## 4 Discussion
Figure 2c presents results from gravimetric analysis during current imposition, with and without UV light (solid and dashed lines, respectively). The solids formed and dispersed inside the reactor are associated with oxides formed at the anode. These solids are responsible for flocculating organic dye molecules, and the amount of solid produced is proportional to the TiO\({}_{2}\) generated electrochemically. The slope is observed to be 0.63 g \(\times\) mA\({}^{-1}\)\(\times\) cm\({}^{2}\), indicating a consistent relationship regardless of UV light imposition. Additionally, a slight increase in mass associated with heterogeneous flocculation of dyes is observed with UV light. Figure 2d illustrates the results of pH potentiometric analysis during current imposition, with and without UV light (solid and dashed lines, respectively). In both cases, a slight increase in pH with imposed current is observed due to the modification of the chemical composition of the solution. On the other hand, Figure 3 illustrates the degradation kinetics with and without the imposition of ultraviolet light (blue squares and red circles, respectively). Experimental data without UV light imposition were fitted using Equation (3), while Equation (4) was employed for fitting the data with UV light. Figure 2: Effect with (solid line) and without imposition (dashed line) of UV light and imposed current on (**a**) dye degradation, (**b**) cell potential, (**c**) recovered mass, and (**d**) pH. The kinetics observed in the electrochemical process without UV light is of zero order and relies on the electrolytic reaction of Ti\({}^{2+}\) production (Equation (5)) along with the chemical oxidation reaction of Ti\({}^{2+}\) with water to form TiO\({}_{2}\) (Equation (6)). Therefore, its electrochemical rate law (Equation (7)) can be expressed as the sum of both oxidation rates 1 and 2, yielding an electrochemical constant \(K_{d}\). This is expressed as the sum of the inverses of oxidation constants 1 and 2. Finally, by solving the differential equation of Equation (5), Equation (8) can be obtained, representing the kinetics. \[Ti_{s}\to Ti^{2+}+2e^{-} \tag{5}\]  
\[Ti^{2+}+2H_{2}O\to TiO_{2}+2e^{-}+4H^{+} \tag{6}\]  
\[v_{d}=\frac{d[TiO_{2}]}{dt}=(k_{ox_{1}}+k_{ox_{2}})\frac{j}{z\
ot{FA}} \tag{7}\]  
\[\left[n\right]_{t}=\left[n\right]_{0}-K_{el}\frac{jA}{zF}\ t \tag{8}\]  
On the other hand, for fitting the data when UV light is imposed, the activation of TiO\({}_{2}\) (h\(\
u\)) (Reaction 9) and its subsequent reaction with the dye (Reaction 10) are considered. Therefore, Reaction 11 represents the overall reaction of the reactor's operation, and its rate law is expressed in Equation (12). \[TiO_{2}+h\
u\to TiO_{2}(h\
u) \tag{9}\]  
\[TiO_{2}(h\
u)+n\to\ TiO_{2}+Degradation \tag{10}\]  
\[Ti_{s}+2H_{2}O+h\
u+Dye\to\ TiO_{2}+Degradation+4e^{-}+4H^{+} \tag{11}\]  
Figure 3: Reaction kinetics of the process with UV light imposition (blue squares) and without UV light (red circles), along with their fits using the kinetic models; electrochemical and photoelectrochemical (solid lines). \[v_{fel}=\left(\frac{1}{k_{ox_{1}}}+\frac{1}{k_{ox_{2}}}\right)\frac{jA}{zF}+k_{ ln}[TiO_{2}(hv)]+k_{deg}[TiO_{2}][Degradation] \tag{12}\]  
To solve Equation (12), the theory of activated complex is considered, where the concentrations of TiO\({}_{2}\) (hv) and Ti\({}^{2+}\) are constants, and their formation and consumption rates are assumed to be zero. For this, the chemical equilibrium of Reaction 6 is considered, as shown in Equation (13), and the value of the TiO\({}_{2}\) concentration in terms of Ti\({}^{2+}\) is obtained in Equation (14). Meanwhile, the concentration of Ti\({}^{2+}\) is obtained by considering its rate to be zero and is expressed in Equation (15), as its production and consumption are equal, representing the concentration of Ti\({}^{2+}\) in Equation (16).