Understanding $S_N2$ Substitution in Optically Active Alkyl Halides

The question asks about the stereochemical outcome when an optically active alkyl halide undergoes an $S_N2$ substitution reaction. Let's break down the $S_N2$ mechanism.

Mechanism of $S_N2$ Reactions

The term $S_N2$ stands for Bimolecular Nucleophilic Substitution. This reaction mechanism has several key features:

• Bimolecular: The rate of the reaction depends on the concentration of both the substrate (alkyl halide) and the nucleophile.
• Concerted Process: The bond to the leaving group breaks, and the bond to the nucleophile forms at the same time. There is no intermediate formed.
• Backside Attack: The nucleophile attacks the electrophilic carbon atom from the side opposite to the leaving group. This is crucial for the stereochemical outcome.

Stereochemical Outcome: Inversion of Configuration

Because the nucleophile attacks from the backside, the groups attached to the carbon atom are pushed to the other side. This process is analogous to an umbrella flipping inside out during a strong wind.

This specific stereochemical result is known as inversion of configuration, often referred to as Walden inversion.

If the starting alkyl halide is chiral (optically active) and the nucleophile has a different priority ranking compared to the leaving group according to Cahn-Ingold-Prelog rules, the configuration at the chiral center will be inverted. For example, an (R)-alkyl halide typically yields an (S)-product, and vice versa.

Analysis of Options

Let's analyze why the other options are incorrect in the context of a standard $S_N2$ reaction:

• Retention of configuration: This means the stereochemistry stays the same. This is characteristic of reactions where the attacking species approaches from the same side as the leaving group, or involves intermediates that allow for randomization, which is not the case in $S_N2$.
• Racemic mixture: A racemic mixture contains equal amounts of both enantiomers (R and S forms). This usually happens when a planar intermediate (like a carbocation in $S_N1$ reactions) is formed, allowing attack from either face. $S_N2$ reactions do not form carbocations and typically lead to a single stereoisomer (the inverted one), not a mixture of enantiomers.
• Inversion of configuration: This directly matches the outcome predicted by the backside attack mechanism of the $S_N2$ reaction.
• Formation of carbocation: Carbocations are intermediates in $S_N1$ reactions, not $S_N2$ reactions. $S_N2$ reactions are concerted, involving a transition state but no stable intermediate like a carbocation.

Conclusion

Therefore, optically active alkyl halides undergoing $S_N2$ substitution characteristically result in inversion of configuration due to the backside attack by the nucleophile.