# Effective Adsorption of Phenoxyacetic Herbicides by Tomato Stem-Derived Activated Carbons
## 3 Results and Discussion
### Adsorption Study
#### 3.2.2 Adsorption Isotherms
The results indicate that both the Langmuir and the Freundlich models effectively describe the experimental data. However, the Langmuir isotherm model exhibited marginally higher \(R^{2}\) values and marginally lower \(\chi^{2}\) values. This suggests that the adsorption of both herbicides on activated carbon from tomato stems (TS-AC) follows the Langmuir model rather than the Freundlich model. This suggests that the adsorption process most likely forms a monomolecular adsorbate layer on the TS-AC surface, implying a finite number of energetically homogeneous adsorption sites and negligible interactions between adsorbed molecules. The Langmuir model also provides insights into the nature and favorability of the adsorption process. The separation factor (\(R_{\rm L}\)), which indicates adsorption favorability, can be calculated from the Langmuir constant (\(K_{\rm L}\)) using the following equation [34]:  
\[R_{L}=\frac{1}{1+K_{L}C_{0}} \tag{15}\]  
Table 8 presents the calculated \(R_{\rm L}\) values (minimum and maximum values for each AC). These values, ranging between zero and one (0 < \(R_{\rm L}\) < 1), confirm the favorable nature of the adsorption process. In another situation, if the value of \(R_{\rm L}\) were equal to 0 or 1, the adsorption would be irreversible or linear, respectively. Conversely, a value of \(R_{\rm L}\) greater than 1 would indicate the unfavorable nature of the adsorption [34]. The Freundlich isotherm constant, \(1/n\), substantiates the conclusions regarding the favorability of adsorption. Values of \(1/n\) exceeding or equaling 1 (\(1/n\geq 1\)) indicate unfavorable or irreversible adsorption processes, respectively. Conversely, a \(1/n\) value within the interval of 0 to 1 (0 < \(1/n\) < 1) is characteristic of favorable adsorption [34]. As shown in Table 6, the \(1/n\) values for all activated carbons ranged from 0.326 to 0.501 for 2,4-D and from 0.251 to 0.424 for MCPA, indicating a favorable adsorption process. The Langmuir constant \(K_{\rm L}\) can be used to calculate the Gibbs free energy change (\(\Delta G^{\circ}\)) [35] for adsorption [36]. The \(\Delta G^{\circ}\) was calculated using the following equation:  
\[\Delta G^{\circ}=-RT\ln(55.5K_{L}) \tag{16}\]  
where \(R\) is the universal gas constant (8.314 J/mol\(\cdot\)K) and \(T\) is the temperature in Kelvin. This parameter quantifies the spontaneity and feasibility of the adsorption process. Negative \(\Delta G^{\circ}\) values indicate a spontaneous reaction. The calculated \(\Delta G^{\circ}\) values are presented in Table 8, all of which are negative, confirming the spontaneous nature of the adsorption. The analysis of the \(q_{\rm m}\) and \(K_{\rm F}\) values shown in Table 7 shows that both herbicides were better adsorbed onto TS-AC activated with NaOH than with KOH at the same temperatures. AC-KOH-550 was the weakest adsorbent, while AC-NaOH-750 showed the highest adsorption capacity. This trend (AC-KOH-550 < AC-NaOH-550 < AC-KOH \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & **2,4-D** & & & **MCPA** & \\ \cline{2-6}
**TS-AC** & \(\Delta G^{\circ}\)** & **Separation Factor (\(R_{\rm L}\))** & \(\Delta G^{\circ}\) & **Separation Factor (\(R_{\rm L}\))** \\ \cline{2-6}  & **(k/mol)** & **Min.** & **Max.** & **(k/mol)** & **Min.** & **Max.** \\ \hline AC-KOH-550 & \(-\)27.9 & 0.395 & 0.685 & \(-\)31.4 & 0.140 & 0.352 \\ AC-KOH-650 & \(-\)31.1 & 0.154 & 0.379 & \(-\)32.3 & 0.101 & 0.271 \\ AC-KOH-750 & \(-\)32.1 & 0.109 & 0.289 & \(-\)32.8 & 0.083 & 0.231 \\ AC-NaOH-550 & \(-\)29.1 & 0.294 & 0.581 & \(-\)29.8 & 0.236 & 0.506 \\ AC-NaOH-650 & \(-\)29.6 & 0.248 & 0.523 & \(-\)31.8 & 0.118 & 0.308 \\ AC-NaOH-750 & \(-\)32.3 & 0.098 & 0.267 & \(-\)33.0 & 0.078 & 0.221 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The Gibbs free energy change (\(\Delta G^{\circ}\)) and separation factors (\(R_{\rm L}\)) associated with the adsorption of 2,4-dichlorophenoxyoxyacetic acid (2,4-D) and 2-methyl-4-chlorophenylohexacetic acid (MCPA) onto tomato stem-derived activated carbon (TS-AC).