To calculate the standard enthalpy of formation Hf of methane CH4 , we need to use Hess's Law, which states that the enthalpy change of a reaction is the same whether it occurs in one step or several steps. We can manipulate the given reactions to create a reaction that forms methane CH4 .First, we need to find the reaction that forms CH4. The balanced equation for the formation of methane is:C graphite + 2H2 g CH4 g Now, we need to manipulate the given reactions to match this equation. For the first reaction, we need to reverse it and divide by 2 to get:H2O l H2 g + 1/2O2 g Hrxn = +286 kJ/molFor the second reaction, we need to reverse it and add 2 moles of hydrogen to both sides:CO2 g + 2H2 g C graphite + 2H2O g Hrxn = +394 kJ/molNow, we can add these two manipulated reactions together:H2O l H2 g + 1/2O2 g Hrxn = +286 kJ/molCO2 g + 2H2 g C graphite + 2H2O g Hrxn = +394 kJ/mol--------------------------------------------------------------CO2 g + H2O l CH4 g + 1/2O2 g Hrxn = +680 kJ/molFinally, we can calculate the standard enthalpy of formation Hf of methane CH4 by subtracting the enthalpy of formation of CO2 and H2O from the enthalpy of the reaction:Hf CH4 = Hrxn - Hf CO2 - Hf H2O Hf CH4 = +680 kJ/mol - -394 kJ/mol - 0Hf CH4 = +680 kJ/mol + 394 kJ/molHf CH4 = +1074 kJ/mol