Why does 1,2-dimethylcyclohexane only possess three stereoisomers? [duplicate]








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[Is cis-1,2-dimethylcyclohexane a meso compound?](/questions/61107/is-cis-1-2-dimethylcyclohexane-a-meso-compound)

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> Why does 1,2-dimethylcyclohexane in chair form have only three stereoisomers?
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I understand that the *trans* isomer doesn't possess plane of symmetry and thus it has two stereoisomers. But my book says that the *cis* isomer has does not have two stereoisomers. Why is this so?


[![cis-1,2-dimethylcyclohexane](https://i.stack.imgur.com/AlM7f.png)](https://i.stack.imgur.com/AlM7f.png)


The structure of *cis*-1,2-dimethylcyclohexane is shown above. Its mirror image is non-superimposable and cannot be obtained by rotation about single single bonds or by a ring flip. Can anyone explain?Thanks 




Quoting , ORGANIC CHEMISTRY second edition by JOSEPH M. HORNBACK, UNIVERSITY OF DENVER


1,2-dimethylcyclohexane has two chirality centers.
[![enter image description here](https://i.stack.imgur.com/RyLcT.png)](https://i.stack.imgur.com/RyLcT.png)


The cis-diastereomer has a plane of symmetry bisecting the ring bond between
the two methyl groups and therefore a meso compound.It is not chiral and does not rotate plane-polarized light.The trans-diastereomer exists as a pair of enantiomers.


The chair conformation of cis-1,2-dimethylcyclohexane shows that it is chiral.
But due to ring-flip , another conformation ,its enantiomer of the original conformation is also formed.These conformers interconvert rapidly at room temperature, therefore cis-1,2-dimethylcyclohexane is not chiral.


Further I quote


"stereochemical analyses such as the preceding one can be done with drawings using planar rings" pg.235.


A molecule cannot be optically active if its chiral conformations are in
equilibrium with their mirror images. We consider such a molecule to
be achiral. PG- 193 - ORGANIC CHEMISTRY .EIGHTH EDITION
L.G. WADE , JR . WHITMAN COLLEGE


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