To calculate the activation energy and reaction rate constant for the formation of hydrogen gas from the reaction of molecular hydrogen with atomic hydrogen, we need to consider the following reaction:H2 + H -> H3 -> 3HThis reaction involves the formation of a short-lived intermediate, H3, which then dissociates into three hydrogen atoms. To calculate the activation energy, we need to determine the energy difference between the reactants and the transition state. Quantum chemical calculations can be used to determine these energies.First, we need to perform a geometry optimization and frequency calculation for the reactants H2 and H and the transition state H3 using a quantum chemical method, such as density functional theory DFT or ab initio methods like Hartree-Fock HF or Mller-Plesset perturbation theory MP2 . These calculations can be performed using quantum chemistry software packages like Gaussian, ORCA, or Psi4.Once the optimized geometries and energies are obtained, we can calculate the activation energy Ea as the difference between the energy of the transition state E_TS and the energy of the reactants E_R :Ea = E_TS - E_RNext, we need to calculate the reaction rate constant k using transition state theory TST . The TST equation is given by:k = k_B * T / h * e^-Ea / R * T where k_B is the Boltzmann constant 1.380649 10^-23 J/K , h is the Planck constant 6.62607015 10^-34 Js , R is the gas constant 8.314 J/ mol K , T is the temperature in Kelvin, and Ea is the activation energy.By plugging the calculated activation energy into the TST equation, we can determine the reaction rate constant for the formation of hydrogen gas from the reaction of molecular hydrogen with atomic hydrogen at a given temperature.It is important to note that the accuracy of the calculated activation energy and reaction rate constant depends on the level of theory used in the quantum chemical calculations. Higher-level methods, such as coupled cluster theory CCSD T , can provide more accurate results but are computationally more expensive.