Does cis-or trans-1-bromo-4-tert-butylcylohexane react faster in an E2 reaction?

The tert-butyl group is bulky, so it prefers to occupy the equatorial position, and it does not suffer from syn-diaxial interaction. Hence it is kept in the equatorial position for both structures.

• When tert-butyl lies in the equatorial position, and the bromide group lies in the axial position, then the conformer is cis.
• When tert-butyl lies in the equatorial position, and the bromide group lies in the equatorial position, the conformer is trans.

The $\text{β}$hydrogen must lie in a trans orientation to that of the leaving group (antiperiplanar orientation). In the case of the cis halide, antiperiplanar orientation is maintained, which is not observed for the trans.

It is observed that cis-1-bromo-4-tert-butylcyclohexane reacts faster because the $\text{β}$hydrogen and the leaving group lies in an antiperiplanar orientation which is not possible in the case of trans-1-bromo-4-tert-butylcyclohexane.

Hence, the E2 reaction is faster for cis-1-bromo-4-tert-butylcyclohexane.

The mechanism is shown in the following for better observation of the explanations:

Representation of the elimination reaction scheme for both cis and trans form