To calculate the standard enthalpy change for the formation of one mole of methane CH4 gas, we can use the following balanced chemical equation for the combustion of methane:CH4 g + 2 O2 g CO2 g + 2 H2O l We are given the heat of combustion of methane gas -890.36 kJ/mol , the heat of formation of water liquid -285.83 kJ/mol , and the heat of formation of carbon dioxide gas -393.52 kJ/mol .We can use Hess's law to find the heat of formation of methane gas. Hess's law states that the enthalpy change of a reaction is the same, whether it occurs in one step or several steps. Therefore, we can write the following equation:H formation of CH4 = H combustion of CH4 + H formation of CO2 + 2 H formation of H2O Now, we can plug in the given values:H formation of CH4 = -890.36 kJ/mol + -393.52 kJ/mol + 2 -285.83 kJ/mol H formation of CH4 = -890.36 kJ/mol + 393.52 kJ/mol + -571.66 kJ/mol H formation of CH4 = -1068.50 kJ/molTherefore, the standard enthalpy change for the formation of one mole of methane CH4 gas is -1068.50 kJ/mol.