Step 1: Understanding the reaction.
When 2-methylpropan-2-ol (tert-butyl alcohol) is treated with alumina (Al\(_2\)O\(_3\)) at 423 K, it undergoes dehydration to form an alkene. The product is isobutylene (2-methylpropene).
Step 2: Analyzing the options.
(A) Propanone: This is a ketone and not formed in this dehydration reaction.
(B) Propene: This is an alkene, but the product from 2-methylpropan-2-ol will be isobutylene, not propene.
(C) Propanoic acid: This is a carboxylic acid and is not the product of this reaction.
(D) Isobutylene: Correct — 2-methylpropan-2-ol undergoes dehydration to form isobutylene.
Step 3: Conclusion.
The correct answer is (D) Isobutylene, as it is the product of the dehydration of 2-methylpropan-2-ol.