To calculate the bond energy required to break all the C-H bonds in a mole of methane CH4 gas, we first need to know the bond energy of a single C-H bond. The bond energy of a C-H bond is approximately 414 kJ/mol.Methane CH4 has four C-H bonds. To break all the C-H bonds in one molecule of methane, we need to multiply the bond energy of a single C-H bond by the number of bonds:Energy required to break all C-H bonds in one molecule of methane = 414 kJ/mol 4 = 1656 kJ/molNow, we need to calculate the energy required to break all the C-H bonds in one mole of methane. Since there are 6.022 x 10^23 molecules in one mole Avogadro's number , we can multiply the energy required to break all C-H bonds in one molecule by Avogadro's number:Energy required to break all C-H bonds in one mole of methane = 1656 kJ/mol 6.022 x 10^23 molecules/mol = 9.97 x 10^26 kJTherefore, the bond energy required to break all the C-H bonds in a mole of methane CH4 gas is approximately 9.97 x 10^26 kJ.