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Q. Which one is most reactive towards $S_N 1$ reaction?

AIPMTAIPMT 2010Haloalkanes and Haloarenes

Solution:

$S_N 1$ reaction involves the formation of carbonation intermediate. More the stability of carbonation, more is the reactivity of alkyl/aryl halides towards $S_N 1$ reaction. The intermediate carbonations formed by given halides are as:
$ C _6 H _5 CH \left( C _6 H _5\right) Br \rightarrow\left( C _6 H _5\right)_2 \overset{+}{C} H + Br ^{-} C _6 H _5 CH \left( CH _3\right) Br \rightarrow C _6 H _5 \overset{+}{ C } H \left( CH _3\right)+ Br ^{-} \text {(c) } C _6 H _5 C \left( CH _3\right)\left( C _6 H _5\right) Br \rightarrow\left( C _6 H _5\right)_2 \overset{+}{C} \left( CH _3\right)+ Br ^{-}C _6 H _5 CH _2 Br \rightarrow C _6 H _5 \overset{+}{ C } H _2+ Br ^{-} $
The order of stability of these carbocations is as
$\left( C _6 H _5\right)_2 \overset{+} {C }\left( CH _3\right)>\left( C _6 H _5\right)_2 \overset{+} {C} H > C _6 H _5 \overset{+} {C } H \left( CH _3\right)> C _6 H _5 \overset{+}{C} _2$
Thus, $C _6 H _5 C \left( CH _3\right)\left( C _6 H _5\right) Br$ is most reactive towards $S _{ N } 1$ reaction.