For trans-1,2-dimethylcyclohexane at 298 K take: each CH $_{3}$ /H syn-diaxial interaction $= 3.7 kJ mo l^{- 1}$ and one gauche CH $_{3}$ /CH $_{3}$ interaction $= 3.8 kJ mo l^{- 1}$ (use $R = 8.314 J mo l^{- 1} K^{- 1}$ ). What is the mole percent of the diequatorial chair at equilibrium with the diaxial chair?

Answer: D

The diaxial chair has four CH

_{3}

/H syn-diaxial interactions (

4 \times 3.7 = 14.8

kJ/mol) and no gauche CH

_{3}

/CH

_{3}

; the diequatorial chair has only one gauche CH

_{3}

/CH

_{3}

(3.8 kJ/mol). So

Δ G = 14.8 - 3.8 = 11.0

kJ/mol.

K = exp (11000/ (8.314 \times 298)) = 84.8

, and the fraction of the diequatorial chair is

K / (1 + K) = 0.988

, i.e. 98.8 %.