I was wondering how these two chair conformations are enantiomers, because they do not seem to be mirror images of each other. The molecule on the left undergoes a ring flip to achieve the conformation of the molecule on the right. Also, I thought that in order for these two molecules to be enantiomers, the carbons would have to change both their R/S configuration, e.g. carbon 1 goes from R to S, and carbon 2 goes from S to R? I would really appreciate any insight!

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Try rotating the one on the right clockwise looking from the top. might be easier if you build 3D models and compare them. – Andrew Oct 22 '21 at 15:21
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1https://chemistry.stackexchange.com/questions/61107/is-cis-1-2-dimethylcyclohexane-a-meso-compound – Mithoron Oct 22 '21 at 16:03
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https://chemistry.stackexchange.com/questions/61107/is-cis-1-2-dimethylcyclohexane-a-meso-compound – Mithoron Oct 22 '21 at 16:04
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A flip of a ring alters the conformation of a cycloalkane, a reversible, gradually wiggle where all atoms remain connected with each other. Passing from one enantiomer to the other enantiomer (e.g., R $\ce{->}$ S) is like driving either on the left, or on the right hand lane; or either light on vs. light off, binary: this is possible only if you break old bonds, and establish new bonds. – Buttonwood Oct 22 '21 at 17:19