## 3 Results and Discussion
### Adsorption Kinetics  
The kinetics for the adsorption of Pb(II) onto G-26 and MTS9570 resins were investigated using Lagergren pseudo-first-order and pseudo-second-order models, represented by Equations (6) and (7), respectively [48; 49].  
\[ln\;(q_{e}\;-q_{t}\;)\;=ln\;(q_{e}\;)\;-\frac{k_{1}\;t}{2.303} \tag{6}\]  
where \(q_{t}\;\) and \(q_{e}\) are the amounts of metal ions adsorbed (mg/g) at equilibrium and at contact time \(t\) (min), respectively; \(k_{1}\;\) (min\({}^{-1}\)) is the first-order rate constant. The plots of ln (\(q_{e}\;-q_{t}\;\)) versus t are presented in Figure 11, and the rate constants ( \(k_{1}\;\)) are listed in Table 4.  
\[\frac{t}{q_{e}}=\frac{t}{q_{e}}+\frac{1}{k_{2}\;q_{e}^{2}} \tag{7}\]  
where \(k_{2}\;\)(g/mg/min) is the rate constant of pseudo-second-order adsorption. The plots of \(\frac{t}{q_{t}}\;\)versus \(t\) are shown in Figure 12, and the rate constants ( \(k_{2}\;\)) are presented in Table 4. Pseudo-first-order and pseudo-second-order parameters are listed in Table 4. The results clearly show that \(R^{2}\) values of the second-order kinetic model for both resins are closer to 1 than the results obtained from the first-order kinetic model. Therefore, the adsorption behavior of Pb(II) onto the resins fits the second-order kinetics. G-26 and MTS9570 resins have about the same order of magnitude for the adsorption rates even if they are characterized by different functional groups.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **G-26** & **MTS9570** \\ \hline Equations & & \\ Pseudo-first-order & & \\ \(q_{e}\), exp (mg/g) & 41.80 & 42.00 \\ \(q_{e}\), cal (mg/g) & 3.49 & 2.513 \\ k1 (m\({}^{-1}\)) & \(-\)0.00017 & \(-\)0.00020 \\ \(R^{2}\) & 0.7243 & 0.9090 \\ Pseudo-second-order & & \\ \(q_{e}\), cal (mg/g) & 42.50 & 42.10 \\ k2 (g/mg min) & 0.00896 & 0.0362 \\ \(R^{2}\) & 0.9994 & 0.9999 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Kinetic parameters for the adsorption of Pb(II) ions onto G-26 and MTS9570.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Sorption Capacity** & & \\  & **for Cu (II) (mg/g)** & **Conditions** & **References** \\ \hline SBA-15 & 41.50 & pH = 2.5–4, 30 \({}^{\circ}\)C & [29] \\ MWCNT & 17.54 & pH = 6.5, 20 \({}^{\circ}\)C & [31] \\ APTS- SBA-15-AB & 43.50 & pH = 6.0, 60 \({}^{\circ}\)C & [38] \\ MCCM & 45.50 & pH = 6.0, 30 \({}^{\circ}\)C & [39] \\
1,8-DAN/XAD-4 & 29.01 & pH = 6.0–7.0, 20 \({}^{\circ}\)C & [40] \\ Copolymer 2- & & \\ hydroxyethyl methacrylate & 31.50 & pH = 6.0–7.0, 20 \({}^{\circ}\)C & [41] \\ Crosslinked chitosan with & & & \\ epichlorohydrin & & & \\ Purolite C100 & 9.64 & pH = NA, 25 \({}^{\circ}\)C & [43] \\ Amberlite XAD-2 & & & \\ functionalized with Tiron & 12.60 & pH = 4.0–5.5, 25 \({}^{\circ}\)C & [44] \\ Purolite A830 & 30.61 & pH = 7.0–9.0, 50 \({}^{\circ}\)C & [45] \\ Bentonite & 28.00 & pH = 6.0–9.0, 25 \({}^{\circ}\)C & [46] \\ Zeolite & 24.40 & pH = 9.0, 20 \({}^{\circ}\)C & [47] \\ G-26 & 45.45 & pH = 3.5, 20 \({}^{\circ}\)C & This work \\ MTS9570 & 38.46 & pH = 3.5, 20 \({}^{\circ}\)C & This work \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of maximum adsorption capacity of G-26 and MTS 9570 resins with some other adsorbents for adsorption of Pb(II).