## 3 Results and Discussion
The results indicate that the photocatalytic activity of FS-NT (3 mL) was very stable. The first-order kinetic model is given by the following:  
\[\ln(\frac{C_{0}}{C_{t}})=kt \tag{3}\]  
where \(t\) (minutes) is the reaction time, \(k\) is the rate constant, and \(C_{0}\) (mg L\({}^{-1}\)) and \(C_{t}\) (mg L\({}^{-1}\)) are the same as those in Equation (1). As shown in Figure 9, the kinetic curves were highly linear, and the correlation coefficients (R\({}^{2}\)) was close to 1. This means that the photocatalytic reaction followed the first-order reaction kinetic model. The initial rate constant \(k\) was obtained using experimental data up to 24 min of simulated irradiation because subsequent data seemed to deviate from the linear plot of \(\ln(C_{0}/C_{t})\) vs. t, owing to the decreasing MO concentration in the  
Figure 7: UV-VIS spectra of MO in MO-Na\({}_{2}\)SO\({}_{4}\) solution after the photocatalytic degradation reaction by (**a**) FS-NT (0 and 2-5 mL). (**b**) Time-dependent UV-VIS spectra of MO degraded by a random batch of FS-NT (3 mL) in MO-Na\({}_{2}\)SO\({}_{4}\) during the photocatalytic degradation process. (**c**) The average degradation rate of MO degraded by three different batches of FS-NT (0 and 2–5 mL) in MO-Na\({}_{2}\)SO\({}_{4}\) solution. bulk solution. The rate constant \(k\) of FS-NT (0 mL) and FS-NT (3 mL) in pure MO solution were calculated to be 0.0575 and 0.08114 min\({}^{-1}\), respectively. By comparing the \(k\) values, it was evident that N doping could improve photocatalytic activity. The corresponding degradation rate constant \(k\) values of FS-NT (0 mL) and FS-NT (3 mL) in the MO-Na\({}_{2}\)SO\({}_{4}\) mixed solution were calculated to be 0.07334 and 0.08209 min\({}^{-1}\), respectively. The results indicate that FS-NT (3 mL) showed better performance in the MO-Na\({}_{2}\)SO\({}_{4}\) mixed solution. Comparing the \(k\) values of the MO and MO-Na\({}_{2}\)SO\({}_{4}\) tests, it was seen that Na\({}_{2}\)SO\({}_{4}\) could accelerate the reaction rate. Figure 10 shows the schematic diagram of the photocatalytic degradation mechanism of MO in pure MO solution. Photogenerated holes (h\({}^{+}\)) can oxidize OH- and H\({}_{2}\)O molecules to produce -OH and -O\({}_{2}\)-. Photogenerated electrons (e\({}^{-}\)) can indeed react with dissolved oxygen in water, leading to the formation of superoxide radicals -O\({}_{2}\)-, which can react with H\({}_{2}\)O to form -OH [41]. As shown in Figure 10, doping with appropriate N content may introduce lattice defects and oxygen vacancies in the photocatalyst. These lattice defects and oxygen vacancies can enhance the visible light absorption ability of photocatalysts, which can improve the photocatalytic degradation effect [42]. The TOC  
Figure 8: The degradation rate of MO in MO-Na\({}_{2}\)SO\({}_{4}\) by (**a**) FS-NT (0 mL) and (**b**) FS-NT (3 mL) for five cycles. Figure 10: Linear fitting of first-order kinetics. Figure 9: Linear fitting of first-order kinetics. pure MO solution, 3.425 mg/L after degradation by FS-NT (0 mL) in pure MO solution, and 5.089 mg/L after degradation by FS-NT (3 mL) in pure MO solution. Combined with the results of Figure 5, the results suggest that FS-NT (3 mL) has good decolorization ability, but its ability to completely degrade MO is weak. Figure 11 shows the schematic diagram of the photocatalytic degradation mechanism of MO in the MO-Na\({}_{2}\)SO\({}_{4}\) mixed solution. Under high-pressure mercury lamp irradiation, on the one hand, -OH and -O\({}_{2}\)- were produced, and on the other hand, SO\({}_{4}\)2- was adsorbed on the surface of the photocatalyst, and SO\({}_{4}\)2- reacted with h\({}^{+}\) to produce SO\({}_{4}\)-, as shown in Figure 11. Thus, SO\({}_{4}\)- and -OH jointly participated in the redox reaction. Dye will be oxidized by free radicals in solution or on the surface of the photocatalyst and SO\({}_{4}\)-, which will increase the reaction rate [39].