The order of ,`S_N 1` reactivity in aqueous acetic acid solution for the compounds
`underset(1)(H_3C -overset(O)overset(||) C- CH_2 - Cl)" "underset(2)(H_3C - CH_2 - CH_2 - Cl) `
` underset(3)((H_3C)_3 C - Cl)` is

Options

A. `1 gt 2 gt 3 `
B. `1 gt 3 gt 2`
C. `3 gt 2 gt 1`
D. `3 gt 1 gt 2 `

Explanation

To determine the order of \( S_N 1 \) reactivity for the given compounds in aqueous acetic acid solution, we need to analyze the stability of the carbocations formed during the reaction. The \( S_N 1 \) mechanism involves the formation of a carbocation intermediate, and the stability of this carbocation is crucial for the reactivity of the compound.

### Step 1: Identify the Compounds and Their Carbocations
1. **Compound 1**: \( H_3C - C(=O) - CH_2 - Cl \)
- Upon losing Cl, the carbocation formed is \( H_3C - C(=O) - CH_2^+ \) (a primary carbocation).

2. **Compound 2**: \( H_3C - CH_2 - CH_2 - Cl \)
- Upon losing Cl, the carbocation formed is \( H_3C - CH_2 - CH_2^+ \) (a primary carbocation).

3. **Compound 3**: \( (H_3C)_3C - Cl \)
- Upon losing Cl, the carbocation formed is \( (H_3C)_3C^+ \) (a tertiary carbocation).

### Step 2: Analyze the Stability of the Carbocations
- **Tertiary Carbocation**: The carbocation from Compound 3 is tertiary and is stabilized by hyperconjugation and inductive effects from the three methyl groups.
- **Primary Carbocations**: The carbocations from Compounds 1 and 2 are primary. However, Compound 1 has a carbonyl group (C=O) which exerts a -I (inductive) effect, reducing the stability of the carbocation. Compound 2, on the other hand, does not have such a group and is more stable than Compound 1.

### Step 3: Order of Stability
Based on the stability of the carbocations:
1. **Most Stable**: Compound 3 (tertiary carbocation)
2. **Moderately Stable**: Compound 2 (primary carbocation without destabilizing groups)
3. **Least Stable**: Compound 1 (primary carbocation with a destabilizing carbonyl group)

### Step 4: Order of \( S_N 1 \) Reactivity
Since the \( S_N 1 \) reactivity is directly related to the stability of the carbocation formed:
- **Order of Reactivity**:
- Compound 3 > Compound 2 > Compound 1

### Final Answer
The order of \( S_N 1 \) reactivity in aqueous acetic acid solution is:
\[ (H_3C)_3C - Cl > H_3C - CH_2 - CH_2 - Cl > H_3C - C(=O) - CH_2 - Cl \]

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