Key idea for $S_N2$ reactivity

In an $S_N2$ reaction, the nucleophile attacks from the back side. Therefore, the rate depends mainly on:

• Steric hindrance around the carbon bearing the leaving group
• Whether the substrate is primary, secondary, tertiary, allylic, benzylic, vinyl, aryl, etc.

General order for $S_N2$ reactivity: $\text{benzylic/allylic} > 1^\circ > 2^\circ \gg 3^\circ$ Also, aryl halides and vinyl halides are very poor for $S_N2$ because back-side attack is not feasible on an $sp^2$ carbon.

Identify the nature of the four compounds

From the answer choices, the most reasonable interpretation is:

• $(III)$ is the most reactive, so it is likely a benzylic or allylic halide
• $(II)$ is next, so it is likely a primary alkyl halide
• $(IV)$ is less reactive than $(II)$ but more than $(I)$, so it is likely a secondary alkyl halide
• $(I)$ is the least reactive, so it is likely an aryl/vinyl halide or a highly hindered substrate

Apply $S_N2$ rules

• Benzylic/allylic halide reacts fastest due to resonance stabilization of transition state and low steric hindrance.
• Primary alkyl halide reacts faster than secondary because of less steric hindrance.
• Secondary alkyl halide is slower than primary.
• Aryl/vinyl halide is least reactive (almost no $S_N2$).

Therefore, the decreasing order is: $(III) > (II) > (IV) > (I)$

Match with the options

This corresponds to Option D.

Comparison with stored answer

Stored correct answer = D

Our derived answer = D

Hence, they agree.