# Low-Cost Goethite Nanorods for As (III) and Se (VI) Removal from Water
## 3 Results and Discussion
### Adsorption Experiments of As(III) and Se(VI)
#### 3.2.2 Adsorption Kinetics  
Figure 5 depicts the adsorption kinetic data and adsorption kinetic isotherms. In view of the above discussion pertaining to adsorption batch and isotherms, the adsorption process was tailored well with Langmuir adsorption isotherm. Besides, the \(Q_{max}\) was calculated for As(III) and Se(VI) to be 8.253 and 4.75 mg/g, respectively. To prove these findings experimentally, kinetic studies at extremely high As(III) and Se(VI) test concentrations (\(\sim\)8.3 mg/L) with respect to contact time were conducted. The results of adsorption kinetic studies are plotted in Figure 5a,d. The results implied a rapid uptake (only 1 h) in spite of high dilutions, which is an adequate time to remove As(III) and Se(VI) from the water below WHO standards stipulated for drinking water. Besides, it can be demonstrated that most of the adsorption process took place in the first 1 h in which a plateau was reached with high removal percentage. Specifically, within 3 h contact time, the removal efficiencies reached \(\sim\)98% and -80% for As(III) and Se(VI), respectively. However, within 24 h contact time, the removal efficiencies were recorded at \(\sim\)99.4% and \(\sim\)84.5% for As(III) and Se(VI), respectively. These results indicate that As(III) ions were completely removed below the WHO standards for drinking water at 8300 ug/L initial dilution. However, \(\sim\)85% of Se(VI) ions were only adsorbed. Recalling the \(Q_{max}\) of \(\alpha\)-FeOOH adsorbent estimated by Langmuir isotherm of As(III) (\(Q_{max}\) = 8.25 mg/g) and Se(VI) (\(Q_{max}\) = 4.75 mg/g); this kinetic study at high concentrations proves experimentally the values of \(Q_{max}\) estimated by Langmuir isotherm. The experimental kinetic data observed from the kinetic study of high arsenic concentration were fitted into pseudo-first-order and pseudo-second-order isotherms. Initially, Pseudo-first-order kinetic isotherm is displayed in Figure 5b,e for As(III) and Se(VI), respectively. The linear form was represented by Equation (7):  
\[\log(Q_{e}-Q_{t})=\log(Q_{e})-K_{1}d_{t} \tag{7}\]  
where \(Q_{t}\) is the adsorbed oxyanions in mg/g at time \(t\) while \(K_{1}\) is the equilibrium rate constant of pseudo-first-order adsorption. Basically, the linearized graphs of \(\log(q_{e}-q_{t})\) vs. time (\(t\)) gives the rate \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Langmuir Adsorption Isotherm** & \multicolumn{4}{c}{**Freundlich Adsorption Isotherm**} \\ \hline
**Parameter** & **As(III)** & **Se(VI)** & **Parameter** & **As(III)** & **Se(VI)** \\ \hline \(R^{2}\) & 0.992 & 0.989 & \(R^{2}\) & 0.97 & 0.946 \\ \(Q_{max}\) (mg/g) & 8.251 & 4.753 & \(K_{f}\) & 12.52 & 5.19 \\ \(R_{L}\) & 0.126 & 0.14 & \(n\) & 0.537 & 1.021 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A representation of [PERSON] and Freundlich adsorption isotherms data of the \(\alpha\)-FeOOH adsorbent for the uptake of As(III) and Se(VI) from water solutions. constants. Obviously, the results obtained from the figures indicate that the adsorption mechanism does not fit with this model. Figure 5c,f represents Pseudo-second-order plots of As(III) and Se(VI), respectively. In general, it describes the physiochemical interaction and migration of adsorbate oxyanions to the adsorbent sites. In other words, chemical bonding and functional groups are responsible for the As(III) and Se(VI) uptake. Notably, the very high values of (\(R^{2}\)) of this model recommend its use to identify the adsorption kinetics. In fact, Pseudo-second-order isotherm usually plotted in its linear form based on Equation (8). \[\frac{t}{q}=\frac{1}{k_{2}.q_{e}^{2}}+\frac{1}{q_{e}}t \tag{8}\]  
where \(K_{2}\) is a sorption rate constant measured by g/(mg\(\cdot\)min) units. For As(III) experiments (Figure 5c), the results of the Pseudo-second-order model are recorded in Table 2. The results implied that the experimental adsorption capacity is \(q_{e}\) = 8.305 and \(k_{2}\) = 0.0235, which is almost similar to that calculated by Langmuir adsorption isotherm.