Which of the following alkyl halides is hydrolysed by `S_(N^1)`mechanism ?
`CH_3 Cl`
`CH_3 CH_2 Cl`
`CH_3CH_2 CH_2 Cl`
`(CH_3)_3 C Cl`

Options

A. `CH_3 Cl`
B. `CH_3 CH_2 Cl`
C. `CH_3CH_2 CH_2 Cl`
D. `(CH_3)_3 C Cl`

Explanation

To determine which of the given alkyl halides is hydrolyzed by the \( S_N1 \) mechanism, we need to analyze the stability of the carbocations formed from each alkyl halide. The \( S_N1 \) mechanism involves the formation of a carbocation intermediate, and the stability of this carbocation is crucial for the reaction to proceed.

### Step-by-Step Solution:

1. **Identify the Alkyl Halides**: We have four alkyl halides to consider:
- \( CH_3Cl \) (Methyl chloride)
- \( CH_3CH_2Cl \) (Ethyl chloride)
- \( CH_3CH_2CH_2Cl \) (Propyl chloride)
- \( (CH_3)_3CCl \) (Tert-butyl chloride)

2. **Draw the Carbocations**:
- For \( CH_3Cl \):
- Hydrolysis gives \( CH_3^+ \) (methyl carbocation), which is a primary (1°) carbocation.
- For \( CH_3CH_2Cl \):
- Hydrolysis gives \( CH_3CH_2^+ \) (ethyl carbocation), which is also a primary (1°) carbocation.
- For \( CH_3CH_2CH_2Cl \):
- Hydrolysis gives \( CH_3CH_2CH_2^+ \) (propyl carbocation), which is a primary (1°) carbocation.
- For \( (CH_3)_3CCl \):
- Hydrolysis gives \( (CH_3)_3C^+ \) (tert-butyl carbocation), which is a tertiary (3°) carbocation.

3. **Analyze Carbocation Stability**:
- The stability of carbocations increases with the degree of substitution:
- Tertiary (3°) > Secondary (2°) > Primary (1°) > Methyl (0°).
- The methyl, ethyl, and propyl carbocations are all primary and less stable compared to the tert-butyl carbocation.

4. **Determine the \( S_N1 \) Mechanism**:
- Since \( S_N1 \) reactions favor the formation of more stable carbocations, the only alkyl halide that can undergo hydrolysis via the \( S_N1 \) mechanism is the one that forms a tertiary carbocation.
- Therefore, \( (CH_3)_3CCl \) (tert-butyl chloride) is the alkyl halide that is hydrolyzed by the \( S_N1 \) mechanism.

### Final Answer:
The alkyl halide that is hydrolyzed by the \( S_N1 \) mechanism is \( (CH_3)_3CCl \).