Which of the following reaction follows `S_N1` mechanism ?

Options

A. `(CH_3)_3C - CH_2Cl+CH_3OK`
B. `(CH_3)_2CHCH_2Cl+KCN`
C. `(CH_3)_3C-Cl+NaOH(aq).`
D. `(CH_3)_2CHI+H_2O`

Answer

To determine which reaction follows the \( S_N1 \) mechanism, we need to understand the characteristics of the \( S_N1 \) mechanism and the stability of carbocations formed during the reaction.

### Step-by-Step Solution:

1. **Understanding the \( S_N1 \) Mechanism**:
- The \( S_N1 \) (Substitution Nucleophilic Unimolecular) mechanism involves two main steps:
1. Formation of a carbocation intermediate by the dissociation of the leaving group (e.g., halide).
2. Nucleophilic attack on the carbocation.
- The rate of the reaction depends only on the concentration of the substrate (alkyl halide), hence it is unimolecular.

2. **Stability of Carbocations**:
- The stability of carbocations is crucial for the \( S_N1 \) mechanism. The order of stability is:
- Tertiary (3°) > Secondary (2°) > Primary (1°) > Methyl (0°).
- More stable carbocations are more likely to form and thus favor the \( S_N1 \) mechanism.

3. **Analyzing the Given Options**:
- We will analyze each option to determine the type of carbocation formed upon dissociation.

**Option 1**: \( \text{(CH}_3)_3C\text{Cl} \)
- Upon dissociation, it forms a tertiary carbocation \( \text{(CH}_3)_3C^+ \).
- This is a stable carbocation, favoring the \( S_N1 \) mechanism.

**Option 2**: \( \text{CH}_3\text{CH}_2\text{Cl} \)
- Upon dissociation, it forms a primary carbocation \( \text{CH}_3\text{CH}_2^+ \).
- This is a less stable carbocation, not favoring the \( S_N1 \) mechanism.

**Option 3**: \( \text{(CH}_3)_2\text{CHCl} \)
- Upon dissociation, it forms a secondary carbocation \( \text{(CH}_3)_2\text{CH}^+ \).
- This is a moderately stable carbocation, which can undergo \( S_N1 \) but is not as favorable as a tertiary carbocation.

**Option 4**: \( \text{CH}_3\text{CH}_2\text{CH}_2\text{Cl} \)
- Upon dissociation, it forms a primary carbocation \( \text{CH}_3\text{CH}_2\text{CH}_2^+ \).
- This is also a less stable carbocation, not favoring the \( S_N1 \) mechanism.

4. **Conclusion**:
- The only option that forms a stable carbocation and thus follows the \( S_N1 \) mechanism is **Option 1**: \( \text{(CH}_3)_3C\text{Cl} \).

### Final Answer:
**Option 1: \( \text{(CH}_3)_3C\text{Cl} \)** follows the \( S_N1 \) mechanism.