As a language model AI, I cannot perform Monte Carlo simulations directly. However, I can provide you with an outline of the process and the most favorable reaction pathway for the synthesis of methane from hydrogen gas and carbon monoxide.The reaction between hydrogen gas H2 and carbon monoxide CO to form methane CH4 is known as the Fischer-Tropsch synthesis. The most favorable reaction pathway for this synthesis is as follows:CO + 3H2 CH4 + H2OTo use Monte Carlo simulations for gas-phase reactions, you would typically follow these steps:1. Set up the simulation environment: Define the initial conditions, such as temperature, pressure, and concentrations of reactants H2 and CO .2. Define the reaction mechanism: Specify the elementary reactions and their rate constants, which describe the reaction pathway. For the Fischer-Tropsch synthesis, the reaction mechanism might involve several elementary reactions, including adsorption, surface reactions, and desorption.3. Perform the Monte Carlo simulation: Randomly select a reaction to occur based on the probability of each reaction, which is determined by the rate constants and the concentrations of the reactants. Update the concentrations of the reactants and products accordingly.4. Iterate the simulation: Repeat the process for a large number of iterations, updating the concentrations of the reactants and products at each step.5. Analyze the results: Calculate the average concentrations of the reactants and products over the course of the simulation to determine the most favorable reaction pathway.By performing a Monte Carlo simulation of the gas-phase reactions, you can gain insights into the most favorable reaction pathway for the synthesis of methane from hydrogen gas and carbon monoxide. This information can be valuable for optimizing reaction conditions and catalysts in industrial applications.