## 3 Results and Discussion
### Characterization of Zr-EPRC
#### 3.3.2 Adsorption Kinetics  
* Adsorption kinetics at different initial concentrations  
Figure 15 illustrates the adsorption kinetics of phosphate via Zr-EPRC particles at different initial concentrations. Initially, the adsorption rate is rapid, gradually slowing down with time until reaching adsorption equilibrium. This behavior is attributed to the ample availability of adsorption sites on the adsorbent at the start of the process, resulting in fast adsorption rates. As time progresses, the adsorption sites become gradually depleted, leading to a slower adsorption rate until equilibrium is attained. Additionally, it is evident from the data in the figure that higher initial phosphorus concentrations in the water result in greater unit adsorption amounts in the Zr-EPRC particles. This can be attributed to the increased number of phosphate ions in the water at higher concentrations, facilitating more frequent interactions between the adsorbent and adsorbate. Furthermore, an elevated phosphorus concentration in the solution enhances the concentration gradient between the material and the solution, promoting the adsorption reaction in the direction of adsorption. 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 for each time period. The data were fitted using both quasi-primary and quasi-secondary kinetic models. The results are presented in Figure 16 and detailed in Table 8. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Temp**} & \multicolumn{3}{c}{**Langmuir**} & \multicolumn{3}{c}{**Freundlich**} \\ \cline{2-7}  & **K\({}_{\text{L}}\)** & **Q\({}_{\text{m}}\)** & **R\({}_{\text{L}}\)\({}^{2}\)** & **K\({}_{\text{F}}\)** & **1/n** & **R\({}_{\text{F}}\)\({}^{2}\)** \\ \hline
15 & 0.0082 & 11.833 & 0.993 & 0.661 & 0.495 & 0.974 \\
25 & 0.0088 & 12.550 & 0.993 & 0.487 & 0.523 & 0.976 \\
35 & 0.0112 & 13.462 & 0.996 & 0.425 & 0.533 & 0.983 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Adsorption isotherms fitted to Zr-EPRC particles. Figure 16: Adsorption kinetics fitting at different concentrations. (**a**) Zr-EPRC adsorption at a phosphorus concentration of 5 mg/g; (**b**) Zr-EPRC adsorption at a phosphorus concentration of 10 mg/g; (**c**) Zr-EPRC adsorption at a phosphorus concentration of 15 mg/g; (**d**) Zr-EPRC adsorption at a phosphorus concentration of 20 mg/g. Figure 15: Adsorption of phosphorus by Zr-EPRC at various concentrations. Figure 16 and Table 8 showcase the fitting results of both kinetic models. The correlation coefficients for both the quasi-primary and quasi-secondary kinetic equations are above 0.97, demonstrating good regressivity for both models. These models effectively describe the adsorption performance of phosphorus by Zr-EPRC particles. However, the correlation coefficients for the quasi-secondary kinetic model, represented as R\({}_{2}\)\({}^{2}\), are slightly higher than those for the quasi-primary kinetics, denoted as R\({}_{1}\)\({}^{2}\), indicating that the quasi-secondary adsorption model better represents this adsorption process. Consequently, the adsorption of phosphorus by Zr-EPRC particles is characterized as chemisorption. The experimental results align with this conclusion as the equilibrium adsorption capacity of Zr-EPRC particles increases with the rising initial concentrations of the phosphorus solution. Furthermore, the rate constant, k\({}_{2}\), decreases because, at higher concentrations, the constant number of adsorption sites leads to increased competition among the adsorbate molecules. Consequently, there is a decrease in the probability of individual molecules binding to the adsorption sites, resulting in a decrease in the equilibrium constant of the adsorption reaction, k\({}_{2}\). * Adsorption kinetics at different initial temperatures  
As depicted in Figure 17, the adsorption of phosphorus by Zr-EPRC particles exhibits an increasing trend with the rising temperature. This behavior is attributed to several factors.