## 2 Materials and Methods
### Kinetic Tests  
The kinetics of adsorption is one of the important characteristics defining the efficiency of adsorption [43]. The study of sorption kinetics provides valuable insights into the reaction pathways and into the mechanism of sorption reactions [44; 45; 46]. Before determining the adsorption isotherms, the kinetics of adsorption of ammonium onto natural soils had been studied using three kinetic models (Table 2). Constants of sorption were determined using the pseudo-first order equation of [PERSON] [47] based on solid capacity, the pseudo-second order equation based on solid phase sorption, and the intra-particle diffusion model, respectively.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Adsorbent**} & \multicolumn{2}{c}{**Bulk**} & \multirow{2}{*}{**Porosity**} & \multirow{2}{*}{**pH**} & **Electrical** & **Organic** & **Hydraulic** \\  & & & & **Conductivity** & **Matter** & **Conductivity** \\ \cline{2-7}  & **[Mg/m\({}^{3}\)]** & **[-]** & **[-]** & **[\(\mu\)S/cm]** & **[\%]** & **[m/s]** \\ \hline Silt loam & 1.63 & 0.40 & 7.4 & 363 & 3.1 & \(1.9\times 10^{-8}\) \\ Loam & 1.60 & 0.40 & 7.5 & 160 & 2.3 & \(3.6\times 10^{-6}\) \\ Sand & 1.70 & 0.34 & 7.2 & 155 & 0.1 & \(3.0\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physical and chemical properties of the tested soils.  
Figure 3: Classification of soil texture of the studied soils.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Kinetic Model**} & \multicolumn{1}{c}{**Equation**} & \multicolumn{1}{c}{**Plot**} & **Reference** \\ \hline Pseudo-first order & \(\log\left(q_{e}-q_{t}\right)=\log\left(q_{e}\right)-\frac{k_{t}t}{2\Delta 63}\) & \(\log\left(q_{e}-q_{t}\right)\) vs. \(t\) & [47] \\ Pseudo-second order & \(\frac{t}{q_{t}}=\frac{1}{k_{t}\cdot q^{2}}+\frac{t}{q_{t}}\) & \(\frac{t}{q_{t}}\) vs. \(t\) & [47; 48] \\  & \(v_{0}=k_{t}\cdot qe^{2}\) & \(q_{t}=k_{t}\cdot t^{1/2}+C_{t}\) & \(q_{t}\) vs. \(t\) & [49] \\ \hline \hline \end{tabular}
\end{table}
Table 2: Kinetic models of ammonium sorption into agricultural soils.  
Prior to the laboratory analyses, the soil samples were prepared by drying at room temperature and sieved through a \(\Phi\)1 mm sieve. For kinetic studies, 5 g of each soil sample were mixed with 50 mL of the ammonium nitrate solution (52 mg NH\({}_{4}\)\({}^{+}\)/L, pH = 6.62, electrical conductivity (EC) = 1.706 mS/cm), maintaining a constant solid-to-liquid ratio of 1:10. Similarly, blank and control samples were prepared using the treatment solution without the soil sample and a soil sample with distilled water, respectively. The time periods of shaking were chosen according to US EPA [50] and were carried out for 1, 4, 8, 16, 24 and 48 h on a rotary shaker GFL 3040 with the speed of 14 min\({}^{-1}\). After the time of a desired period of shaking, the solutions were filtered through paper filters and prepared for chemical analysis. Samples were analysed for their ammonium and nitrate contents by Nessler [51] and cadmium reduction method [52], respectively, using a spectrophotometer UV-VIS DR 6000 ([PERSON] type, Dusseldorf, Germany). Electrical conductivity and pH were measured using a 18.52.01 multimeter (Eijkelkamp type, Giesbeek, the Netherlands). All samples were analysed in duplicate.  
The percent contributions of ammonium adsorbed (%R) and ammonium adsorption capacity (\(q\)) were calculated using the following expressions:  
\[\%R=\frac{C_{0}-C_{\epsilon}}{C_{0}}\cdot 100\% \tag{1}\]  
and:  
\[q=\frac{(C_{0}-C_{\epsilon})\cdot V}{m} \tag{2}\]  
where: \(C_{0}\)--initial concentration of ammonium in the solution, [mg/L]; \(C_{\epsilon}\)--final ammonium concentration in the solution, [mg/L]; \(V\)--volume of the solution, [mL]; \(m\)--amount of sorbent on the dry basis, [g].