## 1 Introduction
The identity of the oxidation product is highly dependent on pH, with proposed reaction pathways includinghydrolytic decomposition of the cyclic ester or direct cleavage by MnO\({}_{4}\)\({}^{-}\) to produce two formic acid molecules [41; 43]. Under certain conditions, all carboxylic intermediates may undergo further oxidation to carbon dioxide (CO\({}_{2}\)) [16; 39; 44]. In recent years, stable isotope fractionation has gained increasing attention as a tool to determine the magnitude and variability of transformation resulting from different degradation processes and environmental conditions [40; 42; 45; 46]. Compound-specific isotope analysis (CSIA) has emerged as a powerful analytical tool for evaluating the effectiveness of in situ remediation of organic contaminants at contaminated sites [29; 45; 47; 48]. This isotope analysis is commonly based on the Rayleigh model (Equation (2)), which describes the relationship between isotope fractionation and changes in contaminant concentration due to specific transformation mechanisms [48]. By applying values for \(\xi^{13}\)C\({}_{0}\) (initial isotope composition) and \(\xi^{13}\)C (remaining substrate isotope composition after reaction), along with the carbon isotope enrichment factor (\(\varepsilon\)) derived from laboratory experiments, the extent of contaminant transformation (B[%]) can be calculated using Equation (3). This enables a quantitative assessment of remediation performance [49; 50]. \[\mathrm{Inf}\times\frac{\varepsilon}{1000}=\mathrm{ln}\left(\frac{1000+\xi^{ 13}\mathrm{C}}{1000+\xi^{13}\mathrm{C}_{0}}\right) \tag{2}\]  
\[\mathrm{B[\%]}=\left(1-\frac{\mathrm{C}}{\mathrm{C}_{0}}\right)\cdot 100= \left[1-\left(\frac{1000+\xi^{13}\mathrm{C}}{1000+\xi^{13} \mathrm{C}_{0}}\right)^{\frac{1000}{\varepsilon}}\right]\cdot 100 \tag{3}\]  
where \(\xi^{13}\)C is the isotope ratio of the TCE at any given fraction of TCE remaining (\(f\)), and \(\xi^{13}\)C\({}_{0}\) is the initial value. Previous studies have documented carbon isotope fractionation during permanganate oxidation of TCE under varying concentrations of chloride, KMnO\({}_{4}\), and TCE [40]. However, the influence of environmental factors on isotope fractionation during this process remains unclear. The objective of this study was to evaluate the effect of environmental variables on carbon isotope fractionation during KMnO\({}_{4}\)-mediated degradation of TCE. Specifically, we examined the impact of varying KMnO\({}_{4}\) and TCE concentrations, the presence of HA, a broad pH range (2-12), and several common inorganic ions (NO\({}_{3}\)\({}^{-}\), HCO\({}_{3}\)\({}^{-}\), SO\({}_{4}\)\({}^{2-}\), and Cl\({}^{-}\)), which collectively represent typical environmental conditions in natural waters. HA may play a competitive role with TCE oxidized by KMnO\({}_{4}\) in this study due to its complex structure (high-molecular-weight subunits, carbon\(-\)carbon double bonds, \(\pi\)-electrons, and long conjugated bonds) [51; 52] Neglecting the influence of these environmental factors could introduce uncertainty in the application of stable carbon isotope analysis for evaluating ISCO performance. The findings of this study aim to support the reliable use of stable carbon isotope analysis as a quantitative tool for assessing ISCO-based remediation efforts. This study systematically explores the stable carbon isotope fractionation of TCE oxidized by KMnO\({}_{4}\) under different environmental conditions.