## 2 Materials and Methods
### Adsorption Experiments  
Batch adsorption experiments for lead and acetaminophen were conducted at 25 \({}^{\circ}\)C in 100 mL Erlenmeyer flasks. Solutions containing Pb from Pb(NO\({}_{3}\))\({}_{2}\) (PanReac AppliChem, Barcelona, Spain) at concentrations ranging from 10 to 300 mg L\({}^{-1}\) and acetaminophen (Merck\(\circled\), Burlington, MA, USA) at concentrations ranging from 10 to 1000 mg L\({}^{-1}\) were prepared, using an adsorbent dose of 2.0 g L\({}^{-1}\), and stirred at 160 rpm, maintaining the temperature at 25 \({}^{\circ}\)C until equilibrium was reached. The samples were filtered through Millipore Millex-GV PVDF 0.45 \(\upmu\)m syringe filters, and the concentration was measured by atomic absorption spectroscopy (PerkinElmer\(\circled\) PinAAcle 500, Waltham, MA, USA) for Pb; high-pressure liquid chromatography (HPLC) using a Waters\({}^{\text{TM}}\) Alliance e2695 HPLC (Milford, MA, USA) with a 2998 photodiode array detector was used for the quantification of acetaminophen. A Zorbax Bonus-RP column (4.6 mm \(\times\) 150 mm, 5 \(\upmu\)m) was used as the stationary phase.  
The adsorption uptake reached at equilibrium (q\({}_{\text{e}}\)) was fitted to the two-parameter models of [PERSON] (Equation (1)) and [PERSON] (Equation (2)), and the three-parameter model of [PERSON] (Equation (3)):  
\[\text{q}_{\text{e}}=\frac{\text{q}_{\text{max}}\text{K}_{\text{L}}\text{C}_{ \text{e}}}{1+\text{K}_{\text{L}}\text{C}_{\text{e}}} \tag{1}\]  
\[\text{q}_{\text{e}}=\text{K}_{\text{F}}\text{C}\text{e}^{\
icefrac{{1}}{{ \text{r}_{\text{e}}}}} \tag{2}\]  
\[\text{q}_{\text{e}}=\frac{\text{q}_{\text{max}}\text{K}_{\text{S}}\text{C}_{ \text{e}}^{\
icefrac{{1}}{{\text{r}_{\text{e}}}}}}{1+\text{K}_{\text{S}} \text{C}\text{e}^{\
icefrac{{1}}{{\text{r}_{\text{e}}}}}} \tag{3}\]  
where q\({}_{\text{e}}\) is the amount of adsorbate per unit mass of adsorbent at equilibrium (mg g\({}^{-1}\)); C\({}_{\text{e}}\) is the equilibrium concentration of adsorbate in the liquid phase (mg L\({}^{-1}\)); q\({}_{\text{max}}\) is the theoretical maximum adsorption capacity (mg g\({}^{-1}\)); K\({}_{\text{L}}\) is the Langmuir constant related to the affinity of the binding sites (mg\({}^{-1}\) L); K\({}_{\text{F}}\) is the Freundlich constant related to the adsorption capacity (mg\(\cdot\)g\({}^{-1}\))/(mg\(\cdot\)L\({}^{-1}\))\({}^{1/\text{nF}}\); n\({}_{\text{F}}\) and n\({}_{\text{S}}\) are the heterogeneity factors, indicating the intensity of adsorption (dimensionless) of the Freundlich and Sips models, respectively; and K\({}_{\text{S}}\) is the Sips constant related to the affinity of the binding sites (mg\({}^{-1}\) L)\({}^{1/\text{ns}}\).  
Finally, the prepared char-based material adsorbents were also subjected to leaching tests under unmodified pH conditions to ensure the sustainability of the treatment process. The experiment involved preparing a mixture of 10 g of char with 100 mL of water, maintaining a ratio of 1:10. This mixture was agitated at a speed of 10 rpm for 24 h. Following the agitation period, the leachate was filtered using a 0.45 \(\upmu\)m filter (PVDF Millex-HV, Merck KGaA, Darmstadt, Germany), and the released metals were quantified by Induced Coupled Plasma-Mass Spectrometry (ICP-MS) in a Perkin Elmer Nexion 300D device (Waltham, MA, USA).