Question

Which isomer of 1-bromo-3-isopropylcyclohexane reacts faster when refluxed with potassium tert-butoxide, the cis isomer or the trans isomer? Draw the structure of the expected product from the faster-reacting compound.

Short answer

Answer: The trans isomer of 1-bromo-3-isopropylcyclohexane reacts faster with potassium tert-butoxide due to the more stable intermediate it forms. The expected product from the faster-reacting compound is 1-isopropyl-3-methylcyclohexene.

Step-by-step solution

Recall the E2 elimination mechanism

The reaction of 1-bromo-3-isopropylcyclohexane with potassium tert-butoxide (t-BuOK) will proceed via E2 elimination mechanism as it involves a strong base, t-BuOK. In an E2 elimination reaction, an alpha hydrogen (adjacent to the leaving group) is abstracted, and the leaving group (bromine) departs simultaneously to form a double bond.

Draw the structures of cis and trans isomers

First, draw both cis and trans isomers of 1-bromo-3-isopropylcyclohexane. In the cis isomer, the bromine and the isopropyl group are on the same side (both axial or both equatorial). In the trans isomer, the bromine and the isopropyl group are on opposite sides (one axial and one equatorial). Cis isomer:  Trans isomer: 

Compare the intermediates' stabilities

Now we need to determine the stability of the intermediates in both cis and trans isomers when t-BuOK abstracts an alpha hydrogen. The more stable intermediate leads to a faster reaction. In the cis isomer, the abstraction of the axial alpha hydrogen by t-BuOK will result in a less stable intermediate, as the axial isopropyl and t-BuO- groups will experience 1,3-diaxial steric interactions. In the trans isomer, the t-BuO- can easily abstract an equatorial alpha hydrogen, resulting in a more stable intermediate due to the lack of 1,3-diaxial steric interactions. Thus, the trans isomer will react faster.

Draw the structure of the expected product

For the trans isomer, the t-BuO- abstracts an equatorial alpha hydrogen, and the bromine leaves to form a double bond between carbons 1 and 2. The expected product is 1-isopropyl-3-methylcyclohexene. Here is the structure of the product: