To calculate the heat of formation of methane CH4 , we can use Hess's Law, which states that the total enthalpy change of a reaction is the same, regardless of the path taken. In this case, we can use the given enthalpy changes to create a reaction pathway that will allow us to calculate the heat of formation of methane.First, let's write down the combustion reaction of methane:CH4 g + 2 O2 g CO2 g + 2 H2O l H = -890.4 kJ mol^-1Now, let's write down the formation reactions for water and carbon dioxide:H2 g + 1/2 O2 g H2O l H = -285.8 kJ mol^-1C s + O2 g CO2 g H = -393.5 kJ mol^-1We want to manipulate these reactions to find the formation reaction of methane. First, we need to reverse the combustion reaction of methane:CO2 g + 2 H2O l CH4 g + 2 O2 g H = 890.4 kJ mol^-1Next, we need to multiply the formation reaction of water by 2 to match the number of moles of water in the reversed combustion reaction:2 [H2 g + 1/2 O2 g H2O l ] H = 2 -285.8 kJ mol^-1 = -571.6 kJ mol^-1Now, we can add the reversed combustion reaction, the formation reaction of carbon dioxide, and the multiplied formation reaction of water together:CO2 g + 2 H2O l CH4 g + 2 O2 g H = 890.4 kJ mol^-1C s + O2 g CO2 g H = -393.5 kJ mol^-12 H2 g + O2 g 2 H2O l H = -571.6 kJ mol^-1--------------------------------------------------------------C s + 2 H2 g CH4 g H = ?Now, we can sum up the enthalpy changes:H = 890.4 kJ mol^-1 - 393.5 kJ mol^-1 - 571.6 kJ mol^-1 = -74.7 kJ mol^-1Therefore, the heat of formation of methane CH4 is -74.7 kJ mol^-1.