What percentage of methylcyclohexane exists in the axial methyl conformation at equilibrium, given that K_eq=19.5 at 25°C? R=1.987 x 10^-3 kcal/mol K

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Quizplus · Accepted Answer

K_eq = e^(-ΔG°/RT) ΔG° = -RTln(K) where ΔG° is the standard free energy change, R is the gas constant, T is the temperature in Kelvin, and K is the equilibrium constant. ΔG° = -1.987 x 10^-3 kcal/mol K x (298 K) x ln(19.5) = -1.47 kcal/mol The energy difference between axial and equatorial methyl conformations is approximately 1.6 kcal/mol. Thus, the equilibrium will favor the more stable equatorial conformer. Assuming the axial conformation is x% and the equatorial is (100-x)%, we can set up the following equation for the equilibrium constant: K_eq = [(100-x)/x] x e^-1.6/1.987x10^-3x298 Solving for x gives x = 5%. Therefore, 95% of methylcyclohexane exists in the equatorial conformation at equilibrium.

What Percentage of Methylcyclohexane Exists in the Axial Methyl Conformation