Write equations for the steps in `SN^1` mechanism of the conversion of tert.butyl bromide into tert.butyl alcohol.

Explanation

i) `"2 - bromopentane "overset("alc KOH,")rarr CH_(3)-CH=CH-CH_(2)-CH_(3)`
ii)
iiii) `C_(2)H_(5)Br+AgCN overset(Delta)rarr C_(2)H_(5)NC or " ethylisocyanide"`
The mechanism involves the following two steps.
Step 1 :
Formation of carbocation : t - butyl bromide undergoes ionization to form a t- butyl carbocation.

This step is the slowest step hence it is the rate determining step.
Step - 2 :
Attack of nucleophile on the carbocation : The nucleophile `OH^(-)` can attack the carbocation either from front side or back side to form t - butyl alcohol. This step is fast.

`therefore "  Rate of the reaction is directly "alpha` [t - butyl bromide] 1 `[OH-]10`
`therefore "  Order = 1"`