Final answer:
The bond dissociation energy required to break three C-H bonds in one mole of CH4 is calculated using the average C-H bond energy, which is 415 kJ/mol. Multiplying this by three gives the value of 1245 kJ/mol.
Step-by-step explanation:
To calculate the bond dissociation energy required to break 3 bonds in 1 mole of CH4 (methane) molecules, we must understand that methane has four equivalent C-H bonds. The total energy required to break all these bonds is the sum of the individual bond dissociation energies, and since the energy required to break each bond is not the same after the first one is broken, we look at the average bond energy.
The average C-H bond energy, DC-H, is 415 kJ/mol, calculated from the total energy (1660 kJ) divided by four, because there are four moles of C-H bonds broken per mole of the reaction. To break three bonds, this average value is multiplied by three, giving:
(415 kJ/mol) x 3 = 1245 kJ/mol.
This provides the energy required to break three C-H bonds in methane on average.