Let's see what we can learn about the dimethylcyclohexanes by examining them with stereochemical eyes. Here's the trans-1,2-dimethyl isomer:

The two carbons bearing methyl groups are identical chiral centers, both having the same configuration in this trans- structure. The molecules are chiral - non-superposable on their mirror images.

• Ring inversion to the diaxial conformers breaks no bonds to the chiral centers, so they must have the same configurations.

• The flipped structures are diastereomers of the starting diequatorial ones, and therefore MUST have different energies.

• The diequatorial structures have one gauche interaction, between the methyl groups, whereas the diaxial have four, two for each methyl with the CH2's 3- and 5- to them.

The cis- isomer

is the equivalent of a meso- diastereomer, having opposite configurations at the two identical chiral centers.

• It does not have a plane of symmetry because the cyclohexane ring is not flat.

• Instead, ring inversion turns each stereoisomer into its own enantiomer.

• Cis-1,2-dimethylcyclohexane could never be resolved; as soon as a single enantiomer was obtained, it would turn into an equilibrium racemic mixture by ring inversion.

The cis-1,3-dimethyl regioisomer is a more traditional meso form:

• The two chiral centers have opposite configurations, and the molecule possesses a plane of symmetry, indicated in green. It is superposable on its mirror image.

• Ring inversion produces another diastereomericmeso form.

Trans-1,3- has the same configurations at its two chiral centers:

The unique feature here is that ring inversion turns each enantiomer into itself!

Neither of the 1,4-dimethylcyclohexanes is chiral; each has a plane of symmetry:

The cis- isomer is turned into itself by ring inversion, whereas the trans- is converted to a diastereomer.

Remember that diastereomers MUST have different energies. Look back at the diastereomers pointed out above and be sure you can estimate the energy of each. Enantiomers must have equal energies; make sure your estimates reflect that requirement.

When you've finished, you can check your answers here: