Give the mechanism of substitution nucleophilic bimolecular, `S_N^2` reactions.

Explanation

`underset("tert-butyl alcohol (A" 3^@ " alkyl halide) ")((CH_3)_3 CBr +KOH(aq) to underset("tert-Butyl bromide")((CH_3)_3 COH +KBr)`
Mechanism of the reaction : The reaction follows `S_(N^1)` mechanism in case of a `3^@` alkyl halide. This is because a `3^@` carbocation is very stable due to hyper-configuration.
` KOH (aq) to K^(+) (aq) to K^(+) (aq ) + OH^(-) (aq)`
` (CH_3)_3 C Br overset("slow")to (CH_3)_3 C^(+) +Br^(-)`
` (CH_3)_3 C^(+) +OH^(-) overset("Fast")to (CH_3)_3 COH`
Kinetics of the reaction : Rate of reaction `= k(CH_3)_3 C Br`
Order of reactivity of alkyl halides in `S_(N^(1))` mechanism : `1^@ lt 2^@ lt 3^@`