Imagine that the staggered and eclipsed conformers of a small, saturated hydrocarbon are separated in energy by 3.2 kcal/mol. Given this information, what would be the ratio of staggered to eclipsed conformers of this molecule at any given instant? Assume that the sample is at thermal equilibrium at 25 °C, and enter your answer to the nearest ones. Hint: the gas constant, R, equals 1.987 cal/K·mol and T in Kelvin equals the temperature in Celsius + 273; also, assume that all the molecules are either staggered or eclipsed.

Explanation:

Staggered        ⇒       Eclipsed

Let the equilibrium constant be K

K = eclipsed / staggered

ΔG = - RT lnK

3200 = 1.987 x 298 lnK

lnK = -5.4

K = e⁻ ⁵°⁴

=4.5 x 10⁻³

eclipsed / staggered = 4.5 x 10⁻³

STAGGERED / ECLIPSED = 222

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