Final answer:
The bond dissociation energy to break 1 H-C bond in 1 mol of HC≡CH molecules is 415 kJ/mol. This is the average value calculated by dividing the total energy required to break all C-H bonds (1660 kJ/mol) by the number of C-H bonds (4).
Step-by-step explanation:
The bond dissociation energy required to break 1 hydrogen-carbon (H-C) bond in 1 mol of HC≡CH molecules (ethylene or acetylene) can be understood by examining the bond energies of similar C-H bonds. The bond dissociation energy is typically the energy required to break a mole of bonds in a substance. For a molecule of ethylene, which has four C-H bonds, the total energy required to break all the C-H bonds is given as 1660 kJ/mol. Hence, to find the energy to break one C-H bond, we divide this value by four.
The average bond dissociation energy (Dc-H) is thus calculated to be 1660 kJ/mol divided by 4, which equals 415 kJ/mol. This is the average value, as the actual energy needed to break the first bond is slightly higher (439 kJ/mol), with subsequent bonds requiring less energy due to the changing molecular structure after each bond breakage.