Diamond converts spontaneously to graphite according to the balanced equation
diamond→graphite
Measurements at 298 K give
ΔG298∘=−2.9kJ mol−1
and an estimated activation energy of
Ea=180kJ mol−1.
Assume the pre-exponential factor for the rate constant is the same order of magnitude for both forms of carbon.
(a) Using the data above, construct a qualitative reaction coordinate diagram for the conversion at 298 K. Include numerical values for the energies of reactants, transition state, and products relative to diamond.
(b) Calculate the Boltzmann factor e−Ea/RT at 298 K (use R=8.314J mol−1K−1), and interpret its value in terms of the fraction of carbon atoms possessing sufficient energy to reach the transition state at this temperature.
(c) Explain, with reference to both parts (a) and (b), why gem-quality diamonds persist for geological time spans even though their conversion to graphite is thermodynamically favored.
(d) Discuss qualitatively how subjecting the diamond to a temperature of 1500 K at ambient pressure would influence both the rate and spontaneity of conversion. In your answer, address changes to the Boltzmann factor and the sign/magnitude of ΔG∘ at the higher temperature.