Final answer:
The trans-1-bromo-3-tert-butylcyclohexane isomer will react faster in an E2 elimination reaction than its cis counterpart because it has less steric hindrance around the beta carbon, making the necessary anti-periplanar alignment more accessible.
Step-by-step explanation:
The student has asked which stereoisomer, cis-1-bromo-3-tert-butylcyclohexane or trans-1-bromo-3-tert-butylcyclohexane, will react faster in an E2 elimination reaction. In such a E2 elimination reaction, the reaction rate is significantly influenced by the steric hindrance around the reacting site. Steric hindrance refers to the repulsion between the electron clouds of the bulky groups attached to the carbons in the molecule, which can slow down chemical reactions.
For E2 reactions, anti-periplanar geometry is necessary, so that the leaving group and the hydrogen atom being removed are aligned opposite to each other, allowing for the simultaneous elimination of the two, resulting in the formation of the double bond. In the case of cyclohexane, the trans isomer is usually more favorable for E2 reactions because the bulky groups are on opposite sides, reducing the steric hindrance and allowing for a more accessible anti-periplanar geometry.
Therefore, trans-1-bromo-3-tert-butylcyclohexane is the isomer that will react faster in the E2 elimination reaction due to less steric crowding around the beta carbon, facilitating easier elimination of the leaving group and the beta hydrogen.