Step 1: Understanding the Question:
The question asks for the major product of a reaction between phenol and 1-bromo-3-methylbut-2-ene in the presence of a base (K\(_2\)CO\(_3\)) and a solvent (acetone), specifically proceeding via an S\(_N\)2 mechanism. This is a variation of the Williamson ether synthesis.
Step 2: Detailed Explanation:
1. Role of Reagents:
- Phenol (C\(_6\)H\(_5\)OH): It is acidic and will act as the source of the nucleophile after deprotonation.
- K\(_2\)CO\(_3\) (Potassium Carbonate): It is a moderately strong base used to deprotonate the phenol to form the much more nucleophilic phenoxide ion (C\(_6\)H\(_5\)O\(^-\)).
\[ \text{C}_6\text{H}_5\text{OH} + \text{K}_2\text{CO}_3 \rightleftharpoons \text{C}_6\text{H}_5\text{O}^- \text{K}^+ + \text{KHCO}_3 \]
- 1-bromo-3-methylbut-2-ene: This is the electrophile, a primary allylic halide.
- Acetone: This is a polar aprotic solvent, which favors the S\(_N\)2 mechanism by solvating the cation (K\(^+\)) but not the nucleophile (phenoxide), leaving the nucleophile highly reactive.
2. The S\(_N\)2 Mechanism:
The reaction proceeds by a nucleophilic substitution (S\(_N\)2) mechanism. The phenoxide ion (C\(_6\)H\(_5\)O\(^-\)) acts as the nucleophile and attacks the carbon atom bonded to the bromine atom (the electrophilic center).
The substrate is a primary halide (CH\(_3\))\(_{2}\)C=CH–CH\(_2\)–Br. The attack occurs at the –CH\(_2\)– group.
In an S\(_N\)2 reaction, the nucleophile attacks the electrophilic carbon, and the leaving group (Br\(^-\)) departs in a single, concerted step. There is no formation of a carbocation intermediate, and therefore, no possibility of rearrangement.
\[ \text{C}_6\text{H}_5\text{O}^- + \text{Br-CH}_2\text{-CH=C(CH}_3)_2 \xrightarrow{\text{S}_\text{N}2} \text{C}_6\text{H}_5\text{O-CH}_2\text{-CH=C(CH}_3)_2 + \text{Br}^- \]
3. Identifying the Product:
The product is phenyl-(3-methylbut-2-enyl) ether. This corresponds to the structure shown in option (B). The other options represent rearranged products or incorrect structures.
Step 3: Final Answer:
The major product of the S\(_N\)2 reaction is phenyl-(3-methylbut-2-enyl) ether, as shown in option (B).