## 3 Results and Discussion
### Resticide Adsorption Studies
#### 3.3.2 Isotherm Adsorption Studies
This model is expressed by the following equation:  
\[q_{e}=\frac{q_{sat}\cdot b\cdot C_{e}}{1+b\cdot C_{e}} \tag{4}\]  
where \(q_{e}\) is the equilibrium adsorption capacity (mg/g), \(C_{e}\) is the equilibrium concentration (mg/L), \(q_{sat}\) is the maximum adsorption capacity in the monolayer (mg/g), and \(b\) is a constant related to the affinity between the adsorbate and adsorbent (mg/L). The Freundlich isotherm is an empirical model used when the adsorption mechanism appears to be mixed and the material surface can be considered energetically heterogeneous. As a consequence, this model can be applied to multilayer adsorption isotherms [44]. The Freundlich equation is as follows:  
\[q_{e}=K_{F}\cdot C_{e}^{1/n_{f}} \tag{5}\]  
where \(q_{e}\) is the equilibrium adsorption capacity (mg/g), \(k_{f}\) (L/g) is the Freundlich constant related to the adsorption capacity of the adsorbent, and \(1/n_{f}\) indicates the intensity of the adsorption process or the surface heterogeneity; when the value of \(n_{f}\) is \(>\)1, the adsorption conditions can be considered as favorable. The Sips model was developed to give the Freundlich model a finite limit at high equilibrium concentrations. The difference from the Langmuir isotherm model is an additional parameter, \(n\); when \(n=1\), the Sips model simplifies to the Langmuir equation. The parameter \(n\) can be defined as a measure of the surface heterogeneity: this heterogeneity may be due to the adsorbent surface, the adsorbate, or both. The value of \(n\) is usually higher than unity, and the greater the value, the more heterogeneous the system. The Sips model can be expressed by the following equation:  
\[q_{e}=\frac{q_{sat}\cdot\left(b\cdot C_{e}\right)^{1/n}}{1+\left(b\cdot C_{e} \right)^{1/n}} \tag{6}\]  
where \(b\) (L/mg) and \(1/n\) are temperature-dependent Sips parameters, and \(q_{sat}\) (mg/g) can be taken as a function (or not) of temperature. Finally, the Guggenheim-Anderson-De Boer (GAB) isotherm model is an extension of the Langmuir isotherm model that considers multilayer adsorption by assuming that each adsorbed molecule provides a site for the second one. The expression of the GAB model is as follows, assuming that only two layers are formed in the adsorption process:  
\[q_{e}=\frac{q_{m}\cdot K_{1}\cdot C_{e}}{\left(1-K_{2}\cdot C_{e}\right)\cdot \left[1+\left(K_{1}-K_{2}\right)\cdot C_{e}\right]} \tag{7}\]  
where \(K_{1}\) and \(K_{2}\) (L/mg) are equilibrium constants attributable to the first and second layer, respectively, and \(q_{m}\) (mg/g) is the maximum adsorption capacity in the first layer. The isotherm model parameters for adsorption onto the synthesized activated carbons are shown in Tables 5 and 6. The best fit to the experimental data of the adsorption isotherms was found for the Freundlich model, with higher values of the correlation coefficient (R\({}^{2}\)); this behavior was expected since it is a model suitable for fitting heterogeneous adsorption systems with an exponential distribution of active sites [45]. Also, it is worth noting that for the adsorption onto AC-Fe\({}_{2}\)(SO\({}_{4}\))\({}_{3}\), the Sips isotherm model fitted equally as well as Freundlich model. Regarding the parameter n\({}_{\text{f}}\) of the Freundlich equation, generally, values higher than unity are indicative that significant adsorption takes place at low concentration values (favorable adsorption isotherms), since the increase in the adsorption capacity with aqueous concentration becomes less significant at a higher concentration (n\({}_{\text{f}}\) values lower than unity). Most of the obtained n\({}_{\text{f}}\) values were greater than unity, thus verifying good adsorption onto a heterogeneous carbon surface [46; 47]. Although the Freundlich isotherm model achieved the best results, it did not provide a complete reproduction of the experimental data, mainly due to the complexity of reproducing multilayer adsorption isotherms and the large plateau region exhibited between the layers.