# Adsorption of Lead and Nickel on to Expanded Graphite Decorated with Manganese Oxide Nanoparticles
## 3 Results and Discussion
### Adsorption Kinetics  
Figure 5 elucidates the fitting of the pseudo-second order model with the experimental kinetics data of Pb\({}^{2+}\) and Ni\({}^{2+}\) adsorbed by the prepared MONPs-EG in single and binary metal systems. The adsorption of both metal ions occurred through two stages, a rapid stage in which most of the adsorption took place within 30 min of contact followed by a slow stage that lasted until the adsorption equilibrium had been reached. The adsorption processes gradually slowed down due to limitation in available active sites of adsorbent, which was supported by the decrease in metal removal efficiency at higher initial concentration (Figure 4b).  
Pseudo-first order and pseudo-second order kinetic model fitting parameters are summarized in Table 4. The results show that the adsorption capacities (q\({}_{\text{e, cal}}\)) of MONPs-EG for metals in all investigated systems, calculated by the pseudo-first order model, are quite different from those obtained experimentally (q\({}_{\text{e, exp}}\)), while the values achieved from the pseudo-second order model are very close to the experimental data. In addition, the correlation coefficient values obtained from the pseudo-second order model are quite good (R\({}^{2}\) > 0.99) and much higher than those from the pseudo-first order model. These observations suggest that the pseudo-second order kinetic model can be used to better describe the kinetic mechanism of Pb\({}^{2+}\) and Ni\({}^{2+}\) adsorption on to the prepared  
Figure 4: (a) Adsorption isotherm of prepared MONPs-EG for metal ions; (b) heavy metals removal efficiencies at different initial concentrations in single and binary metals solutions.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Metal ion** **(System)**} & \multirow{2}{*}{
\begin{tabular}{c} **q\({}_{\text{max, exp.}}\)** \\ **(mmol/g)** \\ \end{tabular} } & \multicolumn{3}{c}{**Langmuir Model**} & \multicolumn{3}{c}{**Freundlich Model**} \\ \cline{3-8}  & & **q\({}_{\text{max}}\)** & **K\({}_{\text{L}}\)** & **R\({}^{2}\)** & **K\({}_{\text{F}}\) (mmol/g)** & **1/n** & **R\({}^{2}\)** \\ \hline Pb & 0.276 & 0.278 & 189.1 & 1 & 0.37 & 0.28 & 0.79 \\ \hline Pb (Pb + Ni) & 0.207 & 0.209 & 174.2 & 1 & 0.33 & 0.32 & 0.81 \\ \hline Pb (Pb + HA) & 0.297 & 0.298 & 217.0 & 1 & 0.40 & 0.27 & 0.61 \\ \hline Pb (Pb + Ni + HA) & 0.219 & 0.220 & 186.8 & 1 & 0.30 & 0.26 & 0.67 \\ \hline Ni & 0.110 & 0.113 & 26.5 & 1 & 0.14 & 0.36 & 0.91 \\ \hline Ni (Pb + Ni) & 0.020 & 0.021 & 21.0 & 0.98 & 0.02 & 0.30 & 0.77 \\ \hline Ni (Ni + HA) & 0.172 & 0.174 & 36.3 & 1 & 0.25 & 0.40 & 0.87 \\ \hline Ni (Pb + Ni + HA) & 0.026 & 0.027 & 22.3 & 0.99 & 0.03 & 0.24 & 0.97 \\ \hline \end{tabular}
\end{table}
Table 3: Adsorption isotherm parameters of prepared MONPs-EG in different metals solutions at 298 K.  
MONPs-EG. The pseudo-second order kinetic rate constant (k\({}_{2}\)) values calculated for Pb\({}^{2+}\) are much higher than those for Ni\({}^{2+}\) in all systems (Table 4), implying that the adsorption of Pb\({}^{2+}\) by MONPs-EG can occur more quickly and easily than can that of Ni\({}^{2+}\). These observations again confirm that MONPs-EG is capable of removing Pb\({}^{2+}\) better than Ni\({}^{2+}\) in aqueous solution.