## 3 Results and Discussion
### Batch Adsorption Performance of EGS@APTES-GT
#### 3.2.4 Adsorption Kinetics  
In order to evaluate the kinetic performance of EGS@APTES-GT and investigate the adsorption mass transfer mechanisms, various models were used [59; 60]. Table 4 shows the parameters obtained after fitting a time-dependent concentration change using three kinetic models: pseudo-second-order (PSO), the Elovich kinetic model, and the intra-particle diffusion model proposed by [PERSON] (WM). The used kinetic models are explained in detail in SM S2.5. The adsorption process was the best fitted using the PSO model (Table 4), assuming the existence of chemisorption adsorption mechanisms for As(V) [61; 62; 37] and physisorption for Iprodione [42]. The correlation coefficients R\({}^{2}\), obtained by W-M, were higher in the case of arsenate, similar to the one obtained using the PSO model. According to the maximum \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Parameter** & **As(V)** & **Iprodione** \\ \hline \multirow{3}{*}{Pseudo-second-order} & k\({}_{2}\) (g mg\({}^{-1}\) min\({}^{-1}\)) & \(4.18\times 10^{-4}\pm 2.1\times 10^{-5}\) & \(7.25\times 10^{-4}\pm 3.1\times 10^{-5}\) \\ \cline{2-4}  & q\({}_{e}\) (mg g\({}^{-1}\)) & \(41.83\pm 0.47\) & \(81.52\pm 0.57\) \\ \cline{2-4}  & R\({}^{2}\) & \(0.997\) & \(0.996\) \\ \hline \multirow{3}{*}{Elovich} & \(\alpha\) (mg g\({}^{-1}\) h\({}^{-1}\)) & \(2.13\pm 0.51\) & \(244.9\pm 235.1\) \\ \cline{2-4}  & \(\beta\) (mg g\({}^{-1}\)) & \(0.130\pm 0.01\) & \(0.119\pm 0.02\) \\ \cline{2-4}  & R\({}^{2}\) & \(0.966\) & \(0.921\) \\ \cline{2-4}  & k\({}_{\rm{4d}}\) (mg g\({}^{-1}\) min\({}^{-0.5}\)) & \(2.54\pm 0.14\) & \(3.318\pm 0.38\) \\ \cline{2-4}  & C\({}_{1}\) (mg g\({}^{-1}\)) & \(1.10\pm 1.18\) & \(35.87\pm 3.26\) \\ \cline{2-4}  & Step 1 & R\({}_{1}\)\({}^{2}\) & \(0.994\) & \(0.975\) \\ \cline{2-4}  & diffusion & k\({}_{\rm{4d}}\) (mg g\({}^{-1}\) min\({}^{-0.5}\)) & \(0.511\pm 0.05\) & \(0.439\pm 0.08\) \\ \cline{2-4}  & Step 2 (Equilibrium) & C\({}_{2}\) (mg g\({}^{-1}\)) & \(25.30\pm 1.05\) & \(68.90\pm 1.69\) \\ \cline{2-4}  & R\({}_{2}\)\({}^{2}\) & \(0.990\) & \(0.966\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Kinetic data obtained using PSO, Elovich, and intra-particle diffusion model for arsenate (C\({}_{1}\) = 4.83 mg dm\({}^{-3}\)) and Iprodione (C\({}_{1}\) = 9.81 mg dm\({}^{-3}\)) adsorption using hybrid adsorbent EGS@APTES-GT at 298 K, pH 7.0 \(\pm\) 0.1, and adsorbent mass/volume ratio 0.1 g L\({}^{-1}\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**adsorbate**} & \multicolumn{3}{c}{\(\Delta G^{\Theta}\) (k) mol\({}^{-1}\))} & \multirow{2}{*}{\(\Delta H^{\Theta}\) (k) mol\({}^{-1}\))} & \multirow{2}{*}{\(\Delta S^{\Theta}\) (J mol\({}^{-1}\) K\({}^{-1}\))} & \multirow{2}{*}{\(\mathbf{R^{2}}\)} \\ \cline{2-2} \cline{5-6}  & **298 K** & **308 K** & **318 K** & & \\ \hline Arsenate & \(-40.99\) & \(-43.15\) & \(-45.16\) & \(21.3\) & \(208.9\) & \(0.996\) \\ \hline Iprodione & \(-43.53\) & \(-45.03\) & \(-46.54\) & \(1.34\) & \(150.5\) & \(0.991\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Thermodynamic parameters calculated for EGS@APTES-GT hybrid adsorbent. equilibrium adsorption capacities, the hybrid adsorbent selectivity sequence can be given as Iprodione > arsenate. The two linear correlation lines, obtained using the intra-particle diffusion model, predict two dominating successive adsorption processes (Figure 6). The first step represents fast kinetics and the second part is followed by a very slow attainment of the equilibrium. A larger intercept found for the fungicide adsorption indicates higher resistance, which amounts to slower ionic transport due to intra-particle diffusion. The first linear step explains the external mass transfer from the bulk solution to the most available adsorbent surface, while the second step discloses processes of species diffusion through the porous structure of the adsorbent into the interior, approaching available surface-active sites, followed by the attainment of specific adsorbate/adsorbent interactions.