Disubstituted Cyclohexanes: The Relative Stability of cis and trans Isomers
The situation is more complex when the effect of conformations on the relative stability of cis and trans disubstituted cyclohexanes is analyzed. Remember, configurational stereoisomers do not interconvert without breaking bonds, whereas conformational isomers normally interconvert rapidly by the ring flip process.
Let’s apply a similar analysis to the cis and trans stereoisomers of 1,2-dimethylcyclohexane.
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In cis-1,2-dimethylcyclohexane, one methyl group is axial and one methyl group is equatorial in both ring flip conformers, so neither conformer is more stable than the other. It is important to note, that this molecule cannot get both methyl groups axial without breaking bonds to make a new molecule.
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In trans-1,2-dimethylcyclohexane, one conformer has both methyl groups axial and the other has both methyl groups equatorial. The conformer with both methyl groups axial is 3.4 kcal/mole (2 x 1.7 kcal/mol) less stable than the conformer with both methyl groups equatorial. Obviously, the equilibrium will favor the conformer with both methyl groups in the equatorial position.
To decide whether the cis or trans isomer of 1,2-dimethylcyclohexane is more stable, compare the relative energy of the most stable conformer of cis-1,2-dimethylcyclohexane to the most stable conformer of trans-1,2-dimethylcyclohexane. The trans-1,2-dimethylcyclohexane has the most stable conformer, so it is the more stable isomer.
Does this mean that the trans isomer of a disubstituted cyclohexane is always more stable than the cis isomer? Let’s examine both the cis and trans isomers of 1,3-dimethylcyclohexane and find out.
As can be seen in the structures above, cis-1,3-dimethylcyclohexane’s most stable conformer has both methyl groups equatorial, while trans-1,3-dimethylcyclohexane always has one methyl group is equatorial and one methyl group axial. This means that the cis isomer 1,3-dimethylcyclohexane is more stable than the trans isomer. And that is opposite what we found for 1,2-dimethylcyclohexane.
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As practice, you should do a similar conformational analysis of the cis and trans isomers of 1,4-dimethylcyclohexane. You should find that the trans isomer of 1,4-dimethylcyclohexane is more stable than the cis isomer.
Summary
The relative stabilities of the cis and trans isomers of disubstituted cyclohexanes depends upon which isomer has the most stable conformer. The most stable isomer for disubstituted cyclohexanes is summarized below.
substitution type most stable isomer 1,2-disubstituted cyclohexanes trans 1,3-disubstituted cyclohexanes cis 1,4-disubstituted cyclohexanes trans
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