The $S_N^1$ mechanism involves two steps: the formation of a carbocation intermediate and then the attack by the nucleophile. This mechanism generally occurs more rapidly when the carbocation formed is more stable. Thus, the stability of the carbocation plays a key role in determining the rate of the reaction.
- Option A: Br$^{-}$ – CH$_2$ = CH – CH$_2$ will form a relatively stable carbocation due to the allyl structure (the positive charge is delocalized over the two carbons of the double bond). This stabilization through resonance makes this substrate undergo $S_N^1$ substitution fastest.
- Option B: C$_6$H$_5$Br: A benzyl halide would form a highly stable carbocation as well, but the allylic carbocation in Option A is slightly more stabilized due to resonance.
- Option C: CH$_3$ – CH = CHBr: This is a simple alkyl halide with a secondary carbocation, which is less stable than an allylic or benzyl carbocation.
- Option D: C$_6$H$_{11}$Br: This is a primary alkyl halide, leading to a less stable carbocation, thus slower in undergoing $S_N^1$ substitution.