## 3 Results and Discussion
### Adsorption of Ammonium Nitrogen on Biochar
#### 3.2.5 Adsorption Isotherm  
In order to understand how NH4+-N is adsorbed onto the biochar adsorbent, as well as to define the equilibrium data, the adsorbed amounts and residual NH4+-N concentration in the solution after adsorption were fitted using both Langmuir and Freundlich isotherms. The Langmuir model (Equation (5)) indicates monolayer adsorption on a homogenous surface, while the Freundlich isotherm (Equation (6)) elucidates nonideal adsorption on heterogeneous surfaces and multilayer adsorption [36; 37]:  
\[Q_{e}=\frac{Q_{m}k_{L}C_{e}}{1+k_{L}C_{e}} \tag{5}\]  
\[Q_{e}=k_{F}C_{e}\frac{1}{} \tag{6}\]  
where \(Q_{e}\) is the amount of NH4+-N absorbed (mg/g) and \(C_{e}\) is the equilibrium concentration (mg/L) of NH4+-N in aqueous solution after adsorption. \(k_{L}\) (L/mg) and \(Q_{m}\) (mg/g) are the Langmuir \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{\(T\) (\({}^{\circ}\)C)} & \multirow{2}{*}{\(Q_{e}\) (mg/g)} & \multicolumn{3}{c}{**Pseudo-First-Order Kinetics**} & \multicolumn{3}{c}{**Pseudo-Second-Order Kinetics**} \\ \cline{3-8}  & & & \(k_{1}\) (1/min) & \(Q_{e,\mathrm{cal}}\) (mg/g) & \(R^{2}\) & \(\frac{k_{2}}{\text{(g/(mg\cdot min))}}\) & \(Q_{e,\mathrm{cal}}\) (mg/g) & \(R^{2}\) \\ \hline
25 & 12.01 & 0.0232 & 11.44 & 0.9688 & 0.0026 & 12.86 & 0.9942 \\
35 & 13.34 & 0.0338 & 12.54 & 0.9543 & 0.0040 & 13.72 & 0.9875 \\
45 & 14.56 & 0.0580 & 14.01 & 0.9876 & 0.0086 & 14.72 & 0.9985 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of pseudo-first-order and pseudo-second-order kinetics, as well as the experimental and calculated \(Q_{e}\) at different temperatures. constant and the monolayer maximum adsorption capacity of NH\({}_{4}\)+-N onto biochar, respectively. The Freundlich constants \(k_{F}\) and \(n\) are the multilayer adsorption capacity (mg/g) and the adsorption intensity, respectively. The plots of the adsorbed NH\({}_{4}\)+-N amounts on biochar versus the residual NH\({}_{4}\)+-N concentration in the solution at different temperatures are given in Figure 3b, as well as the fitting curves using the two isotherm models. The fitting parameters of the biochar adsorption equilibrium data using the two models are shown in Table 2. As shown in Figure 3b, the adsorption process was represented by the Freundlich model very well, and the correlation coefficient (\(R^{2}\)) values were all higher than 0.99 (Table 2). The values of 1/\(n\) in the Freundlich model were lower than 0.1, suggesting that the adsorption process is favorable [35; 38]. The value of 1/\(n\) can be further divided into five levels, and when the value is between 0.1 and 0.01, the adsorption is categorized as a strongly favorable level, indicating the good adsorption performance of NH\({}_{4}\)+-N on biochar [39]. Thermodynamic parameters, including Gibbs free energy \(\Delta G^{0}\) (kJ/mol), entropy \(\Delta S^{0}\) (J/(K-mol)), and standard enthalpy \(\Delta H^{0}\) (kJ/mol), can be used to estimate the temperature effect on NH\({}_{4}\)+-N adsorption onto the biochar and give an idea about the adsorption behavior and mechanism. The thermodynamic parameters can be obtained from the Freundlich model using the following equations [40]:  
\[\Delta G=-RTlnk_{d} \tag{7}\]  
\[lnk_{d}=-\frac{\Delta H^{0}}{RT}+\frac{\Delta S^{0}}{R} \tag{8}\]  
\[k_{d}=k_{F}^{n} \tag{9}\]  
where \(R\) is the gas constant, the value of which is 8.314 J/(K-mol); \(T\) (K) is the absolute temperature; and \(n\) and \(k_{F}\) (umol/g) are Freundlich constants. The slope and intercept of the plots of \(\ln k_{d}\) versus 1/\(T\) are used to calculate the values of \(\Delta H^{0}\) and \(\Delta S^{0}\). Table 2 also presents the thermodynamic parameters calculated from Equations (7)-(9). The negative values of \(\Delta G^{0}\) demonstrated the spontaneous nature and the feasibility of the adsorption of NH\({}_{4}\)+-N on KOH-activated biochar. In addition, the \(\Delta G^{0}\) values became more negative with increasing adsorption temperature, confirming that adsorption is more favorable at higher temperature [35; 41].