The reaction of methane CH4 and chlorine gas Cl2 to form methyl chloride CH3Cl is a radical reaction that proceeds through a chain mechanism. The reaction can be broken down into three main steps: initiation, propagation, and termination.Initiation:Cl2 2Cl homolytic cleavage of Cl2 Propagation:1 CH4 + Cl CH3 + HCl abstraction of H from CH4 by Cl 2 CH3 + Cl2 CH3Cl + Cl formation of CH3Cl Termination:Cl + CH3 CH3Cl recombination of radicals To predict the reaction mechanism and rate constant using quantum chemical calculations and transition state theory, we need to follow these steps:1. Perform quantum chemical calculations: Use computational chemistry software e.g., Gaussian, ORCA, etc. to optimize the geometries and calculate the energies of reactants, products, and transition states at a suitable level of theory e.g., DFT, MP2, CCSD T , etc. . This will provide the energy barriers for each step of the reaction.2. Calculate the partition functions: For each species involved in the reaction, calculate the translational, rotational, vibrational, and electronic partition functions using the calculated energies and geometries.3. Apply transition state theory: Using the partition functions and energy barriers, calculate the rate constants for each elementary step of the reaction using the Eyring equation:k T = k_B * T / h * Q / Q_A * Q_B * exp -E / R * T where k T is the rate constant at temperature T, k_B is the Boltzmann constant, h is the Planck constant, Q is the partition function of the transition state, Q_A and Q_B are the partition functions of the reactants, E is the energy barrier, and R is the gas constant.4. Determine the overall rate constant: The overall rate constant for the reaction can be determined by combining the rate constants for the individual steps, considering the chain mechanism.5. Evaluate the rate constant at the desired conditions: Finally, calculate the rate constant at the given temperature 200C and pressure 1 atm using the Arrhenius equation:k = A * exp -Ea / R * T 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.By following these steps, you can predict the reaction mechanism and rate constant for the reaction of methane and chlorine gas to form methyl chloride at the specified conditions.