## 3 Results and Discussion
### Plasma-Catalytic Conversion of Biogas
This observation aligns with previous studies that have explored direct oxygenate synthesis from CH\({}_{4}\) and CO\({}_{2}\) under non-thermal plasma (NTP) conditions. In NTP environments, highly reactive species such as CH\({}_{3}\), CO, and OH radicals are generated in abundance. The coupling of methyl (-CH\({}_{3}\)) and carboxyl (-COOH) radicals--formed through the reaction of CO with OH--has been identified as a key pathway for the formation of acetic acid (CH\({}_{3}\)COOH). This mechanism is energetically favorable and has been supported by both experimental results and density functional theory (DFT) calculations [16]. Additionally, the role of the catalyst in stabilizing intermediate species through appropriate oxygen adsorption energies further promotes the selective formation of acetic acid over other oxygenates. As demonstrated in earlier studies, such as those by [PERSON] et al. [23] and [PERSON] et al. [10], acetic acid has emerged as a dominant product in similar plasma-catalytic systems. Figure 4A illustrates the impact of altering the carbon dioxide to methane (CO\({}_{2}\)/CH\({}_{4}\)) molar ratio on the catalytic conversion of these gases and the resulting product composition. By systematically adjusting the reactant proportions from a CO\({}_{2}\)/CH\({}_{4}\) ratio of 2:1 to 1:2, a steady decrease in methane conversion was observed, falling from 36.8% to 19.7%. In contrast, carbon dioxide conversion followed a curvilinear pattern, reaching a maximum of 19.7% at a CO\({}_{2}\)/CH\({}_{4}\) ratio of 1:0.5. The selectivity for total liquid products displayed a similar trend to carbon dioxide conversion, indicating a direct correlation with the reactant feed ratio. Notably, a peak liquid product selectivity of 38.6% was achieved at a stoichiometric CO\({}_{2}\)/CH\({}_{4}\) ratio of 1:0.5. Moreover, an excess of carbon dioxide (CO\({}_{2}\)/CH\({}_{4}\) ratio of 2:1) led to a preference for gaseous product formation, resulting in a lower liquid selectivity of 13.7%. This implies that an abundance of methane molecules enhances carbon-carbon bond formation within the plasma environment. Consequently, subsequent experiments were performed using a CO\({}_{2}\)/CH\({}_{4}\) molar ratio of 1:0.5, based on these experimental findings. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Chemical** & **Formaldehyde** & **Isopropyl Alcohol** & **Ethanol** & **Methanol** & **Propanoic Acid** & **Acetic Acid** \\ \hline Selectivity (\%) & 10.5 & 15.7 & 14.5 & 19.1 & 16.3 & 23.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Selectivity of different oxygenate chemicals in liquid products. The effect of input power on CH\({}_{4}\) and CO\({}_{2}\) conversion was investigated by varying the discharge power from 13 W to 23 W. As shown in Figure 4B, increasing the input power led to a noticeable improvement in conversion efficiency for both gases. At 13 W, CH\({}_{4}\) and CO\({}_{2}\) conversions were 30.4% and 15.1%, respectively. When the power was increased to 18 W, CH\({}_{4}\) conversion rose to 32.1%, while CO\({}_{2}\) conversion reached 17.3%. At the highest power level of 23 W, CH\({}_{4}\) and CO\({}_{2}\) conversions further increased to 34.8% and 19.7%, respectively. This trend can be attributed to the enhanced plasma discharge intensity at higher input powers, which generates a greater number of energetic electrons and reactive species such as radicals, ions, and excited molecules. These species are responsible for breaking the strong C-H and C=O bonds in methane and carbon dioxide, thereby promoting the desired chemical transformations. Thus, increasing the input power effectively enhances the activation of reactants and improves overall conversion performance in the plasma-catalytic system. Figure 4C presents the stability test of the Ni-Fe/Al\({}_{2}\)O\({}_{3}\) catalyst during plasma-assisted biogas conversion over a 5 h period.