## 3 Results and Discussion
### Adsorption Kinetics  
To assess the rate and mechanism of the adsorption process, the kinetics of the adsorption of ammonium and orthophosphate onto the investigated substrates were further examined. In order to achieve this, two common kinetic models--the pseudo-first-order and pseudo-second-order equations--were fitted to the experimental data. Figures 2 and 3 show the resulting adsorption patterns and model fits for ammonium and phosphate, respectively, while Table 1 summarizes the kinetic parameters obtained from the model fitting. A thorough analysis of these findings is provided in the section that follows, emphasizing the variations in the materials' adsorption behaviors as well as the models' applicability in explaining the trends that were noticed. The adsorption of ammonium proceeded rapidly during the initial hours in all cases, and its rate decreased as equilibrium approached (Figure 2). The adsorption process was nearly finished in the first 24 h for both coarse-grained and fine-grained zeolite, and the measured equilibrium adsorption capacities (q\({}_{e,m}\)) were 181.87 mg/kg and 174.23 mg/kg for CG-Z and FG-Z, respectively. Moreover, the calculated adsorption capacity at equilibrium (q\({}_{e,c}\)) from the pseudo-second-order model closely matched the q\({}_{e,m}\) values, as they were 181.81 mg/kg and 178.57 mg/kg for CG-Z and FG-Z, respectively (Table 1). Furthermore, the pseudo-second-order model showed a better fit compared to the pseudo-first-order model for zeolite data (i.e., CG-Z and FG-Z), with high values for the correlation coefficient (R\({}^{2}\) = 0.99) and low values for both the normalized objective function (NOF  
Figure 2: Ammonium adsorption on substrate: (**a**) coarse-grained zeolite; (**b**) fine-grained zeolite; and (**c**) coarse-grained gravel. value of 0.03) and mean absolute error (MAE values of 4.66 for CG-Z and 2.87 for FG-Z) (Table 1). These results are in agreement with other previous studies [33; 36; 55; 56]. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Substrate**} & \multirow{2}{*}{
\begin{tabular}{c} **q\({}_{\text{e,m}}\)** \\ **mg/kg** \\ \end{tabular} } & \multicolumn{4}{c}{**Pseudo-First-Order Model**} & \multicolumn{4}{c}{**Pseudo-Second-Order Model**} \\ \cline{2-13}  & & **q\({}_{\text{e,c}}\)** & **k\({}_{\text{1}}\)** & **R\({}^{2}\)** & **NOF** & **MAE** & **q\({}_{\text{e,c}}\)** & **k\({}_{\text{2}}\)** & **R\({}^{2}\)** & **NOF** & **MAE** \\ \cline{2-13}  & & **mg/kg** & **1/h** & & & & **mg/kg** & **kg/(mg h)** & & & & \\ \hline Ammonium & & & & & & & & & & & & \\ \hline CG-Z & 181.87 & 168.57 & 0.083 & 0.94 & 0.14 & 18.51 & 181.81 & 0.0036 & 0.99 & 0.03 & 4.66 \\ FG-Z & 174.23 & 179.47 & 0.088 & 0.95 & 0.09 & 9.92 & 178.57 & 0.0034 & 0.99 & 0.03 & 2.87 \\ CG-G & 29.34 & 30.94 & 0.067 & 0.97 & 0.09 & 1.96 & 34.84 & 0.0039 & 0.87 & 0.13 & 2.26 \\ \hline Phosphate & & & & & & & & & & & \\ \hline CG-Z & 11.76 & 10.84 & 0.0163 & 0.98 & 0.10 & 0.66 & 13.38 & 0.0025 & 0.98 & 0.07 & 0.46 \\ FG-Z & 12.35 & 11.30 & 0.0162 & 0.92 & 0.24 & 1.71 & 12.24 & 0.0093 & 0.95 & 0.06 & 0.53 \\ CG-G & 6.44 & 5.56 & 0.0159 & 0.92 & 0.29 & 1.04 & 6.82 & 0.0123 & 0.98 & 0.07 & 0.26 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Kinetic parameters of ammonium and phosphate adsorption onto various substrates. Figure 3: Phosphate adsorption on substrate: (a) coarse-grained zeolite; (b) fine-grained zeolite; and (c) coarse-grained gravel. The two granulometries of the examined zeolite showed similar ammonium adsorption, indicating that a reduction in the grain size does not significantly affect the adsorption capacity. Ammonium adsorption on the zeolite occurs both on the external surface of the grains and on the internal surfaces of the pores and channels that the zeolite has. With a reduction in grain size, the external surface increases, but the internal pores and channels do not. Thus, for a small grain size, there is a larger external surface but a smaller internal surface compared to a large grain size [55; 57; 58].