Which of the following alcohols on addition of Lucas reagent reacts fast and turns the reagent turbid instantly.

Lucas reagent is a mixture of concentrated $\text{HCl}$ and anhydrous $\text{ZnCl}_2$.

The reaction of alcohols with Lucas reagent proceeds via an $S_N1$ mechanism, which involves the formation of a carbocation intermediate.

The rate of reaction depends on the stability of the carbocation formed. The order of stability of carbocations is tertiary $>$ secondary $>$ primary. Therefore, the reactivity of alcohols towards Lucas reagent follows the order: tertiary $>$ secondary $>$ primary.

Tertiary alcohols react instantly to form an insoluble alkyl halide, producing immediate turbidity.

Secondary alcohols react in about 5 minutes to produce turbidity.

Primary alcohols do not produce turbidity at room temperature.

Among the given options, tert-butyl alcohol is a tertiary alcohol, so it forms a stable tertiary carbocation and reacts instantly to give turbidity.

n-butyl alcohol and iso-butyl alcohol are primary alcohols, while sec-butyl alcohol is a secondary alcohol.

Answer: tert - Butyl alcohol