To calculate the standard enthalpy of formation of methane gas CH4 , we need to use the standard enthalpies of formation for carbon dioxide CO2 and water vapor H2O given, as well as the standard enthalpy of formation for elemental carbon graphite and hydrogen gas H2 , which are both 0 kJ/mol by definition.First, we need to find a balanced chemical equation that involves CH4, CO2, and H2O. The combustion of methane is a suitable reaction:CH4 g + 2 O2 g CO2 g + 2 H2O g Now, we can use Hess's Law to find the standard enthalpy of formation of CH4. Hess's Law states that the enthalpy change of a reaction is the same whether it occurs in one step or several steps. We can use the given standard enthalpies of formation to find the enthalpy change for the combustion of methane:H_combustion = H_f CO2 + 2 * H_f H2O - H_f CH4 - 2 * H_f O2 Since the standard enthalpy of formation for O2 is 0 kJ/mol, the equation simplifies to:H_combustion = H_f CO2 + 2 * H_f H2O - H_f CH4 Now, we can plug in the given values for the standard enthalpies of formation for CO2 and H2O:H_combustion = -393.5 kJ/mol + 2 * -241.8 kJ/mol - H_f CH4 The standard enthalpy of combustion for methane H_combustion is -890.4 kJ/mol. Now we can solve for the standard enthalpy of formation of CH4:-890.4 kJ/mol = -393.5 kJ/mol + 2 * -241.8 kJ/mol - H_f CH4 -890.4 kJ/mol = -877.1 kJ/mol - H_f CH4 H_f CH4 = -877.1 kJ/mol + 890.4 kJ/molH_f CH4 = 13.3 kJ/molSo, the standard enthalpy of formation of methane gas CH4 is 13.3 kJ/mol.