## 3 Results and Discussion
### Kinetic Study of WPET-SiAMPy Chelating Adsorbent Nanofibres  
The adsorption kinetics focused on the adsorption rate of the adsorbate upon the adsorbent. The experiments of Cu\({}^{2+}\) binding kinetics using the WPET-SiAMPy chelating adsorbent was conducted to investigate the adsorption mechanism of Cu\({}^{2+}\) in aqueous solution. The formation of complexes between Cu\({}^{2+}\) and WPET-SiAMPy chelating adsorbent nanofibres was studied to understand the Cu\({}^{2+}\) adsorption dynamics, assuming a homogenous system for WPET-SiAMPy chelating adsorbent nanofibres. The kinetic of the Cu\({}^{2+}\) uptake was illustrated by the effect of contact time on Cu\({}^{2+}\) ions' adsorption onto WPET-SiAMPy nanofibres, which was previously performed, and the results are shown in Figure 4.  
4.1 Relative Rates and Stoichiometry of Cu\({}^{2+}\) Adsorption Based on the WPET-SiAMPy Nanofibres  
The general aim of this kinetic study was to determine the form of the reaction rate equations. The reaction rate equations in this study were determined using the differential method. In adsorption kinetics, it is important to relate the reaction rates for the adsorption of the reactant, Cu\({}^{2+}\), and the formation of the complex compounds Cu-WPET-SiAMPynanofibres. This was performed by varying the Cu\({}^{2+}\) concentration or the average rate of reaction against the contact time as seen in Figure 11. The average rate of the reaction is the change in the concentration per unit time expressed as  
\[\text{Rate of reaction}=\frac{\Delta\Big{[}\text{Cu}^{2+}\text{ }concentration\Big{]}}{\Delta time}\]  
with the consideration that the Cu\({}^{2+}\) ions in the aqueous solution are adsorbed by WPET-SiAMPy nanofibres. These reactions occur according to the following Equations:  
\[\text{Cu}+\text{WPET-SiAMPy}\rightarrow\text{Cu-WPET-SiAMPy}\]  
Figure 12 demonstrated the Cu\({}^{2+}\) uptake by the WPET-SiAMPy nanofibres. During adsorption, a chemical reaction occurred. The quantities of the Cu\({}^{2+}\) ions taken up from aqueous solution decreased with an increase in time, forming compound complexes. The Cu\({}^{2+}\) ion concentration after the adsorption experiment with WPET-SiAMPy nanofibres showed three reactions. The average rate of reactions for the equilibria-specified time intervals are tabulated below:  
\[\text{Rate of reaction}=\frac{\Delta[Cu-WPET-SiAMPy]}{\Delta t}\]  
The rate expression relating all these rates can be determined by dividing each rate expression by the stoichiometric coefficient of the Cu\({}^{2+}\) ions in the balanced chemical equation, which is assumed to be 1 in these balanced equations. As seen in Table 3, the rate of reaction decreases as the concentration of Cu\({}^{2+}\) ions in solution decreases. This illustrated that the rate of reaction is related to the concentration of Cu\({}^{2+}\) ions. This can also be qualitatively deduced from the fact that the graphing of the average reaction rate against time gave a curved line, as can be seen in Figure 13.  
\begin{table}
\begin{tabular}{c c} \hline \hline \(\Delta\)**Time (min)** & **Rate of Reaction (mmol/L\_min)** \\ \hline
0–1 & 1.4887 \\
1–10 & 0.0035 \\
20–60 & 0.0013 \\
90–120 & 0.0024 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Average rate of reactions between Cu\({}^{2+}\) and WPET-SiAMPy nanofibres.  
Figure 12: Cu\({}^{2+}\) metal uptake against contact time using WPET-SiAMPy nanofibres.  
Figure 13 illustrates the average reaction rate against time, where a measure of the rate of the reaction at any point in time is found by measuring the slope of the graph through tangent. As seen in Figure 5, the initial adsorption was steep for WPET-SiAMPy nanofibres, as supported by the steep initial metal uptake in Figure 12, which means that the rate of reaction was fast. Hence, the determination of the initial rate of reaction is important in this study, as the slope at the beginning of the reaction is used.