## 3 Results and Discussion
As the concentration of Na\({}_{2}\)SO\({}_{4}\) increases, SO\({}_{4}\)\({}^{2-}\) robs the active sites on the photocatalyst and reacts with h\({}^{+}\), thus reducing the interaction between the dye and h\({}^{+}\) and inhibiting photocatalytic efficiency. AlthoughSO\({}_{4}\bullet^{-}\) can degrade dyes, photogenerated electrons play a key role [24]. Thus, the rate of photocatalytic removal of MO in MO-Na\({}_{2}\)SO\({}_{4}\)-blended solution decreases with the boost in the concentration of Na\({}_{2}\)SO\({}_{4}\)[25]. Figure 10 illustrates a linear fit of the first-order kinetics. The degradation reaction rate constant, \(k\), is identified using Equation (3):  
\[\text{ln}(\frac{C_{0}}{C_{t}})=kt \tag{3}\]  
In this equation, \(k\) signifies the degradation rate constant, t corresponds to the exposure time, \(C_{0}\) represents the initial concentration of MO, and \(C_{t}\) represents the concentration of MO at time \(t\). The degradation efficiency constant \(k\) was calculated in relation to time \(t\). Plotting in relation to time t in terms of \(\text{ln}(C_{0}/C_{t})\), and thus calculating the incline of the best-fit straight line, yields a rate constant for each sample, \(k\)[40]. Figure 10 illustrates that the kinetic curve is nearly linear, with a correlation coefficient (R\({}^{2}\)) approaching 1. This observation confirms that the photocatalytic process is governed by a first-order kinetic  
Figure 10: First-order kinetics linear fitting. Figure 9: Degradation rate in different concentrations of MO-Na\({}_{2}\)SO\({}_{4}\) using FS-FT (0.36 g). model. The first-order rate constants k for FS-FT (0 g) and FS-FT (0.36 g) in pure MO solution were determined as 0.08181 and 0.12686. A comparison of these \(k\) values clearly shows that Fe doping enhances photocatalytic activity. The first-order rate constants k for FS-FT (0 g) and FS-FT (0.36 g) in MO-Na\({}_{2}\)SO\({}_{4}\)-blended solution were determined as 0.09121 and 0.11097. This suggests that the inclusion of Na\({}_{2}\)SO\({}_{4}\) suppresses the photocatalytic efficiency of FS-FT (0.36 g); however, FS-FT (0.36 g) still maintains good photocatalytic performance. According to the literature, the role of Fe\({}^{3+}\) ions is twofold: firstly, the absorbed wave shifts towards longer wavelengths due to ionic doping; secondly, at appropriate concentrations, Fe\({}^{3+}\) also serves as a carrier for hole and electron transport [41]. Figure 11 illustrates the photodegradation principle of MO using FS-FT (0.36 g). Photogenerated holes (h\({}^{+}\)) oxidize the adsorbed hydroxyl (OH) and water (H\({}_{2}\)O) molecules on the TiO\({}_{2}\) surface, resulting in the production of hydroxyl radicals (\(\bullet\)OH) and superoxide anions (O\({}_{2-}\)). Photoinduced electrons (e\({}^{-}\) react with dissolved oxygen in the aqueous medium via a single-electron transfer process, producing superoxide radical anions (\(\bullet\)O\({}_{2}\)\({}^{-}\)) as intermediates. The introduction of an appropriate amount of Fe doping as an intermediary for the transport of photogenerated carriers effectively reduces their recombination and thereby enhances the degradation efficiency of the FS-FT (0 g) system in the degradation of MO [40]. Figure 12 illustrates the photodegradation principle of MO-Na\({}_{2}\)SO\({}_{4}\)-blended solution using FS-FT (0.36 g). The introduction of Na\({}_{2}\)SO\({}_{4}\) resulted in a significant increase in SO\({}_{4}\)\({}^{2-}\), which adsorbed onto the photocatalyst surface, functioning as a pore-trapping agent. This interaction facilitated the combination of sulfate ions with photogenerated holes to produce SO\({}_{4}\)\({}^{-}\)\(\bullet\)[42]. Fe\({}^{3+}\) ions reacted with free electrons to form Fe\({}^{2+}\), and Fe\({}^{3+}\) plays a crucial role in the photodegradation process. However, the decrease in Fe\({}^{3+}\) and free electron concentration negatively affects the performance of photocatalysis.