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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. Tertiary alcohol by \[{{\text{S}}_{\text{N}}}{\text{1}}\]
B. Secondary alcohol by \[{{\text{S}}_{\text{N}}}{\text{2}}\]
C. Tertiary alcohol by \[{{\text{S}}_{\text{N}}}{\text{2}}\]
D. Secondary alcohol by \[{{\text{S}}_{\text{N}}}{\text{1}}\]

Answer
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Hint: Tertiary carbocation is most stable. Secondary carbocation is more stable than primary carbocation. With decrease in the stability, the rate of reactivity increases. Tertiary alcohols prefer \[{{\text{S}}_{\text{N}}}{\text{1}}\] mechanism. Primary alcohols prefer \[{{\text{S}}_{\text{N}}}{\text{2}}\] mechanism.

Complete answer:
A mixture of concentrated hydrochloric acid and dry anhydrous zinc chloride is called Lucas reagent. By using Lucas reagent, you can perform a test to determine the nature of the alcohol, primary, secondary or tertiary.
When Lucas reagent reacts with an alcohol, it forms a carbocation intermediate. The rate of the reaction depends on the stability and the ease of the formation of the carbocation. The formation of the carbocation is the slow step of the reaction. It is the rate determining step. For the reaction between the Lucas reagent and an alcohol, you can write the following order of reactivity.
tertiary alcohol > secondary alcohol by \[{{\text{S}}_{\text{N}}}{\text{1}}\] mechanism.
Thus, with Lucas reagent, a tertiary alcohol reacts fastest through \[{{\text{S}}_{\text{N}}}{\text{1}}\] mechanism.

Hence, the correct option is the option (A) Tertiary alcohol by \[{{\text{S}}_{\text{N}}}{\text{1}}\]

Note:

\[{{\text{S}}_{\text{N}}}{\text{1}}\] stands for unimolecular nucleophilic substitution reaction. It is a two-step process and involves formation of intermediate carbocation.
On the other hand, \[{{\text{S}}_{\text{N}}}{\text{2}}\] stands for bimolecular nucleophilic substitution reaction. It is a single step process and does not involve formation of carbocation intermediate. It is a concerted mechanism in which bond breaking and bond formation takes place simultaneously.