## 3 Results and Discussion
### Adsorption Kinetics  
As in the case of the isotherms, in order to determine the kinetic model that best describes the adsorption of methylparaben on activated carbon and activated olive stones, the experimental data on the variation of adsorption capacity with time were fitted to the linearized mathematical equations of the four kinetic models studied ([PERSON] pseudo-first order, [PERSON] pseudo-second order, [PERSON] and Avrami), and the correlation coefficients obtained were comparatively analyzed. Linear representations of these four models for activated carbon and activated olive stones are shown in Figure 4, while the kinetic parameters and R\({}^{2}\) values calculated from these kinetic models are included in Tables 6 and 7. These results allow us to state that while in the case of the activated olive stones, the experimental data clearly fit better to a pseudo-first-order kinetic model as the correlation coefficients obtained in this model are clearly higher than in the other three models, in the case of activated carbon, the values of the correlation coefficients of the pseudo-first and pseudo-second-order models are very similar, so it is not possible to establish a definitive conclusion. In order to discern which of these two models best defines the adsorption process of methylparaben on activated carbon, the greater/lesser coincidence of the experimental values of q\({}_{e}\) with the values of this parameter obtained from pseudo-first and pseudo-second-order models was analyzed. Figure 5 shows this coincidence for both activated carbon and activated olive stones. It is observed that the theoretical q\({}_{e}\) values obtained by the pseudo-first-order model practically coincide with the experimental values of q\({}_{e}\); therefore, it can be concluded that \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{Langmuir isotherm} & \multicolumn{4}{c}{Freundlich Isotherm} & \multicolumn{4}{c}{Elovich Isotherm} \\ \hline Temperature & q\({}_{m}\) (Z/g) & K\({}_{L}\) (L/mg) & R\({}^{2}\) & N & (mg/g)(L/mg)\({}^{1/n}\) & R\({}^{2}\) & q\({}_{mE}\) (mg/g) & K\({}_{L}\) (L/g) & R\({}^{2}\) \\ \hline
283 & 24.8756 & 0.0503 & 0.2846 & 0.9964 & 1.5601 & 1.8016 & 0.9923 & 14.8368 & 0.0958 & 0.9887 \\ \hline
293 & 27.3224 & 0.0540 & 0.2701 & 0.9987 & 1.5413 & 2.0311 & 0.9903 & 16.4474 & 0.1015 & 0.9909 \\ \hline
303 & 27.8552 & 0.0604 & 0.2487 & 0.9984 & 1.5309 & 2.2001 & 0.9852 & 16.1290 & 0.1495 & 0.9708 \\ \hline
313 & 28.4900 & 0.0723 & 0.2167 & 0.9947 & 1.6116 & 2.6966 & 0.9920 & 17.1527 & 0.1092 & 0.9940 \\ \hline \multicolumn{8}{c}{Temkin isotherm} & \multicolumn{4}{c}{Jovanovic isotherm} & \multicolumn{4}{c}{Dubinin–Radushkevich isotherm} \\ \hline Temperature (K) & A (L/mg) & B (mg/g) & R\({}^{2}\) & q\({}_{m}\) (Z/g) & K\({}_{l}\) (L/mg) & R\({}^{2}\) & q\({}_{m}\) (Z/g) & K (mol\({}^{2}\)/L\({}^{2}\)) & E (Jmol) & R\({}^{2}\) \\ \hline
283 & 1.9362 & 5.3355 & 0.9890 & 4.0020 & 0.0582 & 0.8876 & 12.4572 & 3.9969 & 0.3537 & 0.8882 \\ \hline
293 & 1.7755 & 5.8183 & 0.9920 & 4.6409 & 0.0532 & 0.8649 & 13.6331 & 3.2111 & 0.3946 & 0.9019 \\ \hline
303 & 1.6175 & 6.0015 & 0.9962 & 4.7870 & 0.0580 & 0.8475 & 13.8696 & 2.5785 & 0.4404 & 0.9222 \\ \hline
313 & 1.3474 & 6.1344 & 0.9881 & 5.2169 & 0.0613 & 0.8644 & 14.8530 & 1.7796 & 0.5301 & 0.8911 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameter values of the different studied isotherm models obtained in the adsorption of MPB onto AOS. the pseudo-first-order model is the one that best describes the adsorption of methylparaben on both activated carbon and activated olive stones.