adsorption process is spontaneous and feasible, without the need for an external energy source. Furthermore, the increase in the value of \(\Delta\)G\({}^{\circ}\) with increasing temperature implies that adsorption is easier at lower temperatures. The negative values of \(\Delta\)H\({}^{\circ}\) for CV and Cr (VI) confirm that the adsorption process of both pollutants is exothermic, which is already indicated by  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Parameters**} & \multicolumn{2}{c}{**Adsorbent**} \\ \cline{3-4}  & & **CV** & **Cr (VI)** \\ \hline \multirow{4}{*}{[PERSON]} & \(\begin{array}{c}\text{q}_{\text{m}}\ (\text{mg}/\text{g})\\ K_{\text{L}}\ (\text{L}/\text{mg})\\ \text{R}^{2}\end{array}\) & 352.1 & 187.6 \\  & \(\begin{array}{c}\text{K}_{\text{L}}\ (\text{L}/\text{mg})\\ \text{R}^{2}\end{array}\) & 0.05 & 0.12 \\  & \(\begin{array}{c}\text{R}^{2}\end{array}\) & 0.999 & 0.999 \\  & \(\begin{array}{c}\text{x}^{2}\end{array}\) & 11.14 & 8.69 \\ \hline \multirow{4}{*}{Freundlich} & \(\begin{array}{c}\text{K}_{\text{F}}\ (\text{mg}/\text{g})\ (\text{L}/\text{mg})\\ \text{1/n}\end{array}\) & 72.2 & 75.1 \\  & \(\begin{array}{c}\text{n}\end{array}\) & 3.45 & 5.45 \\  & \(\begin{array}{c}\text{R}^{2}\end{array}\) & 0.961 & 0.982 \\  & \(\begin{array}{c}\text{x}^{2}\end{array}\) & 505.6 & 51.1 \\ \hline \multirow{4}{*}{Temkin} & \(\begin{array}{c}\text{A}\ (\text{L}/\text{g})\\ \text{B}\end{array}\) & 1.10 & 10.61 \\  & \(\begin{array}{c}\text{B}\end{array}\) & 41.98 & 100.68 \\ \cline{1-1}  & \(\begin{array}{c}\text{R}^{2}\end{array}\) & 0.972 & 0.981 \\ \cline{1-1}  & \(\begin{array}{c}\text{x}^{2}\end{array}\) & 28.13 & 10.26 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Adsorption isotherm constants for CV and Cr (VI) at 30 \({}^{\circ}\)C.  
Figure 14: Separation factor for the adsorption of Cr (VI) and CV on ACSCGs.  
the decrease of the adsorbed amount with increasing temperature. This can be explained by the weakening of the adsorption forces between the active sites of the carbon and the adsorbed species by the increase in temperature. The negative values of \(\Delta\)S\({}^{\circ}\) revealed that the adsorption of CV and Cr (VI) leads to a decrease of disorder at the solid-liquid interfaces. On the other hand, the value of the activation energy (E\({}_{\text{a}}\)) of the adsorption of the two pollutants, estimated by the Arrhenius equation (Equation (13)), shows that the removal of the two pollutants on the activated carbon is physical in nature. A similar thermodynamic behaviour was also observed by [PERSON] et al., for the adsorption of CV on activated carbon prepared by lemon wood [87], and by [PERSON] et al., in their work on the adsorption of Cr (VI) on activated carbon from date seeds [88].