To calculate the bond dissociation energy for the C-H bond in methane, we need to find the enthalpy change for the reaction CH4 g C g + 4H g . We can do this using the given information and Hess's Law, which states that the enthalpy change of a reaction is the same, whether it occurs in one step or several steps.First, let's write down the given reactions:1. CH4 g + 2O2 g CO2 g + 2H2O g H1 = -890.3 kJ/mol2. 2H2 g + O2 g 2H2O g H2 = -484.2 kJ/molWe want to find the enthalpy change for the reaction:3. CH4 g C g + 4H g H3 = ?To do this, we need to manipulate the given reactions in such a way that when we add them, we get the desired reaction. We can start by reversing reaction 2 and then multiplying it by 2:2'. 2H2O g 2H2 g + O2 g H2' = +484.2 kJ/mol reversed sign 2''. 4H2O g 4H2 g + 2O2 g H2'' = +968.4 kJ/mol multiplied by 2 Now, we can add reactions 1 and 2'' to get the desired reaction:1. CH4 g + 2O2 g CO2 g + 2H2O g H1 = -890.3 kJ/mol2''. 4H2O g 4H2 g + 2O2 g H2'' = +968.4 kJ/mol----------------------------------------------3. CH4 g C g + 4H g + CO2 g H3 = H1 + H2'' = -890.3 + 968.4 = 78.1 kJ/molNow, we need to account for the formation of CO2 g from C g and O2 g . The enthalpy change for this reaction is:4. C g + O2 g CO2 g H4 = -393.5 kJ/mol standard enthalpy of formation for CO2 Finally, we can subtract reaction 4 from reaction 3 to get the bond dissociation energy for the C-H bond in methane:3. CH4 g C g + 4H g + CO2 g H3 = 78.1 kJ/mol4. C g + O2 g CO2 g H4 = -393.5 kJ/mol----------------------------------------------5. CH4 g C g + 4H g H5 = H3 - H4 = 78.1 - -393.5 = 471.6 kJ/molThe bond dissociation energy for the C-H bond in methane is 471.6 kJ/mol.