# Potentiality of Rod-Type Chitosan Adsorbent Derived from Sewage Sludge
## 3 Results and Discussion
### Adsorption Study
#### 3.3.2 Isotherms  
Biosorption isotherms can represent the interaction between a biosorbate and biosorbent, and provide information about the distribution of the biosorbate between the liquid and solid phases at several equilibrium concentrations. Isotherm modeling is therefore important for biosorption data interpretation and prediction [7; 27]. In this study, isotherm Freundlich and Langmuir models were used to evaluate biosorption equilibrium data. The Freundlich and Langmuir isotherm equations are as follows:  
\[q_{e}=K_{F}C_{e}^{1/n} \tag{5}\]  
Figure 2: Kinetics of metalloid/metal adsorption (As(V), Cd(II), Cr(VI), and Mn(VII)) onto the sludge–chitosan (biomass dosage = 2 g/L, agitation rate = 200 rpm, contact time = 6 h, temperature = 25 °C, Vw = 200 mL, and pH non shift (pH 5.5)). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Pseudo-First-Order**} & \multicolumn{6}{c}{**Pseudo-Second-Order**} \\ \cline{3-10} \multirow{3}{*}{**Kinetictictictictictic**} & **Metals** & \(K_{1}\) & \(q_{e}\) & \(R^{2}\) & \(K_{2}\) & \(q_{e}\) & \(R^{2}\) & \(h\) \\  & & **(I/h)** & **(mg/g)** & **(-)** & **(g/mg-h)** & **(mg/g)** & **(-)** & **(mg/g-h)** \\ \cline{2-10} \multirow{3}{*}{**Isotherm**} & **As(V)** & 0.85 & 8.64 & 0.9924 & 0.18 & 16.21 & 0.9996 & 47.68 \\  & Cd(II) & 0.51 & 2.91 & 0.8452 & 0.80 & 14.96 & 0.9999 & 178.06 \\  & Cr(VI) & 1.33 & 38.27 & 0.9840 & 0.06 & 19.94 & 0.9974 & 23.06 \\  & Mn(VII) & 1.02 & 34.94 & 0.9642 & 0.01 & 34.75 & 0.9645 & 14.66 \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Langmuir**} & \multicolumn{3}{c}{**Freundlich**} \\ \cline{3-10}  & **Metals** & \(Q_{max}\) & \(b\) & \(R^{2}\) & \(K_{F}\) & \(n\) & \(R^{2}\) \\  & & **(mg/g)** & **(L/mg)** & **(-)** & **(mg/g)** & **(-)** & **(-)** \\ \cline{2-10}  & **As(V)** & 42.25 & 0.0241 & 0.9711 & 6.3703 & 3.18 & 0.8643 \\  & Cd(II) & 28.69 & 0.0398 & 0.8030 & 4.5064 & 2.94 & 0.9048 \\  & Cr(VI) & 70.79 & 0.0201 & 0.9648 & 7.0609 & 2.57 & 0.8447 \\  & Mn(VII) & 275.43 & 0.0163 & 0.8948 & 14.1749 & 1.98 & 0.9766 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Kinetic and isotherm constants for the biosorption of As(V), Cd(II), Cr(VI), and Mn(VII) by RCA. \[q_{e}=\frac{q_{max}bC_{e}}{1+bC_{e}} \tag{6}\]  
where \(K_{F}\) and \(n\) are constants incorporating all parameters affecting the biosorption process in the Freundlich equation and \(b\) is the constant related to the affinity of the binding sites in the Langmuir equation. In the Freundlich equation, \(K_{F}\) (L/mg)\({}^{1/n}\) and \(n\) (dimensionless) are constants. On average, favorable adsorption tends to have an \(n\) between 1 and 10. In the Langmuir equation, \(q_{max}\) is the maximum adsorption capacity (mg/g) and \(b\) (L/g) is the isotherm constant. The Langmuir and Freundlich isotherm models were used to interpret the experimental isotherm data of RCS. The model parameters and \(R^{2}\) values are summarized in Table 3. The sorption experimental data and respective Langmuir and Freundlich isotherms are plotted in Figure 3a-d, respectively. A linear regression of the experimental results for As(V) and Cr(VI) proved a better fit in Langmuir isotherms. This result can be attributed to the fact that As(V) and Cr(VI) biosorption of RCS can be assumed by sorbate, and the equation describing the reaction rate allows for simultaneous adsorption and desorption [28]. When comparing the Langmuir parameter values obtained for As(V) and Cr(VI), \(q_{max}\) was approximately 42.25 mg As(V) or 70.79 mg Cr(VI) per g of RCS. The values for As(V) from the present study are comparable to or considerably greater than other reported sludge sorbents (Table 4). Various types of adsorbents (pyrolyzed form, biochar, alginate immobilized form, and magnetic sludge composite) were prepared from wastewater sludge, and their As(V) removal performance was 0.07-21.79 mg/g [29; 30; 31; 32; 33].