To calculate the heat of formation of methane CH4 , we can use the following reaction:C graphite + 2 H2 g CH4 g We can use Hess's Law to find the heat of formation of methane. Hess's Law states that the total enthalpy change of a reaction is the same, whether the reaction occurs in one step or several steps. We can use the given standard enthalpies of formation of CO2, H2O, and O2 to create a series of reactions that will ultimately give us the desired reaction.First, let's write down the given standard enthalpies of formation:1. C graphite + O2 g CO2 g Hf CO2 = -393.5 kJ/mol2. H2 g + 1/2 O2 g H2O l Hf H2O = -285.8 kJ/mol3. O2 g Hf O2 = 0 kJ/mol since it's an element in its standard state Now, we can manipulate these reactions to get the desired reaction:1. C graphite + O2 g CO2 g H1 = -393.5 kJ/mol2. 2 H2 g + 1/2 O2 g H2O l H2 = 2 * -285.8 kJ/mol = -571.6 kJ/mol3. CO2 g + 2 H2O l CH4 g + 2 O2 g + 2 H2O l H3 = Hf CH4 Now, we can add reactions 1, 2, and the reverse of reaction 3:C graphite + O2 g + 2 H2 g + CO2 g + 2 H2O l CO2 g + 2 H2O l + CH4 g + 2 O2 g + 2 H2O l Simplifying the reaction, we get:C graphite + 2 H2 g CH4 g Now, we can use Hess's Law to find the heat of formation of methane:Hf CH4 = H1 + H2 + -H3 Hf CH4 = -393.5 kJ/mol - 571.6 kJ/mol + H3H3 = 393.5 kJ/mol + 571.6 kJ/molH3 = 965.1 kJ/molTherefore, the heat of formation of methane CH4 is -965.1 kJ/mol.