An S_N1 reaction at the asymmetric carbon of an enantiomerically pure chiral alkyl halide gives a product:

with racemization

The correct answer is option 3. with racemization.

Let us delve into the explanation of why an \(S_N1\) reaction at the asymmetric carbon of an enantiomerically pure chiral alkyl halide leads to racemization of the product:

\(S_N1\) Reaction Overview:

\(S_N1\) (Substitution Nucleophilic Unimolecular) reactions proceed in two main steps:

Formation of Carbocation: The alkyl halide undergoes heterolysis (breaking of the bond between carbon and halogen), resulting in the formation of a carbocation \((R^+)\). This step is rate-determining and leads to the formation of a planar carbocation intermediate.

Nucleophilic Attack: A nucleophile \((Nu^-)\) then attacks the carbocation, forming the substitution product.

Chirality and \(S_N1\) Reactions:

Chiral Center: If the starting material is an enantiomerically pure chiral alkyl halide (for example, \(R-CHBrCl\)), it means that it exists in only one chiral form (either R or S configuration).

Carbocation Intermediate: The carbocation formed during the \(S_N1\) reaction is planar and lacks chirality. It can be attacked by the nucleophile from either side with equal probability.

Racemization Process: Since the nucleophilic attack on the carbocation intermediate is equally probable from both sides, the \(S_N1\) mechanism leads to the formation of both enantiomers (R and S configurations) at the chiral center. As a result, the product of the SN1 reaction is a racemic mixture, containing equal amounts of both R and S enantiomers.

Key Points:

Racemization: In the context of \(S_N1\) reactions with enantiomerically pure starting materials, racemization refers to the process where the product mixture contains both possible enantiomers in equal proportions.

Enantiopurity: The starting material's chirality is lost during the \(S_N1\) reaction due to the formation of an achiral carbocation intermediate and subsequent attack by the nucleophile from both sides.

Stereochemical Outcome: Unlike \(S_N2\) reactions, which typically proceed with inversion of configuration, \(S_N1\) reactions at chiral centers of enantiomerically pure compounds lead to racemic mixtures due to the achiral nature of the carbocation intermediate.

Conclusion: Therefore, an \(S_N1\) reaction at the asymmetric carbon of an enantiomerically pure chiral alkyl halide results in racemization of the product, where both R and S configurations are formed in equal amounts due to the attack of the nucleophile on the planar carbocation intermediate from either side. This phenomenon is a direct consequence of the SN1 mechanism and the planar nature of the carbocation intermediate.