## 3 Results and Discussion  
### Kinetic Model for Sulfamethoxazole Oxidation  
Figure 2 shows the SMX degradation by photo-Fenton, varying the iron catalyst dosage. It is observed that the SMX concentration decreases rapidly in the first minutes of the reaction, suggesting first-order kinetics in the degradation. As the initial Fe(II) concentration increases, the degradation rate increases, achieving a faster elimination of SMX. For higher Fe(II) concentrations (4.0 and 5.0 mg/L), the decrease in SMX is very rapid in the first minutes, reaching concentrations close to zero in approximately 5 min. Although it is necessary to consider that the presence of Fe(II) at higher concentrations accelerates the elimination of SMX, in excess it can generate unwanted effects such as radical recombination. After 10 min, the SMX concentration is practically zero under all experimental conditions, indicating that the process is efficient in degrading this contaminant. Figure 1: Scheme of the photocatalytic reactor for water oxidation. The photo-Fenton process is based on the combination of hydrogen peroxide and ferrous iron in the presence of UV radiation to generate hydroxyl radicals (Equation (1)), which are highly reactive species responsible for the degradation of SMX (Equation (2)). The main chemical reactions involved are outlined below [33]:  
_Fenton Reaction:_ In this reaction, ferrous ion acts as a catalyst and reacts with hydrogen peroxide to generate hydroxyl radicals. \[\mathrm{Fe^{2+}+H_{2}O_{2}\to Fe^{3+}+HO^{\bullet}+HO^{-}} \tag{1}\]  
_Hydroxyl radical attack on SMX_: Hydroxyl radicals oxidize SMX, breaking its chemical structure and generating degradation by-products. The combination of ferrous ion, hydrogen peroxide and UV radiation maximizes the production of radicals, promoting oxidation of the contaminant. \[\mathrm{SMX+HO^{\bullet}\stackrel{{\text{\tiny{SBXY}}}}{{ \rightarrow}}}\mathrm{Degradation\ products} \tag{2}\]  
_Regeneration of ferrous ion by UV radiation_: UV radiation promotes the regeneration of ferrous ion from ferric ion, allowing the cycle to continue and enhancing the production of hydroxyl radicals. \[\mathrm{Fe^{3+}+H_{2}O_{2}+hv\to Fe^{2+}+HO^{\bullet}_{2}+H^{+}} \tag{3}\]  
Compared to the classical Fenton process, the photo-Fenton process significantly enhances the generation of hydroxyl radicals by continuously regenerating Fe(II) through the photo-reduction of Fe(III) under UV light. This not only sustains the catalytic cycle but also prevents the accumulation of Fe(III), which can otherwise inhibit radical formation. Moreover, UV radiation can also directly photolyze hydrogen peroxide (Equation (4)), adding an additional pathway for radical generation. The synergistic effect of UV light and iron catalysis thus leads to a more efficient and sustained production of hydroxyl radicals, resulting in faster and more complete degradation of persistent pollutants like SMX. \[\mathrm{H_{2}O_{2}+hv\to 2 HO^{\bullet}} \tag{4}\]  
The results indicate that SMX degrades following first-order kinetics to degradation intermediates (Equation (2)) with a first-order kinetic constant \(\mathrm{k_{SMX}}\) (1/min). By establishing the material balance for SMX degradation (Equation (5)) and integrating the rate equation, the first-order kinetic equation for SMX degradation is obtained (Equation (6)), whose predictions based on experimental results are shown in Figure 2.  
Figure 2: Predictions of the first-order kinetic model for SMX oxidation by photo-Fenton.