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.
The cis- isomer
is the equivalent of a meso- diastereomer, having opposite configurations at the two identical chiral centers.
The cis-1,3-dimethyl regioisomer is a more traditional meso 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:
|Cis and Trans-1,4-Dimethylcyclohexanes|
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: