Stereoisomers and Cyclic Compounds

The cis- and trans-stereoisomers of cyclic compounds that were presented previously are actually just special cases of the type of stereoisomers that we have just discussed. For example, consider the case of 1,2-dimethylcyclohexane  

There are two chirality centers, so the formula predicts that there are four stereoisomers. However, because the chirality centers are identical, we expect that there are actually fewer than four stereoisomers. In fact, the analysis is identical to the one we just did for tartaric acid. There are three stereoisomers a d,l-pair of enantiomers and a meso-diastereomer. 

The m-diastereomer is meso. It has a plane of symmetry bisecting the ring bond between the two methyl groups. It is not chiral and does not rotate plane-polarized light. 

The tnms-iliastereomer exists as a pair of enantiomers. These stereochemical differences do not depend on the presence of the ring. In fact, suppose the ring is cleaved at the C—C bond opposite the one connecting the chirality centers. The resulting compound, 3,4-dimethylhexane, also has three stereoisomers a weso-diastereomer and two enantiomers of a c/,/-diastereomer. It is just easier to see that the cis- and trans-diastereomers of 1,2-dimethylcyclohexane are different than it is to see that the meso-and c/,/-diastereomers of 3,4-dimethylhexane are different. 

Draw all of the stereoisomers of 1,2-dimethylcyclopropane. Explain which rotate plane-polarized light. 

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