Step 1: Understanding the Question:
The question asks for the major product of the Friedel-Crafts alkylation reaction of tert-butylbenzene with 1-chloro-2-methylpropane in the presence of a Lewis acid catalyst, anhydrous $\text{AlCl}_3$.
Step 2: Key Formula or Approach:
1. Friedel-Crafts alkylation involves the generation of a carbocation electrophile.
2. Primary carbocations are highly unstable and readily undergo rearrangement (hydride or alkyl shifts) to yield more stable secondary or tertiary carbocations.
3. The tert-butyl group on the benzene ring is an ortho/para-directing group due to inductive electron donation.
Step 3: Detailed Explanation:
• First, let us look at the interaction of the alkyl halide, 1-chloro-2-methylpropane (isobutyl chloride), with the Lewis acid catalyst $\text{AlCl}_3$:
\[ \text{(CH}_3)_2\text{CH-CH}_2\text{-Cl} + \text{AlCl}_3 \rightarrow \text{(CH}_3)_2\text{CH-CH}_2^+ + \text{AlCl}_4^- \]
• This forms a primary isobutyl carbocation, which is relatively unstable.
• To achieve greater stability, a 1,2-hydride shift occurs immediately from the neighboring tertiary carbon to the primary carbon:
\[ \text{(CH}_3)_2\text{C(H)-CH}_2^+ \xrightarrow{1,2\text{-H shift}} \text{(CH}_3)_3\text{C}^+ \text{ (tert-butyl carbocation)} \]
• This rearrangement converts the unstable primary carbocation into the highly stable, tertiary tert-butyl carbocation, which serves as the active electrophile in this reaction.
• Now, the electrophile attacks the aromatic ring of the starting material, tert-butylbenzene.
• The tert-butyl substituent already present on the ring is activating and ortho/para-directing.
• However, because the tert-butyl group is extremely bulky, steric hindrance prevents attack at the ortho-position.
• Consequently, the electrophilic aromatic substitution occurs almost exclusively at the less hindered para-position.
• This electrophilic attack and subsequent deprotonation yields 1,4-di-tert-butylbenzene as the major product.
Step 4: Final Answer:
Therefore, the major product is 1,4-di-tert-butylbenzene (Option A).