To calculate the standard enthalpy change for the formation of methane CH4 from its elements carbon C and hydrogen H2 at standard conditions, we can use the following equation:Hf CH4 = Hf products - Hf reactants The balanced chemical equation for the formation of methane is:C s + 2H2 g CH4 g The standard enthalpy of formation Hf for elements in their standard state is 0 kJ/mol. Therefore, Hf C = 0 kJ/mol and Hf H2 = 0 kJ/mol.The given thermodynamic data is the enthalpy of combustion Hc of methane, which is -890.3 kJ/mol. We can use this information to find the enthalpy of formation of methane.The balanced chemical equation for the combustion of methane is:CH4 g + 2O2 g CO2 g + 2H2O l The standard enthalpy of formation for CO2 g and H2O l are -393.5 kJ/mol and -285.8 kJ/mol, respectively.Using the enthalpy of combustion equation:Hc CH4 = Hf products - Hf reactants -890.3 kJ/mol = [1 -393.5 kJ/mol + 2 -285.8 kJ/mol ] - [Hf CH4 + 2 0 kJ/mol]-890.3 kJ/mol = -965.1 kJ/mol - Hf CH4 Now, solve for Hf CH4 :Hf CH4 = -965.1 kJ/mol + 890.3 kJ/molHf CH4 = -74.8 kJ/molThe standard enthalpy change for the formation of methane CH4 from its elements carbon C and hydrogen H2 at standard conditions is -74.8 kJ/mol.