Step 1: Understanding the Concept:
The reaction of chlorides with acetate in acetic acid is a solvolysis-type reaction, which typically follows an \( S_N1 \) mechanism. The rate-determining step is the formation of a carbocation. Therefore, reactivity depends on carbocation stability.
Step 2: Detailed Explanation:
1. Structure (2): Removal of \( Cl^- \) gives a tertiary allylic carbocation stabilized by resonance and the inductive effect of the methyl group. This is the most stable intermediate.
2. Structure (3): Removal of \( Cl^- \) gives a secondary allylic carbocation. It is resonance-stabilized but less so than the tertiary allylic one.
3. Structure (1): This gives an allylic carbocation, but the positioning of the methyl group relative to the double bond in the starting material affects the stability compared to (3).
4. Structure (4): This involves a primary-like environment or less stabilized allylic system compared to others.
Reactivity order in \( S_N1 \): Tertiary allylic \(>\) Secondary allylic \(>\) Primary allylic.
Step 3: Final Answer:
Following the stability of carbocations, the correct order is (2) \(>\) (3) \(>\) (1) \(>\) (4).