Why is a cis-1,3-disubstituted cyclohexane more stable thanits trans isomer?

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Answer:

Explanation has been given below

Explanation:

In diaxial conformation of cis-1,3-disubstituted cyclohexane, 4 gauche-butane interactions along with syn-diaxial interaction are present. Hence it readily gets converted to diequitorial conformation where no such gauche-butane interaction is present
In two possible conformations of trans-1,3-disubstituted cyclohexane, 2 gauche-butane interactions are present in each of them.
Hence cis-1,3-disubstituted cyclohexane exists almost exclusively in diequitorial form. But trans-1,3-disubstituted cyclohexane has no such option.

Trans-1,3-disubstituted cyclohexane experiences gauche butane interaction in each of the two conformations.
Therefore cis-1,3-disubstituted cyclohexane is more stable than trans conformation