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?

Lucas test in alcohol is a test to differentiate between primary, secondary, and tertiary alcohols. It is based on the difference in reactivity of the three classes of alcohols with hydrogen halides. The Lucas reagent is a solution of anhydrous zinc chloride in concentrated hydrochloric acid. Tertiary alcohols react immediately with the Lucas reagent at room temperature, forming a cloudy solution (due to the insolubility of the alkyl chloride formed). Secondary alcohols react within 5-10 minutes, while primary alcohols do not react readily at room temperature. The reaction proceeds through carbocation formation. Since a tertiary carbocation is the most stable, the reaction proceeds through an SN1 mechanism with tertiary alcohols. The reaction rate depends on the stability of the carbocation intermediate formed. Tertiary carbocations are most stable due to the electron-donating effect of the three alkyl groups, followed by secondary carbocations and then primary carbocations. Therefore, tertiary alcohols react fastest, followed by secondary alcohols, and then primary alcohols. The mechanism is SN1 because it involves a carbocation intermediate.