## 3 Results and Discussion
### Transport Study of Cr(VI) through Aliquat 336/PolyHIPE Membrane
#### 3.4.2 pH Effect on the Transport of Cr(VI) through the Aliquat 336/PolyHIPE Membrane  
Figure 6 shows the variations of Cr(VI) concentrations with respect to time. The pH of feeding phase was varied from 2 to 5. The pH of the stripping phase was kept at 12, at which an optimal stripping efficiency can be obtained, as determined in the pre-experiment. Assuming both the extraction and stripping of Cr(VI) follow the first order reaction with \"apparent rate constants\" as a  
Figure 5: Influence of the stirring speed on the removal rate. Feeding solution: [Cr(VI)] = 53 mg/L at pH 4; stripping phase: NaOH solution at pH 12.  
function of extraction reaction, stripping reaction, and the solute diffusion rate [36], the variation of Cr(VI) concentration in feeding, membrane, and stripping phases can be described by a kinetic law of two consecutive first order irreversible reaction (5) [15; 37]. \[Cr(VI)_{f}\xrightarrow{k_{1}}Cr(VI)_{m}\xrightarrow{k_{2}}Cr(VI)_{s} \tag{5}\]  
where \(Cr(VI)_{f}\), \(Cr(VI)_{m}\), and \(Cr(VI)_{s}\) represent the Cr(VI) ions in the feeding, membrane, and stripping phase, respectively. \(k_{1}\) and \(k_{2}\) are the first order apparent rate constants of the extraction and the stripping reaction, respectively. The variation of Cr(VI) concentration can be expressed by the following differential Equations (6)-(8):  
\[\frac{dR_{f}}{dt}=-\alpha k_{1}R_{f} \tag{6}\]  
\[\frac{dR_{m}}{dt}=\alpha k_{1}R_{f}-\beta k_{2}R_{m} \tag{7}\]  
\[\frac{dR_{s}}{dt}=\beta k_{2}R_{m} \tag{8}\]  
where \(\alpha\) and \(\beta\) is the ratio of membrane contact area to the volume of the feeding and stripping phase, respectively (\(\alpha=\beta=13.3\) m\({}^{2}\)/m\({}^{3}\) in this study). \(R_{f}\), \(R_{m}\), and \(R_{s}\) are the dimensionless concentrations of Cr(VI) (with respect to \([C]_{0}\)) in feeding, membrane, and stripping phase, respectively. Table 2 shows the fitted apparent rate constants. The apparent extraction rate constant \(k_{1}\) first increases approximately linearly as the feeding phase pH increases from 2 to 4, and then levels off at pH 5, indicating that the extraction of Cr(VI) at lower pH is a relatively slower process than that at higher pH. The apparent stripping rate constant \(k_{2}\) shows similar trend, despite the fact that the stripping phase is of the same pH (pH 12) for all the transport study. The change of \(k_{2}\) may be due to the difference between stripped Cr(VI)-Aliquat 336 complex formed at different feeding phase pH. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{pH} & \multirow{2}{*}{\(k_{1}\) (\(\times\)10\({}^{-6}\) m/s)} & \multirow{2}{*}{\(k_{2}\) (\(\times\)10\({}^{-6}\) m/s)} & \multicolumn{4}{c}{\(R^{2}\)} \\ \cline{3-8}  & & & **Feeding** & **Membrane** & **Stripping** \\ \hline
2 & 8.33 & 3.96 & 0.99 & 0.95 & 0.99 & 8.54 \\
3 & 12.11 & 4.38 & 0.99 & 0.98 & 0.99 & 12.13 \\
4 & 13.54 & 9.58 & 0.98 & 0.96 & 0.99 & 14.38 \\
5 & 14.58 & 9.79 & 0.97 & 0.98 & 0.99 & 14.52 \\ \hline \hline \end{tabular} Note: Feeding solution: [Cr(VI)] = 53 mg/L; stripping phase: NaOH solution at pH 12; stirring rate: 450 rpm.  
\end{table} 
Table 2: The fitted apparent rate constant and initial flux in the feeding phase. Figure 6: \(Cont.\)  
The initial feeding flux can be used to quantify the transport efficiency of Cr(VI) through the PolyHIPE membrane. At the initial instant of transport, the flux \(J/\!\!^{0}\) based on the concentration in the feeding phase can be described by Equation (9). The derivative \(\mathrm{d}[C]_{f}/\mathrm{d}t\) can be estimated from the fitted equation of Equation (6), provided that the fitted equation has high correlation coefficient (\(R^{2}>0.95\)). \[{J_{f}}^{0}=-\left.\frac{V}{S}\frac{dC_{f}}{dt}\right|_{t=0}=-\frac{V}{S}k_{1}C _{fo} \tag{9}\]  
where \(S\) is the operation membrane area (cm\({}^{2}\)), \(V\) is the volume of the feeding phase (cm\({}^{3}\)). Table 2 also shows the initial flux of Cr(VI) transport through Aliquat 336/PolyHIPE membrane at different feeding phase pH.