To calculate the standard enthalpy change for the combustion of methane gas CH4 , we need to consider the balanced chemical equation for the combustion reaction:CH4 g + 2 O2 g CO2 g + 2 H2O g Now, we can use Hess's Law to determine the standard enthalpy change for the reaction. Hess's Law states that the enthalpy change for a reaction is equal to the sum of the enthalpy changes for the formation of the products minus the sum of the enthalpy changes for the formation of the reactants.H_combustion = [H_formation CO2 + 2 * H_formation H2O ] - [H_formation CH4 + 2 * H_formation O2 ]Since O2 is in its standard state, its enthalpy of formation is 0 kJ/mol. Now, we can plug in the given values:H_combustion = [ -393.5 kJ/mol + 2 * -285.8 kJ/mol ] - [ -74.8 kJ/mol + 2 * 0 kJ/mol ]H_combustion = -393.5 - 571.6 + 74.8 kJ/molH_combustion = -890.3 kJ/molThe standard enthalpy change for the combustion of methane gas CH4 is -890.3 kJ/mol.