An unknown alcohol is treated with the ''Lucas reagent'' to determine whether the alcohol is primary, secondary or tertiary. Which alcohol reacts fastest and by what mechanism:

Options

A. tertiary alcohol by `S_(N)1`
B. secondary alcohol by `S_(N)2`
C. tertiary alcohol by `S_(N)2`
D. secondary alcohol by `S_(N)1`

Answer

To solve the question regarding the reaction of an unknown alcohol with Lucas reagent, we will analyze the reactivity of primary, secondary, and tertiary alcohols and determine which one reacts the fastest and by what mechanism.

### Step-by-Step Solution:

1. **Understanding Lucas Reagent**:
- Lucas reagent consists of concentrated hydrochloric acid (HCl) and anhydrous zinc chloride (ZnCl₂). It is used to differentiate between primary, secondary, and tertiary alcohols based on their reactivity.

**Hint**: Remember that Lucas reagent facilitates the formation of carbocations during the reaction with alcohols.

2. **Reaction Mechanism**:
- The reaction of alcohols with Lucas reagent proceeds via the **SN1 mechanism** (unimolecular nucleophilic substitution). This mechanism involves two main steps:
1. Formation of a carbocation.
2. Nucleophilic attack by chloride ion (Cl⁻) to form the alkyl chloride.

**Hint**: The stability of the carbocation formed is crucial in determining the rate of the reaction.

3. **Carbocation Stability**:
- The stability of carbocations increases in the order:
- Primary < Secondary < Tertiary.
- Tertiary carbocations are the most stable due to hyperconjugation and inductive effects from surrounding alkyl groups.

**Hint**: Recall that the more stable the carbocation, the faster the reaction will proceed.

4. **Reactivity of Alcohols**:
- **Tertiary Alcohols**: React fastest because they form the most stable carbocation. The reaction with Lucas reagent will show immediate turbidity (cloudiness) due to the formation of the alkyl chloride.
- **Secondary Alcohols**: React slower than tertiary alcohols. Turbidity appears after heating, indicating the formation of a secondary carbocation.
- **Primary Alcohols**: React the slowest, and turbidity does not appear even after prolonged heating, indicating the formation of a very unstable primary carbocation.

**Hint**: Think about how the reaction time and conditions (like heating) affect the visibility of the reaction.

5. **Conclusion**:
- Based on the analysis, the tertiary alcohol reacts fastest with Lucas reagent via the SN1 mechanism. The reaction is characterized by immediate turbidity due to the rapid formation of a stable tertiary carbocation.

**Final Answer**: The tertiary alcohol reacts fastest with Lucas reagent via the SN1 mechanism.