## 3 Results
### Optimization and Modeling by Response Surface  
In this study, a three-level, three-factor, 15-assay BBD was used to optimize MC adsorption on adsorbent prepared from SSS. The independent variables evaluated for the study are the initial concentration of the aqueous solution MC (X\({}_{1}\)), the adsorbent dosage (X\({}_{2}\)) and the solution pH (X\({}_{3}\)) (Table 1). The experiments were performed to optimize the adsorption efficiency of the medication on the prepared adsorbent. The obtained results are summarized in Table 6, in which the response evaluated was the MC removal (Y). The obtained responses were analyzed using Minitab 17 software. The polynomial equation that describes the main effects, the interaction effects and the quadratic effects of the selected independent variables show a significant influence on the responses [44]. The results of the analysis were evaluated using ANOVA variance analysis and are presented in Table 7. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Isotherms Models** & **Parameters** & **Values** & **R2** & **ARE (\%)** \\ \hline \multirow{3}{*}{[PERSON]} & q\({}_{\text{m}}\)(mg/g) & 63.29 & 0.986 & 57.611 \\ \cline{2-5}  & K\({}_{\text{L}}\)(L/mg) & 0.275 & & \\ \cline{2-5}  & R\({}_{\text{L}}\) & 0.071–0.652 & & \\ \hline \multirow{3}{*}{[PERSON]} & K\({}_{\text{F}}\) (mg/g) (L/g)\({}^{n}\) & 8.005 & 0.945 & 14.365 \\ \cline{2-5}  & n\({}_{\text{F}}\) & 1.872 & & \\ \hline \multirow{3}{*}{Temkin} & K\({}_{\text{T}}\)(L/g) & 1.093 & 0.970 & 9.804 \\ \cline{2-5}  & RT/b (B\({}_{\text{T}}\)(KJ/mol)) & 13.508 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of the adsorption isotherm models. \begin{table}
\begin{tabular}{c c c} \hline \hline
**T (\({}^{\circ}\)K)** & **\(\Delta\)G\({}^{\circ}\) (KJ/mol)** & **\(\Delta\)S\({}^{\circ}\) (KJ/mol K)** & **\(\Delta\)H\({}^{\circ}\) (KJ/mol)** \\ \hline
298 & \(-\)2.967 & 0.206 & \\ \hline
303 & \(-\)3.245 & 0.204 & \\ \hline
308 & \(-\)3.314 & 0.201 & \\ \hline
313 & \(-\)3.953 & 0.199 & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Obtained thermodynamic parameters in the range of tested temperatures. The high values of the correlation coefficient (R\({}^{2}\)) and the adjusted correlation coefficient (R\({}^{2}\)Adj), 0.97 and 0.91, respectively, show that the proposed model explains more than 91% of the variations in the experimental response [35]. Similar results were determined by [PERSON] and [PERSON] [45] who determined values of 0.9224 and 0.8227 for R\({}^{2}\) and R\({}^{2}\)Adj coefficients, respectively. So, the authors concluded that these values indicated good fitness and high significance for the statistical model. [PERSON] et al. [46] also reported that the obtained R\({}^{2}\) coefficients are in reasonable agreement with the R\({}^{2}\) Adj and more than 95% of the response can be well predicted by the models. The quadratic model is written in the following form:. \[\text{Y}\%=-4.4-0.121\ \text{C}_{i}+29.50\ \text{m}+15.60\ \text{pH}-0.67\ \text{pH}^{2}-1.550\ \text{m}\cdot\text{pH} \tag{18}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**N\({}_{0}\)** & **X\({}_{1}\)** & **X\({}_{2}\)** & **X\({}_{3}\)** & **C\({}_{1}\) (mg/L)** & **m (g/L)** & **pH** & **Y (\%)** \\ \hline
1 & \(-\)1 & \(-\)1 & 0 & 20 & 1 & 7 & 88.5539 \\ \hline
2 & 1 & \(-\)1 & 0 & 90 & 1 & 7 & 75.1651 \\ \hline
3 & \(-\)1 & 1 & 0 & 20 & 3 & 7 & 96.5097 \\ \hline
4 & 1 & 1 & 0 & 90 & 3 & 7 & 93.3073 \\ \hline
5 & \(-\)1 & 0 & \(-\)1 & 20 & 2 & 4 & 77.9135 \\ \hline
6 & 1 & 0 & \(-\)1 & 90 & 2 & 4 & 77.3905 \\ \hline
7 & \(-\)1 & 0 & 1 & 20 & 2 & 10 & 96.6233 \\ \hline
8 & 1 & 0 & 1 & 90 & 2 & 10 & 92.3212 \\ \hline
9 & 0 & \(-\)1 & \(-\)1 & 55 & 1 & 4 & 59.7206 \\ \hline
10 & 0 & 1 & \(-\)1 & 55 & 3 & 4 & 89.1495 \\ \hline
11 & 0 & \(-\)1 & 1 & 55 & 1 & 10 & 85.9411 \\ \hline
12 & 0 & 1 & 1 & 55 & 3 & 10 & 96.7700 \\ \hline
13 & 0 & 0 & 0 & 55 & 2 & 7 & 91.1453 \\ \hline
14 & 0 & 0 & 0 & 55 & 2 & 7 & 92.5922 \\ \hline
15 & 0 & 0 & 0 & 55 & 2 & 7 & 93.4458 \\ \hline \hline \end{tabular}
\end{table}