To calculate the heat of formation of methane CH4 , we need to consider the balanced chemical equation for the formation of methane from its elements in their standard states:C graphite + 2H2 g CH4 g Now, we can use Hess's Law to find the heat of formation of methane. Hess's Law states that the total enthalpy change for a chemical reaction is the same, regardless of the pathway taken. We can use the given enthalpies of formation to create a pathway to the formation of methane.First, we need to form CH3 g from its elements:C graphite + 1.5H2 g CH3 g H1 = 120.6 kJ/molNext, we need to add half a mole of H2 g to CH3 g to form CH4 g :CH3 g + 0.5H2 g CH4 g H2 = Hf CH4 Now, we can add these two reactions together to get the overall reaction:C graphite + 2H2 g CH4 g H = H1 + H2We know the enthalpy of formation of H2 g is 0 kJ/mol, so we can plug in the given values:H = 120.6 kJ/mol + Hf CH4 Now, we need to find the enthalpy of formation of CH4 Hf CH4 . To do this, we can use the bond dissociation energies of the C-H and H-H bonds. The bond dissociation energy of a C-H bond is approximately 414 kJ/mol, and the bond dissociation energy of an H-H bond is approximately 436 kJ/mol.The formation of CH4 involves breaking two H-H bonds and forming four C-H bonds:2H2 g 4H g H = 2 * 436 kJ/mol = 872 kJ/molC graphite + 4H g CH4 g H = 4 * -414 kJ/mol = -1656 kJ/molNow, we can find the enthalpy of formation of CH4:Hf CH4 = -1656 kJ/mol + 872 kJ/mol = -784 kJ/molSo, the heat of formation of methane CH4 is -784 kJ/mol.