Unraveling the Kinetics and Mechanism of Ethane Chlorination in the Gas Phase

Abstract

The selective chlorination of ethane to 1,2-dichloroethane offers a promising route for upgrading ethane, yet its efficiency remains constrained by limited mechanistic insights into gas-phase chlorine-radical-mediated pathways, which govern target product selectivity and competing dehydrochlorination side reactions. This work systematically decouples the kinetics of ethane chlorination and chloroethane functionalization under varying Cl₂ concentrations, revealing that chlorine radicals govern product distribution through thermodynamically favored pathways. This results in an interesting phenomenon whereby the product ratio between 1,1-C₂H₄Cl₂ and 1,2-C₂H₄Cl₂ maintains a constant 2:1 stoichiometry regardless of Cl₂ concentration variation. A critical observation is that the rate of all chlorination steps remains independent of alkane concentrations, highlighting the dominant role of chlorine radicals in rate-determining steps. Furthermore, ethylene byproducts are demonstrated to originate from the dechlorination of chlorine-radical-induced 2-chloroethyl radicals derived from chloroethane, rather than the direct dehydrochlorination of chloroethane itself. These insights into the dual role of chlorine radicals—mediating both the chlorination and dehydrochlorination pathways—establish a foundational framework for integrating gas-phase radical chemistry with catalytic engineering strategies to suppress undesired side reactions and enable scalable, selective ethane chlorination.

1. Introduction

As the second most abundant component of natural gas, ethane (C₂H₆) has great potential as a source for producing higher–value petrochemical feedstocks, such as light olefins, oxygenates, and aromatic hydrocarbons [1,2,3,4,5]. However, several challenges exist in C₂H₆ conversion. The C–H bonds in C₂H₆ are highly stable, with a dissociation energy of 423.2 kJ/mol [6,7,8]. Developing effective C–H activation methods is crucial for its utilization. Oxygen-assisted C–H bond dissociation has been studied to selectively synthesize ethylene (C₂H₄) from C₂H₆ at lower temperatures [9,10,11]. Yet, C₂H₄ is more reactive than C₂H₆, leading to inevitable over–oxidation [12,13,14]. Despite over 50 years of research on C₂H₆ oxidative dehydrogenation, selectivity limitations due to over–oxidation have made the industry rely on cracking methods. These endothermic methods, operating above 900 °C, are highly energy–intensive and produce large amounts of CO₂ [15,16]. There is an urgent need to develop new low-temperature C₂H₆ conversion routes for producing chemical industry platform molecules, which is extremely important for the future of natural–gas-based chemistry [17,18].

Recently, Pérez-Ramírez and colleagues pioneered a catalytic process for the selective synthesis of 1,2-dichloroethane (1,2-C₂H₄Cl₂) via C₂H₆ chlorination under mild conditions [19]. This innovative strategy holds transformative potential for large–scale C₂H₆ valorization, as 1,2-C₂H₄Cl₂ serves as the primary precursor for commercial polyvinyl chloride (PVC)—a commodity chemical with an annual demand of 60 million tons, currently reliant on coal– and petroleum–derived feedstocks [20,21,22,23,24,25,26,27]. The downstream steps of this process leverage established industrial technologies, including cracking of 1,2-C₂H₄Cl₂ to vinyl chloride (C₂H₃Cl) and HCl, Cl₂ recovery from HCl via the Deacon process, and the polymerization of C₂H₃Cl [28,29]. Rare-earth oxyhalides exhibit exceptional structural stability in harsh (oxy)chlorination reactions, a property rooted in the thermodynamically unfavorable chlorination of rare-earth elements compared to transition metals under moderate-to-high temperatures [26,30]. Such robustness enables the retention of unsaturated metal cations with unpaired electrons on catalyst surfaces, which activate alkanes or alkyl halides while avoiding structural degradation into inactive chlorides [31,32,33]. These attributes have propelled rare-earth oxychlorides—particularly europium oxychloride—to the forefront of C₂H₆ chlorination, achieving 90% selectivity with stable performance over 40 h [19]. However, their industrial deployment remains limited by the necessity to operate at sub–20% C₂H₆ conversion and Cl₂-lean concentrations to maintain high 1,2-C₂H₄Cl₂ selectivity. Since its initial discovery by Pérez-Ramírez in 2021, this field has witnessed no substantive breakthroughs, highlighting the persistent challenges in efficiently converting C₂H₆ to target chlorocarbons.

In the chlorination of C₂H₆, gas-phase free radicals pose a critical challenge to improving catalyst performance. Cl₂, when thermally induced to dissociate, generates Cl radicals capable of abstracting hydrogen from C₂H₆ at low temperatures to form ethyl radicals [34]. These ethyl radicals can then react with Cl radicals to form chloroethane (C₂H₅Cl), offering a potential route for low-temperature C₂H₆ conversion [35,36]. However, hydrogen atoms in C₂H₅Cl can be further abstracted by Cl radicals, producing 1-chloroethyl and 2-chloroethyl radicals, with product distribution primarily governed by thermodynamic factors [37,38]. At high temperatures, these chlorinated alkyl radicals undergo dehydrogenation and further chlorination, forming complex reaction networks of competing chlorination and dehydrochlorination pathways (Figure 1a,b). Importantly, the dynamics of these elementary processes may vary under different temperatures and reactant atmospheres, but this knowledge remains incomplete. A thorough understanding of gas-phase chlorine radical behavior is critical for guiding subsequent catalyst design. Through the strategic coupling of gas-phase radicals with catalytic interfaces, we can achieve the selective synthesis of 1,2-dichloroethane (1,2-C₂H₄Cl₂) while suppressing undesired side reactions—such as over-chlorination or dehydrochlorination—that arise from gas-phase chlorine radical pathways. In this study, we systematically examined the kinetics of key elementary steps—including C₂H₆ chlorination, C₂H₅Cl chlorination, and C₂H₅Cl dehydrochlorination-across varied temperatures and pressures. Our results demonstrate that all chlorination steps exhibit low dependence on alkane concentrations, confirming that chlorine radicals are the dominant species governing rate-determining hydrogen abstraction. Furthermore, mechanistic evidence reveals that ethylene byproducts predominantly form via the dechlorination of chlorine-radical-generated 2-chloroethyl radicals (derived from chloroethane intermediates) rather than through the direct dehydrochlorination of chloroethane. These findings elucidate the dual functionality of chlorine radicals in simultaneously mediating both the chlorination and dehydrochlorination pathways. These insights provide a foundational framework for strategically coupling gas-phase radical dynamics with catalytic engineering approaches, enabling the suppression of undesirable side reactions while achieving high 1,2-C₂H₄Cl₂ selectivity at industrially relevant ethane conversion levels.

2. Results

2.1. Temperature-Dependent Ethane Chlorination

The chlorination of C₂H₆ is a stepwise process, and the ratio of C₂H₆ to chlorine (Cl₂) has a critical impact on the product distribution. In our experimental design, we maintained a fixed ethane concentration of 4 vol.% in the feed gas while systematically investigating conversion efficiency and product distribution patterns across varying Cl₂ concentration gradients (4–12 vol.%). Figure 2a shows a clear linear correlation between C₂H₆ conversion rates and Cl₂ concentrations. Increasing the Cl₂ partial pressure significantly enhances C₂H₆ conversion, particularly under low-temperature conditions. For example, at 240 °C, when the Cl₂ concentration increases from 4 vol.% to 12 vol.%, the C₂H₆ conversion rate sharply rises from 10% to 33%. This critical role of Cl₂ in the reaction is further supported by its reaction order, which can reach as high as 1.25 according to kinetic studies (Figure 2b). Interestingly, our experiments revealed that altering the Cl₂ concentration does not significantly affect the activation energy for C₂H₆ conversion, indicating that the reaction mechanism remains unchanged despite variations in Cl₂ concentration (Figure 2c). These results suggest that Cl₂ concentration plays a vital role in promoting chlorine radical proliferation in the gas phase, making it a key and effective method for achieving high-efficiency C₂H₆ conversion under low-temperature conditions.

At temperatures below 240 °C, the products of C₂H₆ chlorination are primarily C₂H₅Cl (with selectivity exceeding 90%) and are minimally influenced by Cl₂ partial pressure. This indicates that the further chlorination of C₂H₅Cl requires a higher activation energy barrier, consistent with chlorinated alkane reactivity decreases with increasing chlorine substitution [35]. Increasing the reaction temperature significantly promotes the further chlorination of C₂H₅Cl, but the product distribution is determined by the Cl₂ concentration. Under the reaction condition of C₂H₆/Cl₂ at a 4:4 ratio, as the temperature rises, the further chlorination of C₂H₅Cl is gradually initiated (Figure 2d). In this process, 1,1-C₂H₄Cl₂ and 1,2-C₂H₄Cl₂ are almost simultaneously generated, but the formation rate of 1,1-C₂H₄Cl₂ is approximately twice that of 1,2-C₂H₄Cl₂. Increasing the Cl₂ partial pressure significantly enhances the chlorination of C₂H₅Cl, shifting the generation curve of dichloroethane to lower temperatures. Notably, the product ratio between 1,1-C₂H₄Cl₂ and 1,2-C₂H₄Cl₂ maintains a constant 2:1 stoichiometry regardless of Cl₂ concentration variation. This phenomenon originates from the regioselective nature of chlorine radical (Cl·)–mediated hydrogen abstraction in gas-phase chlorination. During C₂H₅Cl chlorination, Cl· preferentially abstracts α–H from the chlorine-substituted carbon atom (C–Cl site), generating the thermodynamically favored 1-chloroethyl radical intermediate, which is approximately 15 kJ/mol more stable than the 2-chloroethyl isomer [37,39].

It is noteworthy that under Cl₂-lean conditions (C₂H₆/Cl₂ = 4/4), elevated temperatures enhance C₂H₆ conversion but deplete Cl₂ in the feedstock, thereby suppressing further chlorination of C₂H₅Cl and favoring its decomposition to C₂H₄ (Figure 2d). Our analysis of product distribution reveals that during C₂H₅Cl chlorination, both 1-chloroethyl and 2-chloroethyl radicals are involved. The latter undergoes preferential dechlorination, serving as the primary precursor for ethylene formation. This mechanistic insight explains the experimental observation where C₂H₄ generation coincides with the disappearance of 1,2-C₂H₄Cl₂ (Figure 2d). Under stoichiometric conditions (C₂H₆/Cl₂ = 4/8), C₂H₅Cl readily undergoes chlorination to form dichloroethane. At temperatures exceeding 300 °C, the simultaneous decomposition of 1,1-C₂H₄Cl₂ and 1,2-C₂H₄Cl₂ is activated, accompanied by C₂H₃Cl production. Further increasing the temperature to 320 °C triggers the decomposition of trichloroethane (C₂H₃Cl₃) and tetrachloroethane (C₂H₂Cl₄), leading to the significant formation of dichloroethylene (C₂H₂Cl₂) and trichloroethylene (C₂HCl₃) as byproducts. Conversely, under Cl₂-rich conditions (C₂H₆/Cl₂ = 4/12), temperature elevation predominantly induces the over-chlorination of dichloroethane, while its decomposition is markedly suppressed. Notably, tetrachloroethane (C₂H₂Cl₄) exhibits extreme thermal instability above 300 °C, decomposing to generate C₂HCl₃. Consequently, C₂H₃Cl₃ and C₂HCl₃ dominate the byproduct profile under Cl₂-rich environments.

These experimental results demonstrate that under high-temperature conditions, chlorinated products undergo further chlorination and dehydrochlorination is governed by the Cl₂ concentration. These findings prompted us to further investigate the impact of C₂H₆ concentration on product distribution by maintaining a fixed Cl₂ partial pressure of 8 vol.%. The results are shown in Figure 3. As indicated in Figure 3a, unlike Cl₂, increasing C₂H₆ partial pressure significantly reduces the equilibrium conversion of C₂H₆. The kinetic analysis reveals that changes in C₂H₆ concentration have little effect on the intrinsic conversion frequency (Figure 3b). This suggests that the chlorination of C₂H₆ is primarily driven by chlorine radicals. This conclusion is further supported by the results in Figure 3c, which show that altering C₂H₆ concentration has minimal impact on the activation energy for C₂H₆ chlorination.

Across all experimental conditions examined, the 1,1-C₂H₄Cl₂ isomer exhibited a consistent twofold formation rate advantage over the 1,2-C₂H₄Cl₂ isomer. This observation provides additional evidence that the chlorine-radical-mediated substitution of α–H in C₂H₅Cl proceeds exclusively through a thermodynamically controlled reaction pathway. When the ratio of C₂H₆ to Cl₂ was 6:8, we again observed, at temperatures above 320 °C, that C₂H₄ production was negatively correlated with the formation of 1,2-C₂H₄Cl₂ (Figure 3d). This suggests that 2-chloroethyl radicals are unstable and tend to decompose rather than further chlorinate to form 1,2-C₂H₄Cl₂ at high temperatures. The comparative analysis of the 8:8 versus 4:4 feed ratios reveals an interesting trend: despite maintaining stoichiometric equivalence (C₂H₆:Cl₂ = 1:1), elevated Cl₂ partial pressure promotes progressive chlorination of C₂H₅Cl, thereby inducing competitive Cl₂ consumption (Figure 2d and Figure 3e). This cascade effect ultimately suppresses ethane conversion under the 8:8 condition. Unexpectedly, under Cl₂-lean conditions where the C₂H₆-to-Cl₂ ratio is less than 1, the decomposition of C₂H₅Cl is well-suppressed even when the temperature is increased to 400 °C (Figure 3f). In contrast, under Cl₂-rich conditions (C₂H₆-to-Cl₂ ratio of approximately 1:2), the decomposition of C₂H₅Cl begins at 320 °C and significantly intensifies with increasing temperature. This indicates that C₂H₄ byproducts are not directly generated through the thermal decomposition of C₂H₅Cl, but rather, originate from 2-chloroethyl radicals, which will be discussed in detail in Section 2.2.

2.2. Temperature-Dependent Chloroethane Chlorination

As demonstrated by the experiments, the chlorination of C₂H₆ proceeds stepwise, initially forming C₂H₅Cl, followed by subsequent chlorination or dehydrochlorination side reactions. To further elucidate the factors governing the reaction kinetics of C₂H₅Cl, we systematically investigated its reactivity under varying Cl₂ concentrations (5–8 vol.%) while maintaining a fixed C₂H₅Cl concentration of 5 vol.%. As illustrated in Figure 4a, the light–off curves demonstrate that the chlorination of C₂H₅Cl is highly dependent on Cl₂ concentration, with the onset temperature for chlorination shifting significantly toward lower temperatures as the Cl₂ concentration increases. This observation aligns with the kinetic analysis results, which revealed a reaction order of 1.4 for Cl₂, highlighting its pivotal role in promoting further chlorination of C₂H₅Cl (Figure 4b). Notably, the higher reaction temperature required for chloroethane chlorination compared to ethane chlorination to chloroethane could also be attributed to its smaller kinetic constant, as increasing the chlorine concentration has minimal impact on the activation energy of chloroethane chlorination (164 ± 20 vs. 154 ± 15 kJ/mol) but significantly enhances the low-temperature conversion rate.

In all ranges of Cl₂ concentration, the initial chlorination products of C₂H₅Cl are primarily 1,1-C₂H₄Cl₂, which is twice the amount of 1,2-C₂H₄Cl₂. Interestingly, the product distribution at high temperatures is significantly influenced by Cl₂ concentration. Under Cl₂-lean conditions (C₂H₅Cl/Cl₂ = 5/5 vol./vol.), C₂H₄ and C₂H₃Cl as byproducts are observed at 300 °C, and their formation is significantly enhanced with increasing temperature, accompanied by the substantial consumption of dechlorinated products (Figure 4d). In contrast, under Cl₂-rich conditions (C₂H₅Cl/Cl₂ = 5/8), high temperatures induced the overchlorination of dichloroethane, resulting in products primarily consisting of trichloro and tetrachloroethanes (Figure 4f). These compounds further decomposed to form byproducts such as dichloroethylene and trichloroethylene. These phenomena demonstrate that dehydrohalogenation side reactions of chlorinated alkanes in the presence of Cl₂ are unavoidable. The resulting unsaturated chlorinated hydrocarbons can remain stable under a Cl₂ atmosphere. This poses a significant challenge for designing efficient catalysts targeting selective C₂H₆ chlorination to 1,2-C₂H₄Cl₂, as such unsaturated compounds readily induce catalyst poisoning and deactivation.

With the Cl₂ concentration fixed at 4 vol.%, we further investigated the reaction kinetics of C₂H₅Cl chlorination under varying C₂H₅Cl concentrations. Figure 5a shows that higher C₂H₅Cl concentrations significantly reduce the equilibrium conversion, yet have a limited effect on the low-temperature conversion. This behavior stems fundamentally from the stoichiometric effect—specifically, excess reactant ratios (e.g., higher Cl₂/C₂H₅Cl) will thermodynamically favor higher conversion of the C₂H₅Cl reactant. Kinetic studies indicate a reaction order of 0.35 for C₂H₅Cl (Figure 5b), further confirming that Cl₂ concentration is the main governing factor in the chlorination process. Combined with kinetic data from C₂H₆ chlorination to C₂H₅Cl, these results conclusively demonstrate that the overall rate of C₂H₆ chlorination to dichloroethane is primarily dictated by Cl₂ concentration. An Arrhenius analysis further confirmed that variations in C₂H₅Cl concentration exerted negligible effects on the activation energy of C₂H₅Cl chlorination (Figure 5c).

The chlorination product distribution of C₂H₅Cl exhibits pronounced concentration dependence and temperature-responsive behavior. At low temperatures, the primary products of C₂H₅Cl chlorination are 1,1-C₂H₄Cl₂ and 1,2-C₂H₄Cl₂. However, at high temperatures, the product distribution is governed by the C₂H₅Cl-to-Cl₂ feed ratio. At a C₂H₅Cl/Cl₂ ratio of 4/4 (Figure 5d), as the temperature rises to 280 °C, the dehydrochlorination of C₂H₅Cl is significantly activated. Meanwhile, dichloroethane tends to convert into trichloroethane, accompanied by dehydrochlorination, and by-products like dichloroethylene can be detected in the exhaust gas. Interestingly, when the Cl₂ concentration is reduced (Figure 5e,f), the decomposition of C₂H₅Cl to ethylene is almost unaffected, but the over-chlorination and decomposition of dichloroethane are markedly suppressed, with this inhibition intensifying as Cl₂ concentration further decreases. This indicates that hydrogen on C₂H₅Cl is more easily abstracted by chlorine radicals than that on polychlorinated alkanes. This higher reactivity of C₂H₅Cl allows it to act as a competitive molecule, inhibiting the further conversion of dichloroethane (including over-chlorination or dehydrochlorination). Maintaining a certain amount of C₂H₅Cl in the atmosphere can enhance dichloroethane selectivity. However, the decomposition of C₂H₅Cl under a Cl₂ atmosphere presents new challenges for designing C₂H₆ chlorination catalysts. Specifically, reducing the Cl₂ concentration may suppress the over-chlorination of dichloroethane, but the Cl₂ concentration must be carefully optimized. This is because dehydrochlorination side reactions of C₂H₅Cl will significantly increase, producing unsaturated hydrocarbons, which have a critical impact on the lifespan of the catalyst.

Notably, the thermal decomposition of C₂H₅Cl is markedly inhibited in chlorine-free environments, even at elevated temperatures (400 °C, Figure 6a). This phenomenon clearly demonstrates that ethyl chloride itself exhibits excellent stability under the tested conditions. This behavior originates from the intrinsic bond strength of its carbon–chlorine (C–Cl) and carbon–hydrogen (C–H) bonds. In the absence of an external reactive species, the energy provided by the temperature of 400 °C is not sufficient to break these bonds. Conversely, when Cl₂ is introduced, Cl₂ molecules absorb energy and dissociate into highly reactive chlorine radicals. These radicals exhibit strong electrophilicity due to their unpaired electrons. Upon encountering C₂H₅Cl molecules, they abstract a hydrogen atom from C₂H₅Cl, mediating the formation of 2-chloroethyl radicals.

Under elevated temperatures in chlorine-lean environments, these intermediates predominantly undergo dechlorination to yield ethylene rather than participating in further chlorination pathways to produce 1,2-C₂H₄Cl₂ (Figure 6b). In Cl₂-lean conditions, insufficient Cl₂ molecules are available for the 2-chloroethyl radicals to engage in sequential chlorination. Instead, the 2-chloroethyl radicals undergo intramolecular electronic rearrangement, which weakens the α–C–Cl bond. This facilitates the loss of a chlorine atom, yielding an ethylene molecule and regenerating a chlorine radical. Thermodynamically, this pathway is favored under these conditions due to the significant energy release associated with ethylene formation. This understanding of chlorine-radical-induced dechlorination reactions is crucial for optimizing reaction conditions and designing superior C₂H₆ chlorination catalysts.

3. Materials and Methods

The catalytic tests were performed at ambient pressure in a continuous-flow fixed-bed reactor set-up (Figure 7). The quartz tubular reactor (internal diameter d_i = 8 mm, L = 450 mm) was loaded and placed in an electrical oven. The furnace maintained an isothermal zone (±1 °C) over a 40 mm length. To ensure efficient heating of the feed gas, the quartz tube was packed with a 40 mm layer of quartz wool, as illustrated in Figure 7. A K-type thermocouple fixed in a coaxial quartz thermowell with the tip positioned in the center of the bed was used to monitor the temperature during the reaction. The bed was then heated in the reaction gas (15 mL/min) to the desired temperature (200–400 °C) and stabilized for at least 30 min, and the reaction tail gas was subsequently analyzed. Unless otherwise specified, all thermal treatment processes were carried out with a heating rate of 5 K·min⁻¹.

The gases C₂H₆, C₂H₅Cl, Cl₂, and N₂ (carrier gas) were fed by digital mass flow controllers (Bronkhorst^®, Veenendaa, The Netherlands) to a mixing unit. The effluent gas stream was neutralized by passing it through an impinging bottle containing a saturated NaOH solution. The content of the carbon–containing compounds (C₂H₆, C₂H₄, and their chlorinated derivatives) in the reactor-outlet gas stream were analyzed online by an Agilent 7890B gas chromatograph (GC, manufactured in Santa Clara, CA, USA) equipped with an HP-PLOT Q capillary column and an FID detector. For highly chlorinated products (e.g., C₂H₂Cl₂, C₂HCl₃), additional structural identification was performed by gas chromatography coupled with quadrupole time-of-flight high-resolution mass spectrometry (GC-QTOF HRMS, Agilent7250GC/Q-TOF, manufactured in Santa Clara, CA, USA). All kinetic parameters (e.g., activation energy and reaction orders) were derived from reaction rates measured at low conversion levels (<10%) to ensure a nearly constant reaction rate in the entire reactor volume.

The conversion of reactant i, X(i) (i: C₂H₆, C₂H₅Cl), was calculated from the following equation:

$$\mathrm{X}\left(\mathrm{i}\right)={\displaystyle \frac{\mathrm{n}{\left(\mathrm{i}\right)}^{\mathrm{inlet}}-\mathrm{n}{\left(\mathrm{i}\right)}^{\mathrm{outlet}}}{\mathrm{n}{\left(\mathrm{i}\right)}^{\mathrm{inlet}}}}·100\%$$

where n(i)^inlet and n(i)^outlet are the molar flows of the reactant i at the inlet and outlet of the reactor, respectively. The selectivity (S(j)) of product j (j: C₂H₄, C₂H₅Cl, C₂H₃Cl, 1,1-C₂H₄Cl₂, 1,2-C₂H₄Cl₂, and 1,1,2-C₂H₃Cl₃, etc.) was determined from the following equation:

$$\mathrm{S}\left(\mathrm{j}\right)={\displaystyle \frac{\mathrm{n}{\left(\mathrm{j}\right)}^{\mathrm{outlet}}·N_C\left(\mathrm{j}\right)}{\sum n{\left(\mathrm{j}\right)}^{\mathrm{outlet}}·N_C\left(\mathrm{j}\right)}}·100\%$$

where n(j)^outlet is the molar flow of the product j at the reactor outlet, and N_C(j) is the number of carbon atoms in the compound j.

The reaction order is typically determined experimentally using the rate expression:

$$r=k\cdot {\left[A\right]}^m{\left[B\right]}^n$$

where r is the reaction rate, k is the rate constant, and m and n represent the partial reaction orders with respect to reactants A and B, respectively. The initial reaction rate is measured by varying the initial concentration of one reactant while keeping the concentrations of the other reactants constant. The reaction order for a specific reactant is the slope derived from the logarithmic relationship:

$$\ln r=\ln k+m\cdot \mathit{ln}\left[A\right]+n\cdot \mathit{ln}\left[B\right]$$

The activation energy (Ea) is calculated using the Arrhenius equation:

$$k=A\cdot e^{-E_a/\left(RT\right)}$$

where k is the rate constant, A is the pre-exponential factor, R is the gas constant (8.314 J·mol⁻¹·K⁻¹), and T is the temperature in Kelvin. By measuring rate constants (k) at multiple temperatures, Ea can be determined from the linearized form:

$$\mathit{ln}k=\mathit{ln}A-{\displaystyle \frac{E_a}{R}}\times {\displaystyle \frac{1}{T}}$$

A plot of lnk versus 1/T (Arrhenius plot) yields a straight line with slope (−Ea/R), allowing Ea to be derived.

In a real experiment, both reaction orders and activation energies were calculated based on the average turnover frequencies (TOF) obtained at low conversion levels. The turnover frequency (TOF) can be calculated using the following formula:

$$TOF={\displaystyle \frac{C_{feed}·F_{gas}·X·t}{n_{active sites}· t}}={\displaystyle \frac{C_{feed}·F_{gas}}{n_{active sites}}} ·X$$

where C_feed is the feed gas concentration, F_gas is the volumetric gas flow rate, X is the conversion of the reactant, t is the reaction time, n_{active sites} is the total moles of catalytic active sites.

The active sites on the catalyst surface (here, quartz wool) remain consistent across all experiments, since the same reactor configuration was employed. Additionally, the gas flow rate was intentionally increased when necessary to ensure conversions remained below 10%.

If the gas flow rate (F_gas) remains constant, the terms C_feed, F_gas, and n_{active sites} remain identical across all experimental conditions. Consequently, whether these parameters are explicitly included in the TOF calculation does not affect the slopes of lnTOF ~ lnP (for reaction order) or lnTOF ~ 1/T (for Ea), as they cancel out mathematically.

When F_gas varies between experiments, the TOF formula must explicitly account for flow rate:

$$TOF={\displaystyle \frac{C_{feed}}{n_{active sites}}}·F_{gas}· X$$

4. Conclusions

In conclusion, this study systematically investigates the chlorination and dehydrochlorination of C₂H₆ under varying C₂H₆/Cl₂ molar ratios and reaction conditions. The results demonstrate that the C₂H₆/Cl₂ molar ratio significantly influences the reaction pathways, with lower Cl₂ concentrations favoring the formation of C₂H₅Cl and higher concentrations promoting further chlorination to dichloroethane. Additionally, the study reveals that the dehydrochlorination of C₂H₅Cl is fundamentally driven by the excitation of chlorine radicals, with the 2-chloroethyl radical serving as a critical precursor for ethylene formation. These findings underscore the importance of optimizing the C₂H₆/Cl₂ molar ratio to suppress undesired side reactions and enhance the selectivity of target chlorocarbons. These insights provide a theoretical foundation for designing efficient catalysts and reaction conditions to achieve selective C₂H₆ chlorination to 1,2-C₂H₄Cl₂, a key precursor for polyvinyl chloride production.