As a language model AI, I cannot perform quantum chemical calculations directly. However, I can provide you with an overview of the reaction between methane and chlorine gas and its mechanism.The reaction between methane CH4 and chlorine gas Cl2 is a radical halogenation reaction that occurs in the gas phase. At 25C, the reaction is relatively slow due to the high activation energy barrier. The reaction can be accelerated by the presence of light or heat. The overall reaction is as follows:CH4 + Cl2 CH3Cl + HClThe mechanism of this reaction involves a series of steps involving radical intermediates. It consists of three main stages: initiation, propagation, and termination.1. Initiation:The reaction is initiated by the homolytic cleavage of the Cl-Cl bond, which can be facilitated by light or heat. This generates two chlorine radicals Cl .Cl2 2 Cl2. Propagation:The propagation stage consists of two steps. In the first step, a chlorine radical reacts with methane, abstracting a hydrogen atom and forming a methyl radical CH3 and HCl.Cl + CH4 CH3 + HClIn the second step, the methyl radical reacts with a chlorine molecule, forming chloromethane CH3Cl and another chlorine radical.CH3 + Cl2 CH3Cl + ClThe chlorine radical produced in the second step can then participate in another propagation cycle, allowing the reaction to continue.3. Termination:The termination stage occurs when two radicals react with each other, forming a stable product and effectively stopping the chain reaction. Some possible termination reactions are:Cl + Cl Cl2Cl + CH3 CH3ClCH3 + CH3 C2H6To predict the rate and mechanism of this reaction at 25C using quantum chemical calculations, one would need to employ computational chemistry software, such as Gaussian or ORCA, to calculate the potential energy surfaces and transition states for each step of the reaction. This would provide information on the activation energy barriers and the overall reaction rate. Additionally, the calculations would help to determine the most favorable pathways and intermediates in the reaction mechanism.