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 is a racemic mixture (option c).

Step-by-step solution

Understand the Reaction Type

The reaction specified is an \(\text{SN}^1\) reaction. \(\text{SN}^1\) represents a substitution nucleophilic unimolecular reaction, where the rate-determining step involves only one molecule (the substrate).

Identify the Nature of the Reactant

Here, the reactant is a dextro rotatory alkyl halide. This means the reactant initially has optical rotation.

Explain the \(\text{SN}^1\) Mechanism

In the \(\text{SN}^1\) mechanism, the first step involves the formation of a carbocation intermediate. This intermediate is planar, allowing attack from either side.

Determine the Product's Optical Activity

Due to the planar nature of the carbocation, the nucleophile can attack from either the top or bottom face, leading to an equal mixture of enantiomers. This results in a racemic mixture (50% dextro and 50% leavo).

Conclude the Nature of the Product

A racemic mixture is optically inactive, meaning it will not rotate plane-polarized light, as the rotations caused by the two enantiomers cancel each other out.

Key concepts

Optical Activity

Optical activity refers to a molecule's ability to rotate the plane of polarized light. It is a fundamental property observed in chiral molecules, those having non-superimposable mirror images. Alkyl halides can be one such group, especially when they possess a chiral center. When we say a compound is dextro rotatory (or "+"), it means that it rotates the light to the right. Conversely, levo rotatory (or "-") compounds rotate the light to the left. The degree of rotation depends on the concentration of the optically active compound and its specific rotation:

• Dextro rotatory compounds have a positive specific rotation.
• Levo rotatory compounds have a negative specific rotation.

In chemical reactions, optical activity can be altered or lost, especially in mechanisms like the SN1 reaction. This is why it's crucial to understand how reactions impact the optical activity of the products.

Carbocation Intermediate

In an SN1 reaction, a carbocation intermediate plays a crucial role. The reaction begins with the departure of a leaving group, which results in the formation of a positively charged carbon atom known as the carbocation. This carbocation is unique because of its planar structure.

• The sp² hybridization leads to a flat, triangular shape.
• This planarity means there's no preference for the incoming nucleophile to attack from either side.

The lack of directional preference is what leads to the formation of different stereoisomers, which can drastically impact the optical activity of the final product. The understanding of carbocation intermediates and their symmetrical nature is pivotal in predicting the outcomes of SN1 reactions.

Racemic Mixture

A racemic mixture is a blend of equal amounts of two enantiomers: one dextro rotatory and one levo rotatory. Due to the equal presence of both, which rotate light in opposite directions, the overall optical effect cancels out, rendering the mixture optically inactive. This concept is particularly relevant in SN1 reactions. As nucleophiles can attack the carbocation intermediate from either side with equal probability, the resultant mixture will have:

• 50% of the original orientation.
• 50% of the opposite orientation.

Therefore, when a dextro rotatory alkyl halide undergoes an SN1 reaction, the product is a racemic mixture. This transformation explains the loss of optical activity, emphasizing why racemic mixtures are often a product of reactions involving planar carbocation intermediates.