## 3 Results and Discussion
### Characterization of Zr-EPRC
#### 3.3.2 Adsorption Kinetics
First, higher temperatures result in enhanced molecular thermal motion for both the adsorbent and adsorbate, leading to intensified interaction forces. This, in turn, facilitates the reaction between active sites on the adsorbent and the adsorbate. Additionally, an increased temperature promotes the diffusion of adsorbate molecules, ultimately increasing the adsorption capacity of the adsorbent. Figure 17: Adsorption of phosphorus by Zr-EPRC at various temperatures. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Initial** & **q\({}_{e,\,\mathrm{exp}}\)** & **Pseudo-First-Order** & **Kinetics** & **Pseudo-Second-Order** & **Kinetics** \\
**(mg/L)** & **q\({}_{e}\) (mg/g)** & **k\({}_{1}\)** & **R\({}_{1}\)\({}^{2}\)** & **q\({}_{e}\) (mg/g)** & **k\({}_{2}\)** & **R\({}_{2}\)\({}^{2}\)** \\ \hline
5 & 0.392 & 0.383 & 0.112 & 0.981 & 0.446 & 0.298 & 0.990 \\
10 & 0.675 & 0.660 & 0.098 & 0.987 & 0.787 & 0.138 & 0.991 \\
15 & 0.991 & 0.956 & 0.092 & 0.970 & 1.151 & 0.090 & 0.990 \\
2 For each time period, the adsorption of phosphorus by Zr-EPRC particles was plotted with time as the X-axis, and the adsorption capacity was plotted as the Y-axis. Subsequently, the data were fitted using both the quasi-primary and quasi-secondary kinetic models. The fitting results are detailed in Figure 18 and Table 9.  
From the fitting analyses, it is evident that the correlation coefficients of the quasi-secondary kinetic model for all three different temperature conditions (denoted as \(\text{R}_{2}\)\({}^{2}\)) were higher than those of the quasi-primary kinetic model. Therefore, the quasi-secondary kinetic model more accurately describes the kinetic process of phosphorus adsorption by Zr-EPRC particles compared to the quasi-primary kinetic model, with the correlation  
Figure 18: Adsorption kinetics fitting at different temperatures. (**a**) Zr-EPRC adsorption at phosphorus concentration at 15 \({}^{\circ}\)C; (**b**) Zr-EPRC adsorption at phosphorus concentration at 25 \({}^{\circ}\)C; (**c**) Zr-EPRC adsorption at phosphorus concentration at 35 \({}^{\circ}\)C.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Initial** & **Initial** & \multicolumn{2}{c}{**Pseudo-First-Order Kinetics**} & \multicolumn{2}{c}{**Pseudo-Second-Order Kinetics**} \\ \cline{3-8}
**Temperature** & **Concentration** & **q\textless{} (mg/g)** & **k\textless{} (\textless{}  
coefficients exceeding 0.99. Additionally, when comparing the equilibrium adsorption capacity at the three temperatures, it is apparent that the equilibrium adsorption capacity increases with the rising temperature. This observation aligns with the experimental phenomenon and indicates that elevated temperatures contribute to higher adsorption capacities of the particles. Furthermore, the rate constant K\({}_{2}\) remains relatively stable within the tested temperature range, suggesting that the phosphorus adsorption rate of the material is insensitive to changes in temperature. This implies that increasing the temperature has no significant impact on the adsorption rate of the material. Consequently, in practical applications for treating eutrophic water bodies, the material can maintain a relatively stable phosphorus removal effect, and the influence of seasonal temperature variations can be disregarded.