(Download the ChimeTM plug-in to view structures. How to manipulate structures.) What is the difference in energy between the two chair conformations of cis-1,2-dimethylcyclohexane? Cis-1,2-substitution in a chair cyclohexane means that one group (methyl) group must be equatorial and the other axial [Review]. A chair-chair interconversion would merely switch the position of the two groups: equatorial ---> axial; axial ---> equatorial. Therefore, DGo = 0 kcal/mol and Keq = 1 for chair 1 and chair 2. In fact, the two chairs are mirror images of one another. Stop the rotation of the structures and arrange them so that they reflect one another is nearly as possible.
What is the energy of these mirror images? The green carbons illustrate the presence of a gauche butane interaction [Review: butane] between the two methyl groups (0.9 kcal/mol). Rotate the structure into a Newman projection to see the 60o dihedral angle. The green axial methyl group has two gauche butane interactions with the ring, i. e., the green axial methyl group is diaxial to two blue hydrogens [Review]. The total energy is 3 x 0.9 = 2.7 kcal/mol.
What other chair dimethyl cyclohexanes have Keq = 1?