# Adsorption of Arsenic and Heavy Metals from Solutions by Unmodified Iron-Ore Sludge
## 3 Results and Discussion
### Batch Adsorption Kinetics  
The adsorption kinetic experiments were conducted to assess the rate of metal adsorption onto the adsorbent. The adsorption capacity increased with contact time. Equilibrium was reached after 6 h in the single-metal experiments, and after 1h in the mixed-metal experiments (Figure 6).  
Figure 4: Effect of solution pH on the adsorption.  
Figure 5: Effect of doses of the adsorbent on the adsorption As and heavy metals from (**a**) single-metal experiments and (**b**) mixed-metal experiments.  
In this study, two kinetic models were applied to mathematically describe the intrinsic adsorption constants from both the single- and mixed-metal experiments. The non-linearized forms of the pseudo-first-order model [40] and pseudo-second-order model [41] are expressed in the following equations:  
\[q_{t}=q_{e}\Big{(}1-e^{-k_{1}t}\Big{)} \tag{4}\]  
\[q_{t}=\frac{q_{e}^{2}k_{2}t}{1+k_{2}q_{e}t} \tag{5}\]  
where \(k_{1}\) (min\({}^{-1}\)) and \(k_{2}\) (g\(\cdot\)mg\({}^{-1}\cdot\)min\({}^{-1}\)) are the rate constants of the pseudo-first- and pseudo-second-order models, respectively; \(q_{e}\) (mg/g) and \(q_{t}\) (mg/g) are the amounts of adsorbate uptake per mass of adsorbent at equilibrium and time t (min), respectively.  
The adsorption kinetic data from the single- and mixed-metal experiments are consistent with the pseudo-first- and pseudo-second-order models (Table 2). The relative kinetic parameters demonstrate that the coefficient (R\({}^{2}\)) values of the second-order kinetic model (0.881-1.000) are superior to those of the first-order kinetic model (0.596-0.969), with the exception of Cd. Therefore, the pseudo-second-order model is more suitable for explaining the kinetic behavior of heavy metals in the adsorbent of this study, indicating that the adsorption process might be controlled by chemisorptions processes [42; 43].  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Heavy Metals**} & \multicolumn{4}{c}{**Pseudo-First-Order Model**} & \multicolumn{4}{c}{**Pseudo-Second-Order Model**} \\ \cline{2-7}  & \(K_{1}\) (min\({}^{-1}\)) & \(q_{e}\) (mg/g) & \(R^{2}\) & \(K_{2}\) (g.mg\({}^{-1}\).min\({}^{-1}\)) & \(q_{e}\) (mg/g) & \(R^{2}\) \\ \hline \multicolumn{7}{c}{**Single-metal experiments**} \\ \hline Mn & 0.035 & 0.318 & 0.931 & 0.121 & 0.345 & 0.957 \\ \hline Zn & 0.066 & 0.406 & 0.897 & 0.653 & 0.427 & 0.941 \\ \hline Cd & 0.125 & 0.305 & 0.995 & 0.565 & 0.321 & 0.940 \\ \hline Pb & 0.177 & 0.737 & 0.902 & 0.451 & 0.761 & 0.947 \\ \hline As & 0.018 & 0.641 & 0.954 & 0.039 & 0.692 & 0.985 \\ \hline \multicolumn{7}{c}{**Mixed-metal experiments**} \\ \hline Mn & 0.013 & 0.202 & 0.969 & 0.073 & 0.220 & 0.991 \\ \hline Zn & 0.027 & 0.027 & 0.882 & 0.862 & 0.030 & 1.000 \\ \hline Cd & 0.028 & 0.110 & 0.956 & 0.512 & 0.120 & 0.778 \\ \hline Pb & 0.124 & 0.460 & 0.596 & 0.483 & 0.486 & 0.881 \\ \hline \end{tabular}
\end{table}
Table 2: Relative kinetic parameters (calculated by the non-linear method) for the adsorption of Mn, Zn, Cd, Pb, and As onto the adsorbent from single- and mixed-metal experiments.  
Figure 6: Effect of contact time on the adsorption of As and heavy metals from (**a**) single-metal experiments and (**b**) mixed-metal experiments.  
Based on the value of k\({}_{2}\), the adsorption rate of contaminant cations onto the adsorbent occurred in the following order: Zn > Cd > Pb > Mn > As for both single- and mixed-metal experiments. This result is in agreement with the order reported by [PERSON] et al. [44] for zeolite (Zn > Cd > Pb).