Question

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 (a) secondary alcohol by \(\mathrm{S}_{\mathrm{N}^{2}}\) (b) tertiary alcohol by \(\mathrm{S}_{\mathrm{N}^{2}}\) (c) Secondary alcohol by \(\mathrm{S}_{\mathrm{N} 1}\) (d) tertiary alcohol by \(\mathrm{S}_{\mathrm{N}^{1}}\)

Short answer

Option (d): Tertiary alcohol by SN1.

Step-by-step solution

Understand the Lucas Test

The Lucas reagent is a solution of zinc chloride in concentrated hydrochloric acid. It is used to classify alcohols of low molecular weight into primary, secondary, and tertiary alcohols based on their reactivity.

Identify the Reactivity of Alcohols

The reactivity of alcohols with the Lucas reagent typically increases in the order of primary < secondary < tertiary. Tertiary alcohols react the fastest to form alkyl halides.

Determine the Reaction Mechanism

The reaction mechanism of alcohols with the Lucas reagent depends on the stability of the carbocation formed. Tertiary alcohols undergo the SN1 mechanism as they form stable tertiary carbocations, which facilitates a faster reaction.

Choose the Correct Option

Given the choice that tertiary alcohols react quickly with the Lucas reagent and that their mechanism is predominantly SN1 due to carbocation stability, the correct answer is option (d) - tertiary alcohol by SN1.

Key concepts

Alcohol Reactivity

Understanding the reactivity of alcohols is crucial when predicting how they interact with different reagents, such as the Lucas reagent. When alcohols are treated with the Lucas reagent, they undergo a reaction to form alkyl halides. This transformation is quite handy because it helps distinguish between primary, secondary, and tertiary alcohols based on the speed of their reactions.
A primary alcohol reacts very slowly with the Lucas reagent because the resulting primary carbocation is relatively unstable. Secondary alcohols react faster than primary ones, but tertiary alcohols outpace both. This is because tertiary alcohols form highly stable tertiary carbocations, enabling quicker reactions.

• Primary alcohol: Slow reaction
• Secondary alcohol: Moderate reaction
• Tertiary alcohol: Fast reaction

Thus, the increased reactivity of tertiary alcohols with the Lucas reagent helps distinguish them from primary and secondary alcohols.

SN1 Mechanism

The SN1 mechanism, or substitution nucleophilic unimolecular mechanism, is a two-step reaction that involves the formation of a carbocation intermediate. This mechanism is typically seen in the reaction of alcohols with the Lucas reagent, particularly tertiary alcohols. Let's break down the SN1 mechanism:

1. **Formation of Carbocation:** In the first step, the hydroxy group of the alcohol is protonated by the acidic Lucas reagent, creating water, which is a good leaving group. It leaves behind a carbocation.
2. **Nucleophilic Attack:** In the second step, the chloride ion from the reagent quickly attacks the carbocation, resulting in the formation of an alkyl halide.

Because tertiary carbocations are more stable due to their electronic environment—they have more alkyl groups donating electron density—the formation of a carbocation is more favorable. This increases the likelihood of a successful SN1 reaction, explaining why tertiary alcohols react faster in the Lucas test.

Tertiary Alcohols

Tertiary alcohols are a class of alcohols characterized by the hydroxyl group (-OH) attached to a carbon that is itself bonded to three other carbon atoms. This structural arrangement plays a significant role in their behavior in chemical reactions.

Tertiary alcohols react rapidly and decisively with the Lucas reagent due to the stability of the tertiary carbocation formed during the SN1 mechanism. In these alcohols, the central carbon atom is surrounded by three other carbon groups, which provide significant stabilization through hyperconjugation and the inductive effect.

• Hyperconjugation: The sharing of electrons from \(\sigma\) bonds of adjacent \(\alpha\)-carbons enhances carbocation stability.
• Inductive effect: Electron-donating groups stabilize the positive charge on the carbocation.

This stabilization impacts their reactivity, making tertiary alcohols the most reactive type in the context of the Lucas test. Their swift conversion to alkyl halides is observed because the tertiary structure allows for efficient and stable formation of the necessary carbocation intermediate.