Question

A sample of \((S)-\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}\left(\mathrm{CH}_{3}\right) \mathrm{Cl}\) is hydrolyzed by water, and the resulting solution is optically inactive. (a) Write the formula of the product. (b) By which nucleophilic substitution reaction mechanism does this reaction occur?

Short answer

The product's formula is CH3CH2CH(CH3)OH, but as a racemic mixture, and the type of nucleophilic substitution reaction mechanism involved is SN1 because a racemic mixture is formed.

Step-by-step solution

Identify the Starting Compound

The starting compound mentioned here is (S)-CH3CH2CH(CH3)Cl, a chiral compound consisting of a chiral center marked by the carbon atom bonded to a hydrogen, a methyl group, an ethyl group, and a chloride.

Perform the Hydrolysis

The hydrolysis of a compound involves a reaction with water. In this case, the starting compound reacts with water, leading to the replacement of the chloride atom by a hydroxyl group (OH). This results in the following compound: CH3CH2CH(CH3)OH.

Identify the Product's Optically Activity

Given that the resulting compound is optically inactive, that implies that the product is achiral. This could mean either an achiral molecule or a racemic mixture. Considering that the starting compound has a chiral center (caused by the 4 different groups attached to the carbon) and the product still retains this carbon center with four different constituencies (H, OH, CH3, and CH2CH3), the product itself likely remains chiral. The optical inactivity would, therefore, suggest that a racemic mixture, an equal mixture of enantiomers, is formed.

Determine the Type of Nucleophilic Substitution

Given that the product is an equal mixture of enantiomers (racemic mixture), this infers that the nucleophilic substitution mechanism involved is SN1. This is due to the fact that the SN1 mechanism involves a carbocation intermediate which can be attacked from either side by the nucleophile, forming an equal mixture of enantiomers.

Key concepts

Chirality

Chirality is an essential concept in organic chemistry, particularly when studying molecules like the one in the exercise. A chiral molecule is one that cannot be superimposed on its mirror image. Chiral molecules have a carbon atom with four different substituents, known as a chiral center. This unique arrangement leads to molecules having non-superimposable mirror images called enantiomers.

In the given exercise, the starting compound (S)-CH3CH2CH(CH3)Cl is chiral, as it has a chiral center. The chiral center in this compound is the carbon atom bonded to a hydrogen, a methyl group, an ethyl group, and a chlorine atom. Each of these groups is different, which means the molecule can exist in two distinct forms—non-superimposable on each other, like left and right hands. These two forms are called R and S configurations.

Optical Activity

Optical activity refers to the ability of a chiral molecule to rotate the plane of polarized light. This property is unique to chiral substances and is used to determine whether a substance is optically active. The degree to which a substance can rotate light is measured using a polarimeter.

For instance, an optically active solution contains molecules that either rotate light to the right (dextrorotatory) or left (levorotatory). In the exercise, after hydrolysis, the resulting compound is described as optically inactive. This optical inactivity implies that the product does not have a net effect on the rotation of light. Such inactivity can occur when the compound becomes achiral or more commonly, when it forms a racemic mixture—a balanced mix of two enantiomers that counteract each other's optical activities.

Racemic Mixture

A racemic mixture is an equimolar mixture of two enantiomers. In such a case, the optical activities of the enantiomers cancel each other out, resulting in a solution that appears optically inactive. In the context of the given exercise, after the (S)-CH3CH2CH(CH3)Cl reaction with water, the resulting product was a racemic mixture.

This suggests that the hydrolysis using the SN1 reaction mechanism produced equal amounts of both enantiomers. The equal mix of enantiomers (R and S forms) means the optical activity is neutralized, thus explaining why the solution does not rotate plane-polarized light despite individual enantiomers being able to do so. Recognizing a racemic mixture is crucial when predicting the outcome of nucleophilic substitution reactions.

SN1 Reaction Mechanism

The SN1 reaction mechanism is a nucleophilic substitution pathway that occurs in two main steps. Firstly, the leaving group departs from the substrate, forming a carbocation intermediate. Secondly, the nucleophile attacks the carbocation from either side, leading to the formation of a racemic mixture.

In the outlined exercise, the hydrolysis of (S)-CH3CH2CH(CH3)Cl proceeds via the SN1 mechanism. This mechanism is characteristic of reactions that lead to a loss of chirality in the final product or form a racemic mixture. The intermediate carbocation is planar and can be attacked by the nucleophile (water in this instance) from either face, resulting in a 1:1 mix of enantiomers. This process is what underlies the changes seen from a chiral and optically active starting material to an inactive racemic product.