Reaction of Lucas reagent with alcohols:
The Lucas reagent is a mixture of concentrated hydrochloric acid (HCl) and zinc chloride (ZnCl2). It is commonly used to differentiate between primary, secondary, and tertiary alcohols based on their reactivity.

SN1 and SN2 reactions:
SN1 and SN2 are two major types of nucleophilic substitution reactions. In an SN1 reaction, the nucleophile attacks the carbocation formed after the leaving group leaves, while in an SN2 reaction, the nucleophile directly displaces the leaving group.

Reactivity of alcohols with Lucas reagent:
The reactivity of alcohols with the Lucas reagent is based on the stability of the carbocation intermediate formed during the reaction. Tertiary carbocations are more stable than secondary carbocations, which are more stable than primary carbocations. Therefore, tertiary alcohols react the fastest, followed by secondary alcohols, and finally primary alcohols.

Explanation of the correct answer:
The correct answer is option 'B', which states that the tertiary alcohol reacts fastest with the Lucas reagent via an SN1 mechanism.

When a tertiary alcohol reacts with the Lucas reagent, the hydroxyl group is protonated by the HCl present in the reagent, forming a positively charged carbocation intermediate. This carbocation is highly stable due to the presence of three alkyl groups, which provide electron-donating inductive effects, stabilizing the positive charge. The nucleophile (Cl-) then attacks the carbocation, resulting in the formation of an alkyl chloride.

Since the reaction proceeds via an SN1 mechanism, the rate-determining step is the formation of the carbocation intermediate. As tertiary carbocations are more stable than secondary carbocations, the reaction occurs at a faster rate for tertiary alcohols compared to secondary alcohols. Therefore, the tertiary alcohol reacts fastest with the Lucas reagent via an SN1 mechanism.

Summary:
- The Lucas reagent is used to differentiate between primary, secondary, and tertiary alcohols.
- Tertiary alcohols react the fastest, followed by secondary alcohols, and finally primary alcohols.
- Tertiary alcohols react with the Lucas reagent via an SN1 mechanism, where the carbocation intermediate is formed and then attacked by the nucleophile.
- The stability of the carbocation intermediate determines the reactivity of alcohols with the Lucas reagent. Tertiary carbocations are the most stable, leading to the fastest reaction rate.