Which alkyl halide exhibits complete racemisation in `S_(N^1)` reaction?

Options

A. `(CH_3)_2CHCl`
B. `CH_3CH_2CH_2CH_2Cl`
C. `CH_3CH_2Cl`
D. `C_6H_5CH_2Cl`

Answer

To determine which alkyl halide exhibits complete racemization in an \( S_N1 \) reaction, we need to analyze the stability of the carbocations formed during the reaction. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the \( S_N1 \) Mechanism
The \( S_N1 \) (substitution nucleophilic unimolecular) reaction involves two steps:
1. Formation of a carbocation after the leaving group departs.
2. Nucleophilic attack on the planar carbocation, which can occur from either side, leading to racemization.

### Step 2: Analyze the Given Options
We have four alkyl halides to consider:
1. \( \text{CH}_3\text{C}(\text{Cl})(\text{CH}_3) \) - 2-chloro-2-methylpropane
2. \( \text{CH}_3\text{CH}_2\text{CH}_2\text{CH}_2\text{Cl} \) - 1-chlorobutane
3. \( \text{CH}_3\text{CH}_2\text{Cl} \) - 1-chloroethane
4. \( \text{C}_6\text{H}_5\text{CH}_2\text{Cl} \) - benzyl chloride

### Step 3: Determine Carbocation Stability
- **Option 1**: 2-chloro-2-methylpropane forms a tertiary carbocation, which is stable but not the most stable.
- **Option 2**: 1-chlorobutane forms a primary carbocation, which is less stable.
- **Option 3**: 1-chloroethane also forms a primary carbocation, which is even less stable.
- **Option 4**: Benzyl chloride forms a benzylic carbocation, which is highly stable due to resonance stabilization.

### Step 4: Identify the Most Stable Carbocation
Among the carbocations formed:
- The benzylic carbocation (from benzyl chloride) is the most stable due to resonance.
- The tertiary carbocation (from 2-chloro-2-methylpropane) is stable but not as stable as the benzylic carbocation.
- Primary carbocations (from 1-chlorobutane and 1-chloroethane) are the least stable.

### Step 5: Conclusion on Racemization
The stability of the carbocation directly affects the racemization. The more stable the carbocation, the more likely it is to lead to complete racemization when attacked by a nucleophile from either side.

Since the benzyl carbocation is the most stable, benzyl chloride will exhibit complete racemization in an \( S_N1 \) reaction.

### Final Answer
The alkyl halide that exhibits complete racemization in an \( S_N1 \) reaction is **benzyl chloride (C6H5CH2Cl)**.

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