# Chromium(III) Removal from Wastewater by Chitosan Flakes
## 3 Results
### Adsorption Isotherms  
To determine the maximum adsorption capacity of Cr(III) on chitosan, a study was carried out on the adsorption isotherm by comparing the most common models; in particular, data were analyzed using the Langmuir and Freundlich equations:  
\[q_{e}=Q^{{}^{\circ}}k_{L}C_{eq}/\left(1+k_{L}C_{eq}\right)\quad\text{or, linearized}\quad 1/q_{e}=1/\left(Q^{{}^{\circ}}k_{L}\right)\left(1/C_{eq} \right)+1/Q^{{}^{\circ}} \tag{4}\]  
\[q_{e}=k_{F}C_{eq}^{1/n}\quad\text{or, linearized}\quad Log\;(q_{e})=Log\;(k_{F} )+1/n\;Log\;(C_{eq}) \tag{5}\]  
where \(q_{e}\) (mg g\({}^{-1}\)) is the amount of Cr(III) on the solid phase at equilibrium, and \(C_{eq}\) (mg L\({}^{-1}\)) is the equilibrium concentration of Cr(III) in the aqueous phase. According to [PERSON]'s equation, \(Q^{\circ}\) (mg g\({}^{-1}\)) is the amount of Cr(III) required for a complete coverage of available adsorption sites, while \(k_{L}\) is an empirical coefficient related to the affinity of adsorption sites for the adsorbed species. With reference to [PERSON]'s equation, \(k_{F}\) and \(n\) are empirical constants representing the adsorption capacity and adsorption intensity, respectively; all parameters can be estimated through the intercepts and slopes of the linearized forms of isotherm equations.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Cr(III) (ppm)** & **pH** \\ \hline
50 & 5.16 \\
100 & 5.02 \\
200 & 4.98 \\
400 & 4.67 \\
500 & 4.47 \\ \hline \hline \end{tabular}
\end{table}
Table 2: pH variation vs. Cr(III) concentration (pH\({}_{\text{in}}\) = 3.8).  
Figure 3: Effect of pH (initial value) on chromium(III) adsorption on chitosan (C\({}_{0}\) = 500 mg L\({}^{-1}\)).  
The essential characteristics of the Langmuir equation can be expressed in terms of a dimensionless separation factor \(R_{L}\), which has been defined in [27] as:  
\[R_{L}=1/[1+(k_{L}C_{o})] \tag{6}\]  
where \(C_{o}\) is the highest initial Cr(III) ion concentration (mg L\({}^{-1}\)). \(R_{L}\) is related to the shape of the isotherm: the adsorption is unfavorable if \(R_{L}>1\), favorable if \(0<R_{L}<1\), irreversible if \(R_{L}=0\), and linear if \(R_{L}=1\). All the estimated isotherm parameters are reported in Table 3. The \(R_{L}\) value confirms the affinity between chitosan and chromium ions, and the adsorption equilibrium data correlate well with the Langmuir isotherm equation, with a maximum adsorption capacity estimated at 138.04 mg g\({}^{-1}\). This implies a monolayer interaction of chromium on the adsorbent [31]. [PERSON] and colleagues [23] found that \(Q^{\circ}\) was 30.03 mg g\({}^{-1}\) using Cr(III) in the range 4-14 mg L\({}^{-1}\) and identified the Langmuir isotherm as the best model for the adsorption on cross-linked chitosan. However, the chromium concentrations considered were much lower than those investigated in the present work, and the number of amino groups available for ions coordination in cross-linked chitosan is limited, which obviously results in a lower adsorption capacity. [PERSON] and colleagues [32] found that \(Q^{\circ}\) was 62 mg g\({}^{-1}\) for chitosan flakes at pH = 4, but no information regarding chitosan characteristics was provided (especially regarding its degree of deacetylation).  
Indeed, the basis of the high adsorption capacity found in our study lies precisely in the fact that the investigated chromium concentrations are much higher than those reported in other works (see Figure 2, which shows that adsorption on chitosan increases with the concentration of the target species). Although the different experimental conditions make it difficult to compare the results obtained, it can be observed that at lower concentrations, the adsorption is in line with the values found in the literature (Figures 2 and 4).