## 3 Results and Discussion
### Adsorption of Lead and Acetaminophen  
The modification of the activated carbon with CA was first studied on the adsorption of lead in water, a metal whose occurrence remains a problem in drinking water at the ppb level [64]. The performance of each sample is illustrated with the isotherms in Figure 5. From the isotherm, it is possible to define the maximum adsorption capacity (q\({}_{\text{max}}\)) for each material, as shown in Table 4. The isotherms were fitted to common models such as Langmuir, Freundlich, and Sips. The Langmuir isotherm is an empirical model that assumes monolayer formation, with homogeneous sites on the surface, and all the adsorbent sites display equal affinity towards the adsorbate, with no adsorbate transmigration in the surface plane [65]. In contrast, the Freundlich model considers the plausible formation of a multilayer and the heterogeneity of the absorbent surface [66]. The Sips model emerges as a combination of the former two, considering the heterogeneity of the adsorption systems as well as circumventing the limitations associated with the high concentration registered by the adsorbate under the Freundlich model [67]. The three-parameter Sips model was selected as the best due to a better definition of the initial increase and the plateau at high concentration. The better fitting provides insights into the plausible mechanism in which a low concentration may promote the formation of multilayers due to considerable heterogeneity, and when the activated sites are saturated, no extra adsorption takes place, reaching the characteristic plateau of the Langmuir model. The results show notable variations in the q\({}_{\text{max}}\) values based on the treatment conditions, underscoring their significant influence on the char's adsorption potential. The untreated char exhibits a low value, i.e., q\({}_{\text{max}}\) = 3.1 mg g\({}^{-1}\), indicating minimal adsorption capacity. However, after activation with Na\({}_{2}\)CO\({}_{3}\), the CA solid displayed a higher uptake, q\({}_{\text{max}}\) = 37.2 mg g\({}^{-1}\). This significant enhancement can be attributed to the improved surface area and a higher presence of surface oxygenated groups linked to the carbon matrix, facilitating better adsorption thanks to their interactions with lead-hydrated ions. Figure 5: (**A**) Adsorption isotherms of lead with char and the activated carbon after citric acid modification. The dashed lines correspond to the Sips modeling. (**B**) Maximum experimental uptake of lead registered. In the case of the char modified with CA, the q\({}_{\rm max}\) rises slightly to 5.3 mg g\({}^{-1}\), revealing the limited effectiveness of the functionalization on the non-activated char. In contrast, the CA functionalization of the activated samples boosts the metal adsorption uptake. Specifically, the values obtained were 41.7 mg g\({}^{-1}\) (AC-CA-0.5), 52.3 mg g\({}^{-1}\) (AC-CA-1.0), and 36.4 mg g\({}^{-1}\) (AC-CA-1.5). This performance matches the contribution of oxygenated carbon as deduced with XPS, with the sample AC-CA-1.0 being the most enriched. Thus, there exists an optimal range for citric acid concentration, which leads to an enhanced contribution of oxygenated groups in the carbon matrix that triggers the maximum lead adsorption efficiency. Therefore, an optimum functionalization of the carbon material maximizes the capacity to retain metal, which is crucial for applications in environmental remediation. Comparative studies have reported similar results for Na\({}_{2}\)CO\({}_{3}\)-activated carbon derived from other feedstocks. For example, the activation of rapeseed oil cake with Na\({}_{2}\)CO\({}_{3}\) improves the adsorption capacity for lead ions if compared to the non-activated material, achieving a maximum lead uptake of q\({}_{\rm max}\) = 130 mg g\({}^{-1}\), indicating the effectiveness of this activating agent [68].