## 3 Results and Discussion  
### Initial Concentration of TCE and KMnO\({}_{4}\)  
Figure 1a,d showed that TCE removal efficiencies strongly depended on the initial concentrations of KMnO\({}_{4}\) and TCE. The TCE oxidation by KMnO\({}_{4}\) was monitored until its concentrations fell below the detection limit. As shown in Figure 1a, the half-lives of TCE degradation at KMnO\({}_{4}\) concentrations of 50, 150, 250 and 400 mg/L were approximately 120, 21, 15, and 12 min, respectively. Higher KMnO\({}_{4}\) concentrations led to faster degradation rates and higher final removal efficiencies, consistent with [PERSON] and Dong [44]. Figure 1d  
indicates that after 60 min, the removal efficiencies for initial TCE concentrations of 25, 75, 150, and 250 mg/L were 92%, 90%, 83%, and 74%, respectively. These results confirm that TCE removal is highly dependent on both the initial concentrations of KMnO\({}_{4}\) and TCE. In other words, the molar ratio of KMnO\({}_{4}\)/TCE can influence the removal efficiency. When 75 mg/L TCE was treated with 50-400 mg/L KMnO\({}_{4}\), the molar ratios of KMnO\({}_{4}\) to TCE (n(KMnO\({}_{4}\))/n(TCE)) ranged from 0.55-4.42. When 250 mg/L KMnO\({}_{4}\) was used with 25-250 mg/L TCE, the molar ratios ranged from 0.83-8.29. According to proposed mechanisms, the initial step of TCE oxidation involves cleavage of the C=C bond, forming an acyclic ester and consuming 1 mol of KMnO\({}_{4}\) per mol of TCE [41]. However, complete mineralization into CO\({}_{2}\) requires further oxidation of intermediate carboxylic acids (formic, oxalic and glyoxylic acids), consuming an additional 1 mol of KMnO\({}_{4}\)[16]. Thus, when n(KMnO\({}_{4}\))/n(TCE) exceeds 1, complete TCE removal can be achievable. This was observed for 75 mg/L TCE with KMnO\({}_{4}\) concentrations of 150-400 mg/L. However, with only 50 mg/L KMnO\({}_{4}\) (n(KMnO\({}_{4}\))/n(TCE) = 0.55), the removal efficiency dropped to around 50%, even though the molar ratio is close to the theoretical 1:1 for the first oxidation step. Interestingly, 250 mg/L (1.58 mM) KMnO\({}_{4}\) was able to degrade 250 mg/L (1.91 mM) TCE with 88.5% efficiency, despite a sub-stoichiometric molar ratio of 0.83. This suggests additional degradation pathways may be at play, such as the involvement of MnO\({}_{2}\), a byproduct of KMnO\({}_{4}\) which can further oxidize TCE [55]. The decreasing reaction rate at higher TCE concentrations may result from increased MnO\({}_{2}\) colloid formation, which contributes to oxidation but may also limit accessibility or slow reaction dynamics. Although high KMnO\({}_{4}\) concentrations improved the degradation rate, their effect on carbon isotope fractionation was investigated through the enrichment factor \(\varepsilon\) values. Figure 1: **(a)** Effect of initial concentrations of KMnO\({}_{4}\) on the oxidative degradation of TCE in the KMnO\({}_{4}\) reaction. **(b)** The evolution of \(\xi^{13}\)C values of TCE with initial concentrations of KMnO\({}_{4}\). **(c)** The variation of Rayleigh plots of TCE with respect to initial concentrations of KMnO\({}_{4}\). Experimental boundary conditions: [TCE]\({}_{0}\) = 75 mg/L at initial suspension pH 8. **(d)** Effect of initial concentrations of TCE on the oxidative degradation of TCE in the KMnO\({}_{4}\) reaction. **(e)** The evolution of \(\xi^{13}\)C values of TCE with initial concentrations of TCE. **(f)** The variation of Rayleigh plots of TCE with respect to initial concentrations of TCE. Experimental boundary conditions: [KMnO\({}_{4}\)]\({}_{0}\) = 250 mg/L at initial suspension pH 8. As shown in Figure 1b,e, \(\delta^{13}\)C values of TCE changed with increasing KMnO4 and TCE concentrations. Figure 1c shows \(\varepsilon\) values increasing from \(-25.2\)\(\pm\) 1.3% to \(-22.8\)\(\pm\) 0.9% as KMnO4 concentration increased from 50-400 mg/L. In contrast, Figure 1f shows a slight decreasing trend in \(\varepsilon\) value from \(-22.9\)\(\pm\) 1.1% to \(-26.5\)\(\pm\) 0.5% as initial TCE concentrations increased from 25-250 mg/L.