Consider the gas-phase conversion of cyclopropane (C3H6) to propene (C3H6), a reaction that proceeds by a ring-opening mechanism consisting of two elementary steps:
Step 1 C3H6 (cyclopropane) ⇌C3H6∗ (intermediate with a stretched C–C bond)
Step 2 C3H6∗⟶C3H6 (propene)
The asterisk denotes a high-energy intermediate in which one of the C–C bonds is partially broken and converted into a C=C bond.
Relevant average bond energies (kJmol−1):
C–C 348 C=C 614 C–H 414
Assume that each cyclopropane molecule initially contains three equivalent C–C bonds and that the intermediate contains one elongated C–C bond whose energy may be approximated as the arithmetic mean of the C–C and C=C bond energies.
(1) Part 1: (a) For one mole of cyclopropane molecules undergoing Step 1, estimate the energy absorbed to reach the intermediate state. Explain any approximations you make.
(2) Part 2: (b) For Step 2, estimate the energy released when the intermediate converts to propene, assuming one new C=C bond is fully formed and one C–C bond is fully broken relative to cyclopropane.
(3) Part 3: (c) Using your answers from parts (a) and (b), determine the overall enthalpy change, ΔHoverall, for the ring-opening reaction.
(4) Part 4: (d) Sketch a two-step potential energy diagram on labeled axes, indicating reactants, the intermediate, products, the two activation energies, and ΔHoverall.
(5) Part 5: (e) Discuss how the strain energy in cyclopropane is implicitly accounted for—or not accounted for—by the bond-energy approach used in your calculations.