Answer :
Final answer:
The C=C bond energy can be determined by subtracting the known bond energies of the C-H bonds and the atomization energies of C and H from the total energy change during the formation of ethylene, yielding a value of 537.9 kcal.
Explanation:
To determine the C=C bond energy, we need to perform an energy bookkeeping based on the given heat of formation and atomization values, as well as known bond energies.
First, we calculate the total energy required to atomize the reactants into individual atoms. For ethylene (C2H4), atomization would require:
- Breaking two C-H bonds: 2 x 99.3 kcal = 198.6 kcal
- Breaking two more C-H bonds: 2 x 99.3 kcal = 198.6 kcal
- Atomization of two carbon atoms: 2 x 171 kcal = 342 kcal
- Atomization of four hydrogen atoms: 4 x 52.1 kcal = 208.4 kcal
The total energy required for atomization of C2H4 is then 198.6 + 198.6 + 342 + 208.4 = 947.6 kcal.
However, the heat of formation of C2H4 from its elements is given as 12.5 kcal. This means that when ethylene is formed from its atoms, 947.6 kcal - 12.5 kcal = 935.1 kcal is released due to bond formation, including the formation of the C=C double bond.
We know the energy for all bonds except for the C=C bond. Therefore, we can isolate the C=C bond energy by subtracting the energies of all other bonds from the total energy change:
935.1 kcal - (4 x 99.3 kcal) = C=C bond energy
After performing the subtraction, the C=C bond energy is found to be 537.9 kcal.
