The Lucas reagent will react fastest with:

$\mathrm{(CH_3)_3COH} $

The correct answer is Option (1) → $\mathrm{(CH_3)_3COH} $

Lucas test distinguishes alcohols based on rate of formation of alkyl chloride via SN1 mechanism. Lucas reagent (ZnCl2 + conc HCl) reacts fastest with tertiary(3°) alcohols, typically producing immediate turbidity at room temperature due to the rapid formation of an insoluble tertiary alkyl chloride via an mechanism. Examples include 2-methylpropan-2-ol and tert-butyl alcohol.

Reactivity order:

Tertiary alcohol > Secondary alcohol > Primary alcohol

Option 1: $(CH_3)_3COH$

This is tertiary alcohol (tert-butanol).

Tertiary carbocation formed is highly stable.

Hence reacts immediately with Lucas reagent.

Option 2: $CH_3CH_2OH$

This is primary alcohol.

Primary carbocation is unstable.

Reaction is very slow.

Option 3: $CH_3(CH_2)_2OH$

Also primary alcohol.

Shows slow reaction.

Option 4: $CH_3CH(CH_3)OH$

This is secondary alcohol.

Forms moderately stable carbocation.

Reacts slower than tertiary alcohol.