Question

When a dextro rotatory alkyl halide is subjected to \(\mathrm{SN}^{1}\) reaction, the product obtained is (a) Dextro rotatory (b) Leavo rotatory (c) A racemic mixture (d) Meso.

Short answer

The product obtained is a racemic mixture (Option c).

Step-by-step solution

Understanding SN1 Reaction Mechanism

An SN1 reaction proceeds through a two-step mechanism where the first step is the formation of a carbocation intermediate. This occurs when the leaving group departs from the substrate, creating a planar, sp2 hybridized carbocation center.

Formation of Racemic Mixture

Since the carbocation intermediate is planar, the nucleophile can attack the carbocation from either side with equal probability. This leads to the formation of two enantiomers in equal amounts, resulting in an optically inactive racemic mixture.

Conclusion

Given that the SN1 reaction mechanism involves the formation of a racemic mixture due to the attack on the planar carbocation from either side, the product of the reaction is not optically active.

Key concepts

Carbocation Intermediate

In an SN1 reaction, the key player is the carbocation intermediate. You might wonder what a carbocation is. Quite simply, a carbocation is a positively charged ion with a carbon atom at its center. This ion forms when a leaving group, which is typically a halide, detaches from a molecule. What remains is a carbocation, which plays a crucial role in dictating the path of the reaction.

This carbocation is sp² hybridized, creating a planar structure. This flat shape is crucial because it allows the nucleophile to attack from either side. This symmetrical access means that both sides have equal probability for the incoming group to approach and bond with the positively charged carbon atom.

The stability of the carbocation can vary depending on its structure. Generally, tertiary carbocations are more stable than secondary, and secondary are more stable than primary. The stability influences not just the speed of the reaction but also its likelihood to occur at all.

Racemic Mixture

In SN1 reactions, when the nucleophile attacks the planar carbocation, the outcome is a fascinating one: a racemic mixture.

A racemic mixture contains two enantiomers—mirror image molecules—which are produced in equal proportions. This happens because the nucleophile can attack from either the top or the bottom of the planar carbocation.

So, why is this mixture important? Racemic mixtures are optically inactive. Each enantiomer can rotate plane-polarized light, but they do so in opposite directions by equal amounts. This means that the optical rotations cancel each other out, resulting in no net rotation.

It's like having a set of spinning coins where half spin one way and half spin the other, balancing each other out and creating no overall movement.

Optical Activity

Optical activity is the ability of a substance to rotate the plane of polarized light. This phenomenon is observed in substances that have chiral centers, meaning they have a non-superimposable mirror image, much like your left and right hands.

In SN1 reactions, optical activity becomes a central concept when considering isomers. However, due to the formation of a racemic mixture during the SN1 reaction, the product is not optically active. Even though each constituent enantiomer is optically active on its own, their effects negate one another in the racemic mixture.

• A substance rotating light to the right is called dextrorotatory, often marked as "+".
• A substance rotating light to the left is called levorotatory, often shown as "−".

In a chemistry context, we'd be curious about whether our reaction products will twist light—and in the case of SN1 reactions producing racemic mixtures, they won't.