To calculate the enthalpy change for the combustion of methane, 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 calculate the enthalpy change for the reaction. The enthalpy change for the reaction H is equal to the sum of the enthalpies of formation of the products minus the sum of the enthalpies of formation of the reactants:H = [Hf CO2 + 2 * Hf H2O ] - [Hf CH4 + Hf O2 ]Since O2 is an element in its standard state, its enthalpy of formation is 0 kJ/mol. Now, we can plug in the given values for the enthalpies of formation:H = [ -393.5 kJ/mol + 2 * -241.8 kJ/mol ] - [ -74.8 kJ/mol + 0]H = -393.5 - 2 * 241.8 + 74.8 kJ/molH = -393.5 - 483.6 + 74.8 kJ/molH = -802.3 kJ/molThe enthalpy change for the combustion of methane at standard conditions is -802.3 kJ/mol.