To calculate the bond energy of a carbon-hydrogen bond in methane, we need to consider the enthalpy change of combustion for methane and the enthalpy change for breaking carbon-hydrogen bonds.The enthalpy change of combustion for methane is given as -890 kJ/mol. This means that 890 kJ of energy is released when one mole of methane is combusted. The balanced combustion reaction for methane is:CH4 + 2O2 CO2 + 2H2OIn this reaction, one mole of methane reacts with two moles of oxygen to produce one mole of carbon dioxide and two moles of water. The enthalpy change for breaking carbon-hydrogen bonds is given as 413 kJ/mol. This means that 413 kJ of energy is required to break one mole of carbon-hydrogen bonds.Methane CH4 has four carbon-hydrogen bonds. Therefore, the total energy required to break all the carbon-hydrogen bonds in one mole of methane is:4 C-H bonds 413 kJ/mol energy to break one C-H bond = 1652 kJ/molNow, we can use Hess's Law to calculate the bond energy of a carbon-hydrogen bond in methane. According to Hess's Law, the enthalpy change of a reaction is the same, whether it occurs in one step or several steps. In this case, we can consider the combustion of methane as a two-step process:1. Breaking all the carbon-hydrogen bonds in methane: CH4 C + 4H requires 1652 kJ/mol 2. Forming new bonds to produce CO2 and H2O: C + 4H + 2O2 CO2 + 2H2O releases energy The overall enthalpy change of combustion for methane is the sum of the enthalpy changes for these two steps:H_combustion = H_breaking C-H bonds + H_forming new bonds-890 kJ/mol = 1652 kJ/mol + H_forming new bondsSolving for H_forming new bonds:H_forming new bonds = -890 kJ/mol - 1652 kJ/mol = -2542 kJ/molNow, we can calculate the bond energy of a carbon-hydrogen bond in methane by dividing the total energy required to break all the carbon-hydrogen bonds in one mole of methane by the number of carbon-hydrogen bonds:Bond energy of C-H bond = 1652 kJ/mol / 4 C-H bonds = 413 kJ/molSo, the bond energy of a carbon-hydrogen bond in methane is 413 kJ/mol.