## 3 Results and Discussion
### Isotherm  
Figure 6 shows Pb(II) sorption by non- and acid-modified clinoptilolite-rich tuffs. It can be observed that the isotherms for the HCLI-0.1 M and HCLI-0.2 M were similar to those for Nat-CLI; whereas the isotherms for the Pb(II) sorption for HCLI-0.5 M and HCLI-1.0 M presented a different behavior. These differences can be attributed to the dealumination of the clinoptilolite-rich tuff after the treatment with 0.5 and 1.0 M H\({}_{2}\)SO\({}_{4}\) solutions. The amount of aluminum in HCLI-0.5 M and HCLI-1.0 M were 1.7 and 2 times lower than Nat-CLI, respectively. In these cases, it is probably that the Ca\({}^{2+}\) and K\({}^{+}\) from the zeolitic materials had played a role on the Pb(II) sorption. The experimental equilibrium data for Pb(II) sorption by non- and acid-modified clinoptilolite-rich tuffs were fitted to the Langmuir and Freundlich models (Equations (4) and (5)) with the purpose of describing the sorption mechanism [6]. The values of the isotherm constants, including the determination coefficients (\(R^{2}\)), are summarized in Table 3. It was found that the Langmuir model better described Pb(II) uptake by Nat-CLI, HCLI-0.1 M, and HCLI-0.2 M (\(R^{2}\geq 0.99\)). Comparison of the Langmuir constants (\(q_{m}\)) between non- and acid-modified clinoptilolite-rich tuffs, shows that Pb(II) removal decreases as Si/Al ratio increases (\(q_{m}=48.54\), 37.037, and 14.992 mg g\({}^{-1}\) for Si/Al = 4.37, 5.30, and 7.91, respectively). This result can be explained by the decrease in exchangeable ions from the zeolite network with the increase in sulfuric acid concentration due to the dealuminization of the zeolitic material or the greater competition of Pb(II) with the H\({}^{+}\) from the ion exchange sites in the zeolite network. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & & & & & & \\ \cline{3-8}
**Sample** & \multirow{2}{*}{**Si/Al**} & \multicolumn{4}{c}{**Kinetic Models**} \\ \cline{3-8}  & & \multicolumn{3}{c}{**Pseudo-Second Order**} & \multicolumn{4}{c}{**Pseudo-First Order**} \\ \cline{3-8}  & & \(q_{e}\)**(exp)** & \(q_{e}\)**(cal)** & \(k_{2}\times 10^{2}\) & \(R^{2}\) & \(q_{e}\)**(cal)** & \(k_{1}\times 10^{2}\) & \(R^{2}\) \\ \hline Nat-CLI & 4.37 & 10.14 & 10.21 & 2.39 & 1.0 & 0.53 & 0.27 & 0.60 \\ HCLI-0.1 M & 5.31 & 9.77 & 9.90 & 0.63 & 1.0 & 1.76 & 0.24 & 0.69 \\ HCLI-0.2 M & 7.91 & 9.64 & 9.82 & 0.40 & 0.99 & 2.53 & 0.23 & 0.76 \\ HCLI-0.5 M & 9.04 & 5.98 & 6.37 & 0.08 & 0.96 & 5.00 & 0.17 & 0.99 \\ HCLI-1.0 M & 9.52 & 4.98 & 5.25 & 0.11 & 0.97 & 3.97 & 0.21 & 0.99 \\ \hline \hline \end{tabular} Note: (exp) experimental data, (cal) calculated data; \(q_{e}\)(exp) and \(q_{e}\)(cal) in mg g\({}^{-1}\); \(k_{2}\) in g mg\({}^{-1}\)min\({}^{-1}\); \(k_{1}\) in min\({}^{-1}\).  
\end{table} 
Table 2: Kinetic parameters for Pb(II) sorption by non- and acid-modified clinoptilolite-rich tuffs obtained by applying the pseudo-second order and pseudo-first order models. For sorbents with Si/Al ratios of 9.05 and 9.52, the Freundlich isotherm adjusted better to the Pb(II) uptake (\(0.99\geq R^{2}\geq 0.98\)) than the Langmuir isotherm. This suggests that sorption did not occur on a uniform site; instead a multilayer sorption occurred in this system. Moreover, \(n\) values were between 1 and 10, indicating that the physical sorption of Pb(II) ions by acid-modified clinoptiolite-rich tuffs with Si/Al ratios of 9.04 and 9.5 is favorable [14]. It is important to mention that a unique mechanism is not involved on the sorption processes. For instance, the speciation of the heavy metal in solution, the surface charge of the sorbent as well as the nature and structure of the zeolitic materials could be some of the factors which are involved on the ion exchange or adsorption mechanisms.