## 3 Results and Discussion
### Batch Adsorption Evaluation  
Table 4 displays the experimental matrix along with the responses obtained for the simultaneous adsorption of pharmaceuticals in the batch process. ### Batch Adsorption Evaluation  
Table 4 displays the experimental matrix along with the responses obtained for the simultaneous adsorption of pharmaceuticals in the batch process. \begin{table}
\begin{tabular}{c c c c c c} \hline  & \multicolumn{2}{c}{**Independent Variables**} & \multicolumn{2}{c}{**Response**} \\ \hline
**Run Order** & **pH** & **Solid Mass (g)** & **Time (min)** & **Removal (\%)** & **Qe (mg/g)** \\ \hline
1 \({}^{*}\) & 7 & **2.00** & **60** & **98.1** & **4.0** \\
2 & 3 & 1.25 & 60 & 97.5 & 3.4 \\
3 & 3 & 0.50 & 30 & 76.3 & 2.7 \\
4 & 3 & 2.00 & 30 & 96.1 & 2.1 \\
5 & 11 & 2.00 & 30 & 93.6 & 1.6 \\
6 & 7 & 1.25 & 30 & 85.8 & 1.4 \\
7 & 7 & 1.25 & 30 & 83.4 & 1.3 \\
8 & 7 & 1.25 & 30 & 89.7 & 1.6 \\
9 & 7 & 0.50 & 10 & 56.7 & 2.1 \\
10 & 11 & 0.50 & 30 & 72.2 & 2.5 \\
11 & 11 & 1.25 & 60 & 97.3 & 3.2 \\
12 & 11 & 1.25 & 10 & 71.1 & 1.1 \\
13 & 3 & 1.25 & 10 & 72.7 & 1.2 \\
14 & 7 & 2.00 & 10 & 77.1 & 0.8 \\
15 & 7 & 0.50 & 60 & 86.2 & 3.1 \\ \hline \end{tabular} Legend: * optimized results.  
\end{table} 
Table 4: Experimental matrix and responses for the simultaneous batch adsorption of pharmaceuticals. Figure 3: FTIR spectrum of the activated carbon before adsorption process. Figure 2: X-ray diffraction pattern of the carbon activated before the adsorption. Figure 4 illustrates the response surface plots of the variable interactions derived from the applied experimental design. Figure 4: _Cont_. The results indicate the impact of the independent variables on the effectiveness of the adsorption process. Overall, it appears that the pH effect does not lead to significant variations in the removal rates and adsorption capacity, suggesting an indirect relationship between the medium pH and the response variables (Figure 4a-e). The mass of the adsorbent does not show a clear trend concerning the adsorption capacity results (Q\({}_{e}\); Figure 4d-f), revealing a non-linear relationship between mass and adsorption efficiency. However, when assessing the removal of pharmaceuticals, it is observed that the interaction between solid mass and solution pH (Figure 4a) results in the highest removal rates, with values approaching 98% as the amount of solid increases. A similar trend can be noted in the interaction between solid mass and process time (Figure 4c). [PERSON] et al. [39] investigated the adsorption of TC on commercial activated carbon similar to that used in this study. They found that the efficiency of TC removal increased gradually with the concentration of the adsorbent, reaching a maximum removal rate of 92.7% at a concentration of 3 g/L. Likewise, [PERSON] et al. [51] reported that the percentage of pharmaceutical removal rose with an increase in GAC concentration, with pollutant removal gradually increasing until equilibrium was reached. These findings can be attributed to the adsorption behavior of porous materials with a high specific surface area. Contact time consistently affects all experiments, with a general increase in removal efficiency and adsorption capacity as contact time lengthens (Figure 5b,c,e,f). This behavior is expected and is characteristic of adsorption processes, where longer contact times facilitate more complete interactions between the adsorbent and adsorbate [24; 52]. Figure 4: Surface area and contour plots for pharmaceuticals batch adsorption for %R: (**a**) solid mass and pH, (**b**) time and pH, (**c**) time and solid mass; Q\({}_{e}\) (mg/g): (**d**) solid mass and pH, (**e**) time and pH, (**f**) time and solid mass. Red areas indicate maximum response, green shows minimum, and yellow represents intermediate values. The response is maximized in red zones. Figure 5: \(Cont\). [PERSON] et al.