Explain `S_(N) - 1` reaction mechanism.

Explanation

`SN^(1)` reaction
When tertiary butyl bromide is heated with aqueous potassium hydroxide, tertiary butyl alcohol is formed and follows the first order kinetics. i.e. The rate of reaction depends on the concentration of only one reactant i.e. tertiary butyl bromide
`underset(" "r=K[(CH_(3))_(3)CBr]^(1))((CH_(3))CBr+KOH to CH_(3)-underset(CH_(3))underset(|)overset(CH_(3))overset(|)C-OH+KBr)`
Mechanism :
Step-1 : Formation of Carbocation.
`CH_(3)-underset(CH_(3))underset(|)overset(CH_(3))overset(|)C-Br overset("Slow")toCH_(3)-underset(CH_(3))underset(|)overset(CH_(3))overset(|)(" C"^(o+))+Br^(-)`
This is the rate determining step.
Step-2: Attack of nucleophile on carbocation
The nucleophile `OH^(-)` attacks the positive center of carbocation from any one of the direction forming tertiary butyl alcohol