Compare SN2 Reaction Rates of Alkyl and Acyl Chlorides with Potassium Iodide

To determine the relative rates of the $S_N2$ reaction of the given substrates with potassium iodide ($KI$) in acetone (the Finkelstein reaction), we examine the electronic and steric factors affecting the transition state of each substrate:

1. Substrate $S$ ($\text{Ph}-\text{C}(=\text{O})-\text{CH}_2-\text{Cl}$, Phenacyl chloride):

   • It is an $\alpha$-haloketone. The adjacent carbonyl group ($\text{C}=\text{O}$) exerts a strong electron-withdrawing inductive effect ($-I$), creating a significant partial positive charge ($\delta^+$) on the $\alpha$-carbon and making it exceptionally electrophilic.
   • More importantly, in the $S_N2$ transition state, the partially formed and broken bonds (represented by a developing $p$-orbital on the reaction center) overlap effectively with the adjacent $\pi^*$ orbital of the carbonyl group. This conjugated interaction significantly stabilizes the transition state, leading to a drastically lowered activation energy ($E_a$).
   • As a result, $\alpha$-haloketones undergo $S_N2$ substitution thousands of times faster than simple alkyl halides. Thus, substrate $S$ has the highest rate of reaction.

2. Substrate $P$ ($\text{H}_3\text{C}-\text{Cl}$, Methyl chloride):

   • Methyl halides possess negligible steric hindrance around the carbon undergoing nucleophilic attack. Since the $S_N2$ reaction is extremely sensitive to steric hindrance, the absence of alkyl substituents allows for a rapid backside attack by the iodide ion ($I^-$).

3. Substrate $R$ ($\text{CH}_2=\text{CH}-\text{CH}_2-\text{Cl}$, Allyl chloride):

   • Although the allylic system offers transition state stabilization through $\pi$-orbital overlap, it is a primary halide with a vinyl substituent, which offers greater steric bulk than the hydrogens in methyl chloride ($P$).

4. Substrate $Q$ ($(\text{CH}_3)_2\text{CH}-\text{Cl}$, Isopropyl chloride):

   • This is a secondary ($2^\circ$) alkyl halide with two bulky methyl groups attached to the reacting center. The increased steric hindrance substantially disfavors the backside attack required in an $S_N2$ mechanism, resulting in the slowest reaction rate among the given substrates.

Comparing the relative rates across the options, only Option (B) correctly places the exceptionally reactive $\alpha$-haloketone ($S$) as the fastest substrate: $S > P > R > Q$

Therefore, the correct option is (B).