Step 1: Understanding the Concept:
Lucas reagent (ZnCl\(_2\)/HCl) reacts with alcohols to form alkyl chlorides. The rate depends on the stability of the carbocation intermediate.
Step 2: Detailed Explanation:}}
\begin{itemize}
\item (A) butan-1-ol: Primary alcohol, forms primary carbocation (least stable), no reaction at room temperature.
\item (B) butan-2-ol: Secondary alcohol, forms secondary carbocation, reacts slowly (turbidity in 5-10 min).
\item (C) 2-methyl propan-1-ol: Primary alcohol (neopentyl type), forms primary carbocation, no reaction at room temperature.
\item (D) 2-methyl propan-2-ol: Tertiary alcohol, forms tertiary carbocation (most stable), reacts immediately (turbidity instantly).
\end{itemize}
Step 3: Final Answer:
2-methyl propan-2-ol (tert-butyl alcohol) reacts fastest, option (D).