## 3 Results and Discussion
### Adsorption of Phenol during the Immersion Process  
An interesting aspect of this study is the fact that during the calorimetric experience, the adsorption of phenol generated a quantity of heat that is proportional to the solid-liquid interactions. The adsorption of phenol on the activated carbons was carried out for a period of 2 h; this corresponds to a calorimetric measurement. A modification to the Langmuir model proposed by [PERSON] and collaborators [3] was used to describe the adsorption process from a solution of activated carbons using the results obtained. This model was used because it allows an evaluation between two types of interactions: a specific enthalpy-driven and another non-specific measurement wherever the adsorption occurs between the fundamental surface of the activated carbon and the non-polar parties in the molecules by hydrophobic links. The Modified Langmuir model is given by the following Equation:  
\[q_{e}=\frac{K_{1}K_{2}C_{e}}{1+K_{1}C_{e}}+K_{HB} \tag{3}\]  
in which \(qe\) (mmol\(\cdot\)g\({}^{-1}\)) represents the quantity of phenol adsorbed on the balance, \(C_{e}\) (mmol\(\cdot\)L\({}^{-1}\)) is the final concentration of phenol in the solution, \(K_{1}\) (L\(\cdot\)mmol\({}^{-1}\)) is a constant of affinity associated with the amount of polar groups on the surface of the activated carbon, \(K_{2}\) (mmol\(\cdot\)g\({}^{-1}\)) is the adsorption capacity of the adsorbent by the solute, and \(K_{HB}\) (mmol\(\cdot\)g\({}^{-1}\)) is a constant that allows the non-specific adsorption to be determined through hydrophobic links between the non-polar parties in the adsorbate and the basal carbon surface. The adsorption isotherms of phenol obtained during the calorimetric determinations adjusted to the Modified Langmuir model are shown in Figure 4.  
Figure 4 shows the phenol adsorption on activated carbons during the first two hours of the adsorption process. These are similar to type L or Langmuir isotherms according to the classification established by [PERSON] for the adsorption of a solid-liquid [19]. This adjustment would indicate that the molecules adsorbed are arranged horizontally on the surface of the activated carbon, that there  
Figure 3: Distribution of micropore size from QSDFT model. is strong competition between the water and the solute by the adsorption sites, and that there are attractions between the adsorbate molecules. Table 2 presents the parameters resulting from the adjustment of adsorption data obtained during the calorimetric determination to the modified Langmuir model. For comparative purposes, the adjustments of adsorption data results to the Langmuir model are presented. Table 2 shows that the highest adsorption value is obtained for the activated carbon impregnated with nitric acid and subsequently kept on to reflux with a solution of ammonium hydroxide, GNA, and that the lowest adsorption is presented for the activated carbon subjected to oxidation with nitric acid, GN. The adsorption is analysed from the values of the constants associated with the adsorption capacity of the activated carbons Q\({}_{0}\) and K\({}_{2}\) of Langmuir and Langmuir modified models, respectively. The pH values at the end of each calorimetric determination were measured; the results are shown in Figure 5.  
Figure 5 shows that the pH values for GNA sample were between 6.5 and 7.6 and for the GN sample were between 5.3 and 7.3. Taking into account that the pKa value for phenol is 9.98 [20], this is protonated just like the polar groups on the activated carbon surface. The activated carbon GN contains many acid groups, mainly carboxyl groups on the surface by impregnation with nitric acid