## 3 Results and Discussion
### Kinetic Tests  
Table 5 shows the parameters of three kinetic models chosen for this study. Comparison of the values of correlation coefficients (\(R^{2}\)) values of the pseudo-first order, pseudo-second order, and intra-particle diffusion models shows that the ammonium sorption data were best described by the pseudo-second order kinetic model.  
The results of the studies by [PERSON] et al. [60] have shown that the kinetics of ammonium sorption follows the pseudo-second order kinetic model (Figures 5-7). [PERSON] and [PERSON] [49] suggested that the mechanism of sorption is via intra-particle diffusion when the plot of \(q_{t}\) versus \(t^{1/2}\) is linear, and if the sorption process is controlled by more than one mechanism, the plot of \(\mathrm{q_{t}}\) versus \(t^{1/2}\) is multi-linear [61]. Our study shows that certainly more than one process is responsible for the sorption of ammonium onto agricultural soils. Based on the coefficients of determination, \(R^{2}=0.91\), \(R^{2}=0.87\), \(R^{2}=0.94\) for silt loam, loam, and sand, respectively, it can be concluded that this model best describes the sorption of ammonium onto agricultural soils. Taking into consideration the high values of \(\mathrm{R^{2}}\) for the pseudo-first and intra-particle diffusion models, we can assume that the sorption of ammonium can be additionally controlled by physical processes and surface and pore-volume diffusion, respectively [47; 49].  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Soil**} & \multicolumn{6}{c}{**Contact Time [h]**} \\ \cline{2-7}  & **1** & **4** & **8** & **16** & **24** & **48** \\ \hline \multicolumn{7}{c}{Reduction of ammonium [\%]} \\ \hline Silt loam & 3.1 & 8.1 & 9.1 & 10.4 & 18.7 & 19.4 \\ Loam & 5.0 & 6.9 & 10.5 & 11.3 & 18.4 & 18.5 \\ Sand & 3.8 & 4.2 & 5.5 & 5.8 & 11.2 & 14.4 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Effect of contact time on the reduction of ammonium on agricultural soils.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{3}{c}{**Soil**} \\ \cline{2-5}  & **Silt Loam** & **Loam** & **Sand** \\ \hline \multicolumn{5}{c}{Pseudo-first order kinetic model} \\ \hline \(q_{e}\) & mg/g & 0.1011 & 0.0960 & 0.0752 \\ \(k_{1}\) & 1/min & 0.0016 & 0.0024 & 0.0016 \\ \(R^{2}\) & - & 0.89 & 0.80 & 0.89 \\ \hline \multicolumn{5}{c}{Pseudo-second order kinetic model} \\ \hline \(q_{e}\) & mg/g & 0.1189 & 0.1110 & 0.0880 \\ \(k_{2}\) & mg/g min & 0.0140 & 0.0167 & 0.0306 \\ \(v_{0}\) & mg/g min & 0.0002 & 0.0002 & 0.0002 \\ \(R^{2}\) & - & 0.91 & 0.87 & 0.94 \\ \hline \multicolumn{5}{c}{Intra-particle diffusion} \\ \hline \(k_{int}\) & mg/g min\({}^{1/2}\) & 0.0018 & 0.0016 & 0.0013 \\ \(C_{i}\) & mg/g & 0.0080 & 0.0161 & 0.0029 \\ \(R^{2}\) & - & 0.86 & 0.77 & 0.89 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Kinetic parameters for ammonium adsorption onto natural soils.  
Figure 5: Kinetics of ammonium removal by soils according to the pseudo-first order equation and standard deviation error bars for the experimental data.  
Figure 6: Kinetics of ammonium removal by soils according to the pseudo-second order equation and standard deviation error bars for the experimental data.  
Figure 7: Kinetics of ammonium removal by soils according to the intra-particle diffusion model and standard deviation error bars for the experimental data.