Which one of the following alcohols reacts instantaneously with Lucas reagent?

The correct answer is:
$C{H}_3-\underset{C{H}_3}{\underset{|}{\stackrel{C{H}_3}{\stackrel{|}{C}}}}-OH$

Step-by-step Explanation:

1. Understanding Lucas Reagent and the Reaction Mechanism
Lucas reagent is a mixture of concentrated hydrochloric acid ($HCl$) and anhydrous zinc chloride ($ZnC{l}_2$). It is used to distinguish between primary, secondary, and tertiary alcohols.
The reaction proceeds via a nucleophilic substitution mechanism ($S_{N}1$), where the rate-determining step is the formation of a carbocation intermediate.

2. Stability of Carbocations
The rate of reaction of alcohols with Lucas reagent depends directly on the stability of the carbocation formed during the reaction:
$\text{Tertiary (3}°\text{) carbocation}>\text{Secondary (2}°\text{) carbocation}>\text{Primary (1}°\text{) carbocation}$

3. Reactivity Behavior
- Tertiary alcohols (3°) react instantaneously with Lucas reagent to produce turbidity (cloudiness due to the formation of insoluble alkyl chlorides) at room temperature.
- Secondary alcohols (2°) react within 5 to 10 minutes.
- Primary alcohols (1°) do not produce turbidity at room temperature unless heated.

4. Analyzing the Options
Let us determine the degree of each given alcohol:
1. $C{H}_3-C{H}_2-C{H}_2-C{H}_{2}OH$ (Butan-1-ol): The $-OH$ group is attached to a primary carbon. This is a primary (1°) alcohol.
2. $C{H}_3-C{H}_2-CH\left(C{H}_3\right)-OH$ (Butan-2-ol): The $-OH$ group is attached to a carbon that is bonded to two other carbons. This is a secondary (2°) alcohol.
3. $C{H}_3-CH\left(C{H}_3\right)-C{H}_{2}OH$ (Isobutyl alcohol): The $-OH$ group is attached to a primary carbon. This is a primary (1°) alcohol.
4. $(C{H}_3{)}_{3}C-OH$ (2-Methylpropan-2-ol / tert-Butyl alcohol): The $-OH$ group is attached to a tertiary carbon (a carbon bonded to three other methyl groups). This is a tertiary (3°) alcohol.

Since tertiary alcohols form the highly stable tertiary carbocation intermediate, 2-methylpropan-2-ol reacts instantaneously with Lucas reagent at room temperature to form a precipitate of tert-butyl chloride.