To calculate the standard enthalpy change for the combustion of methane gas at standard conditions, we need to use the standard enthalpies of formation for each compound involved in the reaction.The standard enthalpy of formation Hf is the change in enthalpy during the formation of 1 mole of a substance from its constituent elements in their standard states at 25C and 1 atm pressure.The standard enthalpies of formation for the compounds involved in the reaction are as follows:Hf CH4 = -74.8 kJ/molHf O2 = 0 kJ/mol since it's an element in its standard state Hf CO2 = -393.5 kJ/molHf H2O = -285.8 kJ/molWe can calculate the standard enthalpy change H for the reaction using the following equation:H = [Hf products ] - [Hf reactants ]For the given reaction:H = [1 -393.5 + 2 -285.8 ] - [1 -74.8 + 2 0 ]H = -393.5 - 571.6 - -74.8 H = -965.1 + 74.8H = -890.3 kJ/molTherefore, the standard enthalpy change for the combustion of methane gas at standard conditions is -890.3 kJ/mol.