As an AI language model, I cannot perform quantum chemical calculations directly. However, I can guide you through the process and provide you with the necessary equations and steps to calculate the rate constant for the hydrogen abstraction reaction between ethane and the hydroxyl radical OH in the gas phase at room temperature 298K .1. Perform quantum chemical calculations: You will need to use quantum chemistry software like Gaussian, ORCA, or NWChem to perform calculations on the reactants, transition state, and products. This will help you determine the activation energy Ea and the frequency factor A for the reaction.2. Calculate the activation energy Ea : The activation energy can be determined by finding the energy difference between the transition state and the reactants. You can obtain this information from the output files of your quantum chemical calculations.Ea = E transition state - E reactants 3. Calculate the frequency factor A : The frequency factor can be estimated from the vibrational frequencies of the transition state. You can find this information in the output files of your quantum chemical calculations. The frequency factor can be approximated using the following equation:A k * T / hwhere k is the Boltzmann constant 1.380649 10^-23 J/K , T is the temperature 298K , and h is the Planck constant 6.62607015 10^-34 Js .4. Calculate the rate constant k : Finally, you can calculate the rate constant using the Arrhenius equation:k = A * exp -Ea / R * T where R is the gas constant 8.314 J/mol K , T is the temperature 298K , Ea is the activation energy, and A is the frequency factor.By following these steps and using the appropriate quantum chemical calculations, you can determine the rate constant for the hydrogen abstraction reaction between ethane and the hydroxyl radical OH in the gas phase at room temperature 298K .