As a chemist, I can provide you with a general understanding of how temperature affects the reaction rate of methane and oxygen gas undergoing a gas-phase reaction to form carbon dioxide and water. However, I cannot perform Monte Carlo simulations as I am an AI language model and do not have the capability to run such simulations. Nevertheless, I can explain the concepts and guide you on how to perform the simulations.The reaction between methane CH4 and oxygen O2 is an exothermic reaction, which can be represented by the following balanced equation:CH4 g + 2 O2 g CO2 g + 2 H2O g The reaction rate depends on several factors, including temperature, concentration of reactants, and the presence of catalysts. According to the collision theory, the reaction rate increases with temperature because the molecules have more kinetic energy, which leads to more frequent and energetic collisions between the reactants.The Arrhenius equation describes the temperature dependence of reaction rates:k = Ae^-Ea/RT where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.To use Monte Carlo simulations to determine the energy barriers and activation energies at different temperatures, you would need to follow these steps:1. Set up a computational model of the reaction system, including the potential energy surfaces PES for the reactants, products, and transition states.2. Generate a large number of random initial conditions for the reactants, such as positions, velocities, and orientations.3. Perform classical trajectory calculations for each set of initial conditions, propagating the system forward in time to determine whether a reaction occurs.4. Calculate the fraction of trajectories that result in a reaction, and use this to estimate the reaction rate constant k.5. Repeat steps 2-4 for different temperatures, and use the resulting rate constants to determine the activation energy Ea and other parameters in the Arrhenius equation.6. Analyze the results to predict the effect of temperature on the reaction rate.Keep in mind that performing Monte Carlo simulations requires specialized software and a solid understanding of computational chemistry methods. If you are interested in pursuing this approach, I recommend consulting with an expert in the field or referring to relevant literature for more detailed guidance.