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(B) The rate of an $S_{N}1$ reaction depends on the stability of the carbocation intermediate formed after the leaving group departs.In option $(c)$,t

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$CH_{3}C(Br)(CH_{3})CH_{2}CH_{3}$ or $CH_{3}CH(Br)CH(CH_{3})_{2}$

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(B) The rate of an $S_{N}1$ reaction depends on the stability of the carbocation intermediate formed after the leaving group departs.In option $(c)$,the first compound is bromocyclohexane,which forms a secondary carbocation.The second compound is $3-$bromocyclohexene,which forms an allylic carbocation upon the loss of the bromide ion.An allylic carbocation is resonance-stabilized,making it significantly more stable than a simple secondary carbocation.Therefore,$3$-bromocyclohexene reacts faster than bromocyclohexane.In option $(b)$,the first compound is $CH_{3}C(Br)(CH_{3})CH_{2}CH_{3}$ (a tertiary alkyl bromide),which forms a tertiary carbocation.The second compound is $CH_{3}CH(Br)CH(CH_{3})_{2}$ (a secondary alkyl bromide),which forms a secondary carbocation.Since a tertiary carbocation is more stable than a secondary carbocation,the first compound reacts faster than the second.Thus,both $(b)$ and $(c)$ are correct,but $(b)$ is the standard textbook example for tertiary vs secondary carbocation stability.

Among the given pairs,in which pair does the first compound react faster than the second compound in an $S_{N}1$ reaction?

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