# Study of the Ciprofloxacinacin Adsorption of Activated Carbon Prepared from Mangosteen Peel
## 3 Results and Discussion
### CIP Adsorption Kinetics of the ACMP  
[PERSON]'s apparent first-order adsorption kinetics equation has the form:  
\[\lg(q_{e}-q_{t})=\lg q_{e}-\frac{k_{1}}{2303}t \tag{12}\]  
[PERSON]'s apparent second-order adsorption kinetics equation has the form:  
\[\frac{t}{q_{t}}=\frac{1}{k_{2}q_{e}^{2}}+\frac{1}{q_{e}}t \tag{13}\]  
where \(q_{e}\) and \(q_{t}\) are the adsorption capacities at the time of reaching equilibrium and at time \(t\) (mg/g), respectively; and \(k_{1}\) and \(k_{2}\) are the apparent first-order (time\({}^{-1}\)) and second-order (g.mg\({}^{-1}\). time\({}^{-1}\)) adsorption rate constants. From the values of the parameters of the first-order kinematics equation in Table 7, the coefficient of determination \(R^{2}\) ranges from 0.9812 to 0.9905. However, the equilibrium adsorption capacity values calculated from the kinetics equations are different from the experimental values. Therefore, the first-order kinetics equation is not suitable for the CIP adsorption by the ACMP (Figure 15). \begin{table}
\begin{tabular}{c c c} \hline
**Isotherm Models** & **Parameters** & \\ \hline \multirow{2}{*}{[PERSON]} & b (L/mg) & 0.173 \\  & \(q_{max}\) (mg/g) & 29.76 \\  & \(R^{2}\) & 0.9986 \\ \hline \multirow{3}{*}{[PERSON]} & \(K_{F}\) (mg/g)-(mg/L)1/n & 13.57 \\  & N & 6.73 \\  & \(R^{2}\) & 0.9421 \\ \hline \multirow{3}{*}{[PERSON]} & \(K_{T}\) & 138.49 \\  & \(b_{T}\) (kj-mol) & 0.88 \\  & \(R^{2}\) & 0.9653 \\ \hline \multirow{3}{*}{[PERSON]} & \(q_{max}\) (mg/g) & 3.44 \\  & \(K_{e}\) & 198.25 \\  & \(R^{2}\) & 0.9508 \\ \hline \multirow{3}{*}{Redlich–Peterson} & \(\beta\) & 0.8515 \\  & \(A\) (mg\(\cdot\)L\({}^{-1}\)) & 13.57 \\ \cline{1-1}  & \(R^{2}\) & 0.9982 \\ \hline \end{tabular}
\end{table} 
Table 6: Values of the constants calculated from the [PERSON], [PERSON], [PERSON], [PERSON], and Redlich–Peterson isotherm adsorption models for the ACMP materials. \begin{table}
\begin{tabular}{c c c c c} \hline
**CIP Concentration** & \(\begin{array}{c}\mathbf{q_{Uexp}}\\ \mathbf{(mg/L)}\end{array}\) & \(\begin{array}{c}\mathbf{q_{Ucal}}\\ \mathbf{Experiment}\\ \mathbf{(mg/g)}\end{array}\) & \(\begin{array}{c}\mathbf{Calculation}\\ \mathbf{(mg/g)}\end{array}\) & \(\begin{array}{c}\mathbf{Constant}\mathbf{k_{1}}\\ \mathbf{(min^{-1})}\end{array}\) & \(\mathbf{R^{2}}\) \\ \hline
46.91 & 15.24 & 4.86 & 0.0509 & 0.9875 \\
64.03 & 19.17 & 6.13 & 0.0403 & 0.9812 \\
110.25 & 25.96 & 10.10 & 0.0463 & 0.9905 \\ \hline \end{tabular}
\end{table} 
Table 7: Values of the parameters from the first-order adsorption kinetics equation. In addition to the R\({}^{2}\) constant, the accuracy of the quadratic kinematics equation is also determined through the standard deviation %\(\Delta\)q. The accuracy of the equation is determined by the standard deviation %\(\Delta\)q as the following equation:  
\[\%\Delta\)q = 100\(\times\sqrt{\frac{\sum\left[(\text{q}_{\text{t,exp}}-\text{ q}_{\text{t,cal}})/\text{q}_{\text{t,exp}}\right]^{2}}{\text{n}-1}}\)  
where n is the number of data points, q\({}_{\text{t,exp}}\) is the experimental adsorption capacity at time t, and q\({}_{\text{t,cal}}\) is the adsorption capacity at time t according to the kinetic equation. From the values in Table 8, the coefficients of determination (R\({}^{2}\)) are all 0.99. Further, the equilibrium adsorption capacity values calculated from the kinetics equations are very close to the experimental values, and the k\({}_{2}\) values are also approximately the same. The calculation results of the %\(\Delta\)q value in the table are low. Therefore, it can be concluded that the CIP adsorption process of the ACMP follows [PERSON]'s apparent quadratic kinetics equation. Therefore, the uptake of the CIP by the ACMP depends on the concentration of the CIP in the aqueous medium and the number of active sites on the adsorbent surface.