First, let's calculate the energy required to break all the bonds in 1 mole of methane gas CH4 . Methane has 4 C-H bonds, and the bond energy of a C-H bond is 413 kJ/mol.Energy required to break 1 mole of C-H bonds in CH4 = 4 C-H bonds 413 kJ/mol C-H bond energy = 1652 kJ/molNow, let's calculate the energy released or absorbed during the combustion of 1 mole of methane gas with oxygen gas to form carbon dioxide gas and water vapor. The balanced chemical equation for the combustion of methane is:CH4 + 2 O2 CO2 + 2 H2OThe bond energies for the relevant bonds are as follows:C-H bond energy: 413 kJ/molO=O double bond bond energy: 498 kJ/molC=O double bond bond energy: 799 kJ/molO-H bond energy: 467 kJ/molEnergy required to break bonds in reactants:1 mole CH4: 4 C-H bonds 413 kJ/mol = 1652 kJ/mol2 moles O2: 2 O=O bonds 498 kJ/mol = 996 kJ/molTotal energy required to break bonds in reactants = 1652 kJ/mol + 996 kJ/mol = 2648 kJ/molEnergy released when bonds are formed in products:1 mole CO2: 2 C=O bonds 799 kJ/mol = 1598 kJ/mol2 moles H2O: 4 O-H bonds 467 kJ/mol = 1868 kJ/molTotal energy released when bonds are formed in products = 1598 kJ/mol + 1868 kJ/mol = 3466 kJ/molTotal energy released or absorbed during the combustion of 1 mole of methane gas = Energy released when bonds are formed in products - Energy required to break bonds in reactants = 3466 kJ/mol - 2648 kJ/mol = 818 kJ/mol released So, the total energy released during the combustion of 1 mole of methane gas with oxygen gas to form carbon dioxide gas and water vapor is 818 kJ/mol.