Problem 27 - A Complete Resource Book in Chemistry for JEE Main

Question

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

Step-by-Step Solution

Answer

The product of an SN1 reaction of a dextro rotatory alkyl halide is a racemic mixture (option c).

Step 1: Understanding SN1 Mechanism

The SN1 reaction stands for nucleophilic substitution unimolecular. In this type of reaction, the rate-determining step involves the formation of a carbocation intermediate from the alkyl halide. The reaction mechanism involves two steps: the loss of the leaving group to form a carbocation and the attack of the nucleophile on the carbocation.

Step 2: Formation of Carbocation

When the dextro rotatory alkyl halide undergoes an SN1 reaction, the first step is the formation of a carbocation intermediate. This carbocation is planar and sp2 hybridized, making it achiral and capable of being approached by the nucleophile from either side.

Step 3: Nucleophilic Attack

The nucleophile can attack the planar carbocation from either the front or the back. Due to this, the attack is not stereospecific and can happen on either side of the planar structure, resulting in the formation of both stereoisomers (R and S configuration of the product).

Step 4: Formation of Racemic Mixture

Since the nucleophile can approach the carbocation with equal probability from either side, both enantiomers are formed in equal amounts. This leads to the formation of a racemic mixture, which contains equal amounts of dextro and leavo rotatory isomers, resulting in an optically inactive product.

Key Concepts

Carbocation Intermediate

In SN1 reactions, one significant step is the formation of the carbocation intermediate. This is a positively charged ion created when the leaving group detaches from the alkyl halide in the first stage of an SN1 reaction. The carbocation is described as being planar, meaning it is flat and perfectly two-dimensional.
This planarity is due to its sp2 hybridization, where the carbon atom involved is bonded to only three other atoms, leaving the fourth space open for the nucleophile to attack. Due to this flat structure, the carbocation is achiral, which means it does not possess handedness or chirality. This achiral character allows the nucleophile to attack from either side of the carbocation, leading to various possible outcomes in terms of the final product configuration.

Nucleophilic Substitution

SN1 is an abbreviation for a type of chemical reaction known as nucleophilic substitution unimolecular. It's called unimolecular because the rate-determining step depends on the concentration of only one reactant: the substrate. An SN1 reaction proceeds via a two-step mechanism.

• First, the leaving group departs, generating a carbocation intermediate.
• Then, the nucleophile launches an attack on this carbocation.
  This second step is fast and because the carbocation is planar, the nucleophile may approach from either side.

Due to the random approaches from either side, the product often has no specific preference for configuration and therefore both enantiomers can be produced.

Racemic Mixture

A racemic mixture is a mixture of equal amounts of two enantiomers - molecules that are mirror images of each other. In the context of the SN1 reaction, the equal formation of two enantiomers occurs because the nucleophile can approach the carbocation intermediate from either side.
This leads to the production of both the R and S configurations in equal amounts. As these enantiomers rotate plane-polarized light in opposite directions, the overall product does not rotate light at all, rendering it optically inactive.
This 1:1 mixture of the two forms is what defines it as a racemic mixture, a hallmark of SN1 reactions where chiral centers are present.

Chiral and Achiral

Chirality is a property of a molecule that arises when it has a non-superimposable mirror image, much like left and right hands. A chiral molecule must have at least one chiral center, often a carbon atom bonded to four different groups. Such molecules exhibit optical activity, meaning they can rotate plane-polarized light.

• Chiral molecules exist in two enantiomeric forms: R and S.
• A product is achiral when it does not exhibit chirality, often due to symmetrical arrangements or the presence of a plane of symmetry.

In the SN1 reaction, although starting from a chiral alkyl halide, the carbocation intermediate is achiral, leading to the possibility of forming both enantiomers equally, which results in a racemic mixture. Hence, the final product, being a mixture of equal forms, is optically inactive.