Chair Conformation Energies

Question

The standard free-energy difference between the two chair conformations of isopropylcyclohexane is 9.2 kJ/mol. What is the ratio of concentrations of the two conformations at 25 degrees celsius?

Answer 1

K_eq = e^–ΔG/RT

T = 25 °C = 298 K,

ΔG = 9.2 kJ/mol = 9200 J/mol

R = 8.314 J/mol-K

ΔG/RT = (9200 J/mol)/(8.314 J/mol-K)(298 K) = 3.7133

K_eq = e^–3.7133 ≈ 1/40.99

Answer (rounded to 2 significant figures)

The ratio of concentrations of the two conformations

[axial conformer]/[equatorial conformer] = 1/41