## 3 Results and Discussion
### Adsorption Equilibrium  
In order to find out which isotherm model best describes the adsorption of methylparaben on activated carbon and activated olive stones, the experimental equilibrium data were fitted to the linearized mathematical equations of each of the six equilibrium models described above (Langmuir, Freundlich, Elovich, Temkin, Jovanovic and Dubinin-Radushkevich) by analyzing the correlation coefficients obtained in the corresponding linear regression. Figures 2 and 3 show the linear representation of these six models for activated carbon and activated olive stones, respectively, while the values of their model constants and correlation coefficients (R\({}^{2}\)) are included in Tables 4 and 5, respectively. Figure 2: Isotherm plots for the adsorption of MPB onto AC. The Langmuir isotherm best describes the adsorption process of methylparaben on both activated carbon and activated olive stones, showing the highest correlation coefficient values in all cases. The fit of the experimental data to the Langmuir isotherm model suggests that in the two adsorbents, the adsorption sites are homogeneously distributed and energetically equivalent, each adsorption site adsorbs only one methylparaben molecule and there is no interaction between the adsorbed methylparaben molecules. Moreover, the values of the R\({}_{\rm L}\) parameter are less than 1 in both adsorbents, indicating the favorable character of methylparaben adsorption on both activated carbon and activated olive stones [31]. The analysis of the Langmuir model constants for both adsorbents allows some significant conclusions to be drawn. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{Langmuir isotherm} & \multicolumn{3}{c}{Freundlich Isotherm} & \multicolumn{3}{c}{Elovich Isotherm} \\ \hline Temperature & qn (K) & K\({}_{\rm L}\) (\(\rm{m}\)/g) & R\({}_{\rm L}\) & R\({}^{2}\) & n & K\({}_{\rm F}\) (\(\rm{m}\)/g)\({}^{\rm(L}\)/\(\rm{m}\))\({}^{\rm 1/n}\) & R\({}^{2}\) & qn\({}_{\rm L}\) (\(\rm{m}\)/g) & K\({}_{\rm E}\) (L/g) & R\({}^{2}\) \\ \hline
283 & 86.9565 & 0.3412 & 0.0554 & 0.9965 & 2.1277 & 23.2174 & 0.9561 & 35.7143 & 1.2451 & 0.9481 \\ \hline
293 & 92.5926 & 0.3763 & 0.0505 & 0.9916 & 2.1418 & 26.1723 & 0.9901 & 36.7647 & 1.4985 & 0.9825 \\ \hline
303 & 95.2381 & 0.4086 & 0.0467 & 0.9991 & 2.0509 & 27.3523 & 0.9687 & 39.8406 & 1.4412 & 0.9758 \\ \hline
313 & 98.0392 & 0.4976 & 0.0386 & 0.9997 & 2.0631 & 30.5266 & 0.9537 & 41.6667 & 1.6557 & 0.9428 \\ \hline  & \multicolumn{3}{c}{Ternkin isotherm} & \multicolumn{3}{c}{Jovanovic isotherm} & \multicolumn{3}{c}{Dubinin–Radushkevich isotherm} \\ \hline Temperature (K) & A (L/mg) & B (mg/g) & R\({}^{2}\) & q\({}_{\rm m}\) (mg/g) & K\({}_{\rm J}\) (L/mg) & R\({}^{2}\) & q\({}_{\rm m}\) (mg/g) & K (mol\({}^{2}\)/L\({}^{2}\)) & E (Jmol) & R\({}^{2}\) \\ \hline
283 & 3.5135 & 18.7006 & 0.9941 & 25.9378 & 0.0868 & 0.7008 & 61.2767 & 0.3284 & 1.2339 & 0.9305 \\ \hline
293 & 4.1867 & 19.3489 & 0.9828 & 25.9352 & 0.1116 & 0.7689 & 61.3626 & 0.1978 & 1.5899 & 0.8620 \\ \hline
303 & 4.2481 & 20.4452 & 0.9969 & 27.3086 & 0.1144 & 0.6915 & 63.5991 & 0.1904 & 1.6205 & 0.8993 \\ \hline
313 & 5.0017 & 21.1908 & 0.9945 & 28.9595 & 0.1222 & 0.6542 & 68.1492 & 0.1581 & 1.7784 & 0.9211 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameter values of the different studied isotherm models obtained in the adsorption of MPB onto AC. Figure 3: Isotherm plots for the adsorption of MPB onto AOS. The maximum monolayer adsorption capacity (q\({}_{m}\)) of methylparaben on activated carbon is 3.4 times higher than its value on activated olive stones, and the increase in temperature in both adsorbents indicates that the adsorption of methylparaben on both activated carbon and activated olive stones is endothermic. The values of the Langmuir constant (K\({}_{L}\)), related to the adsorbate-adsorbent affinity, allow us to affirm that the MPB/AC affinity is 6.85 times higher than the MPB/AOS affinity.