## 2 Experimental Section
### NTP-Catalytic Conversion of Biogas  
The experimental setup used for biogas conversion is illustrated in Figure 1. Reactions were carried out in a coaxial dielectric barrier discharge (DBD) reactor made of quartz, with an inner diameter of 8 mm, outer diameter of 10 mm, and wall thickness of 1 mm. A central tungsten rod (4 mm diameter) served as the high-voltage electrode, while a silver mesh wrapped around the outer surface acted as the ground electrode. Plasma was generated using a LEAP100(r) power supply (PlasmaLeap Technologies, Marrickville, Australia), delivering up to 700 W with a peak-to-peak voltage of 80 kV. The discharge frequency was set at 500 Hz, and the resonance frequency was automatically adjusted to approximately 56.99 kHz by the generator. For each run, 0.5 g of finely powdered catalyst was loaded into the center of the reactor. Quartz wool plugs were placed at both ends of the catalyst bed to keep it fixed and prevent displacement by the gas flow. The experiments were conducted at a discharge power of 23 W, with a total gas flow rate of 20 cm\({}^{3}\)/min with gas residence time of 0.3 min.  
Figure 1: Schematic diagram of plasma-assisted catalytic biogas conversion.  
The gas products were analyzed using a four-channel micro-GC (Agilent 490, Agilent Technologies, Inc., Santa Clara, CA, USA), which was equipped with a thermal conductivity detector. The first channel, fitted with a 10 m molecular sieve 5A column, facilitated the precise analysis of H\({}_{2}\), O\({}_{2}\), CH\({}_{4}\), and CO. The second channel, utilizing a 10 m PPU column, was employed for the analysis of CO\({}_{2}\), C\({}_{2}\)H\({}_{2}\), C\({}_{2}\)H\({}_{4}\), and C\({}_{2}\)H\({}_{6}\). Hydrocarbons ranging from C\({}_{3}\) to C\({}_{6}\), were quantified in the third and fourth channels, which were equipped with a 10 m alumina column and an 8 m CP-Sil 5 CB column, respectively. Argon (Ar) served as the carrier gas for the first channel, while hydrogen (H\({}_{2}\)) was used for the remaining three channels. The gaseous products resulting from the reaction were analyzed using micro-gas chromatography, enabling the quantification of methane and carbon dioxide conversion percentages, as well as the determination of gaseous product yields, utilizing the principles of the ideal gas law. Additionally, a soap-film flowmeter was used to assess the difference in gas flow rates before and after the process. To collect and condense the liquid products, a cooling unit maintained at \(-15\)\({}^{\circ}\)C was attached to the condenser. Then, 1 mL of carbon disulfide (99.9%, Sigma-Aldrich) was introduced to aid in the extraction of the condensed liquids from the condenser. The chemical makeup of the liquid products was then determined using a previously calibrated gas chromatography-mass spectrometer (Agilent 6890N/5973 GCMS). The conversion of carbon dioxide and methane was measured via following equations.  
\[CH_{4}\textit{conversion}\;(\%)=\frac{\textit{moles of CH${}_{4}$ converted}}{\textit{moles of CH${}_{4}$ in feed}}\times 100\]  
\[CO_{2}\textit{conversion}\;(\%)=\frac{\textit{moles of CO${}_{2}$ converted}}{\textit{moles of CO${}_{2}$ in feed}}\times 100\]  
\[H_{2}\textit{Yield}\;(\%)=\frac{\textit{moles of H${}_{2}$ produced}}{\textit{2}\times\textit{moles of CH${}_{4}$ converted}}\times 100\]  
\[CO\;\textit{Yield}\;(\%)=\frac{\textit{moles of CO produced}}{\textit{moles of CH${}_{4}$ converted}+\textit{moles of CO${}_{2}$ converted}}\times 100\]  
\[C_{3}\textit{H${}_{y}$ Yield (\%)}=\frac{\sum_{x}x\times\textit{moles of C${}_{x}$H${}_{y}$ produced }(x=2,3,\textit{ and }4)}{\textit{moles of CH${}_{4}$ converted+moles of CO${}_{2}$ converted}}\times 100\]  
\[\textit{Yield od liquid products}\;(\%)=100-\left(Y_{CO}+Y_{C_{5}H_{y}}\right)- \textit{Coke}\]