## 3 Results
### Lactic Acid Adsorption Isotherms  
Figure 3 shows the linearized plots for three different adsorption isotherms (Langmuir, Freundlich and Temkin) of lactic acid adsorption at 303.15 K. Table 4 presents the isotherm parameters and regression coefficients for all the isotherm plots. Figure 3a shows the linear fit (\(1/q_{e}\) versus \(1/C_{e}\)) of the Langmuir isotherm model. The maximum monolayer adsorption capacity (\(q_{m}\)) value was found to be the highest for GAC (126.6 mg lactic acid/g adsorbent), followed by RLX425 (108.7 mg lactic acid/g adsorbent) and AMB400 (63.5 mg lactic acid/g adsorbent). In addition, the separation factor (\(R_{L}\)) values, calculated to be in the range of 0.05-0.6 for GAC, 0.2-0.9 for RLX425 and 0.2-0.8 for AMB400, \begin{table}
\begin{tabular}{c c c c} \hline
**Adsorbents** & **GAC** & **RLX425** & **AMB400** \\ \hline
**Temperature (K)** & \(\Delta G^{0}\) **(kJ/mol)** & \(\Delta G^{0}\) **(kJ/mol)** & \(\Delta G^{0}\) **(kJ/mol)** \\ \hline
303.15 & \(-\)10.9 & \(-\)4.5 & \(-\)5.5 \\ \hline
313.15 & \(-\)10.7 & \(-\)4.0 & \(-\)5.8 \\ \hline
323.15 & \(-\)10.5 & \(-\)3.5 & \(-\)6.0 \\ \hline
333.15 & \(-\)10.4 & \(-\)3.0 & \(-\)6.3 \\ \hline
343.15 & \(-\)10.2 & \(-\)2.4 & \(-\)6.5 \\ \hline
353.15 & \(-\)9.9 & \(-\)1.9 & \(-\)6.8 \\ \hline \end{tabular}
\end{table} 
Table 3: Gibbs free energy for adsorption of lactic acid onto GAC, RLX425 and AMB400 at temperature ranges from 303.15 to 353.15 K (\(\Delta H^{0}\) = \(-\)16.7 kJ/mol and \(\Delta S^{0}\) = \(-\)0.02 kJ/mol K) for GAC; \(\Delta H^{0}\) = \(-\)19.9 kJ/mol and \(\Delta S^{0}\) = \(-\)0.05 kJ/(mol K) for RLX425; \(\Delta H^{0}\) = 2.0 kJ/mol and \(\Delta S^{0}\) = 0.02 kJ/(mol K) for AMB400). Figure 2: (a) Effect of temperature (303.15–353.15 K) on the adsorption capacities of the adsorbents with 4.5 g/L of lactic acid in the bulk solution accompanied by initial pH corrections and 10% (\(w/v\)) adsorbent dose and (b) plot of \(ln\)\(K_{L}\) versus \(1/T\) at a lactic acid concentration of 4.5 g/L in the temperature range of 303.15–353.15 K.  
indicate a favorable adsorption process. A good agreement (\(R^{2}>0.96\)) was observed between the experimental data and the Langmuir isotherm model. Figure 3b shows the plot between \(log\ q_{e}\) versus \(log\ C_{e}\) for the Freundlich isotherm model. The adsorption intensity (\(n\)) was the highest for AMB400, followed by GAC and RLX425 (Table 4). The slope (\(1/n\)) in Figure 3b ranges between 0 and 1 and is a measure of surface heterogeneity, where the adsorption becomes more heterogeneous as the \(1/n\) value approaches 0 [29]. Table 4 shows \(n>1\) for all the adsorbents investigated, indicating a nonlinearity due to adsorption site heterogeneity. The Temkin isotherm model shows the adsorption potential of the adsorbent towards the adsorbate. The Temkin isotherm parameters such as \(A_{T}\) and \(K_{T}\) were calculated from the linear plots of \(q_{e}\) versus \(ln\ C_{e}\) as shown in Figure 3c. The Temkin isotherm model showed a reasonably good fitting between the experimental results of lactic acid adsorption and the model prediction for all the adsorbents investigated. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Isotherms** & **Coefficients** & **Units** & **GAC** & **RLX425** & **AMB400** \\ \hline \multirow{3}{*}{Langmuir} & \(q_{m}\) & mg/g & 126.6 & 108.7 & 63.5 \\  & \(K_{L}\) & L/mg & \(4.4\times 10^{-4}\) & \(6.9\times 10^{-5}\) & \(1.9\times 10^{-4}\) \\  & \(R^{2}\) & - & 0.98 & 0.98 & 0.96 \\ \hline \multirow{3}{*}{Freundlich} & \(n\) & - & 1.8 & 1.4 & 1.9 \\  & \(K_{F}\) & mg/g (L/g)\({}^{n}\) & 1.2 & 3.3 & 1.6 \\  & \(R^{2}\) & - & 0.96 & 0.95 & 0.90 \\ \hline \multirow{3}{*}{Temkin} & \(A_{T}\) & L/g & 251.7 & 887.6 & 371.3 \\  & \(K_{T}\) & - & 31.9 & 19.2 & 15.3 \\ \cline{1-1}  & \(R^{2}\) & - & 0.97 & 0.93 & 0.91 \\ \hline \end{tabular}
\end{table} 
Table 4: The Langmuir, Freundlich and Temkin isotherm model parameters obtained from the linear fitting for the three adsorbents (GAC, RLX425 and AMB400).