Question

Electrophilic addition of \(\mathrm{HCl}\) to \(\mathrm{cis}-2\) -butene gave 2-chlorobutane, which was determined not to be optically active when examined with a polarimeter. Which of the following is the better explanation for the lack of optical activity in the 2 -chlorobutane formed in this reaction? (a) 2 -Chlorobutane is not chiral. (b) Two enantiomers of 2 -chlorobutane were formed in equal amounts.

Short answer

(b) Two enantiomers of 2-chlorobutane were formed in equal amounts.

Step-by-step solution

Understanding Optical Activity

Molecules are optically active if they are chiral, meaning they lack an internal plane of symmetry and have non-superimposable mirror images (enantiomers). An optically inactive sample can consist of a racemic mixture, where equal amounts of enantiomers are present, canceling each other's optical activity.

Molecular Structure of 2-Chlorobutane

2-Chlorobutane is a compound that can be chiral. It is made up of four different substituents attached to the second carbon, making it a chiral center. This means 2-chlorobutane can exist in two different chiral forms (enantiomers).

Determine if 2-Chlorobutane is Chiral

Since 2-chlorobutane has a chiral center, it is a chiral molecule. This means option (a), which suggests 2-chlorobutane isn't chiral, is not correct.

Racemic Mixture Formation

During electrophilic addition reactions like that of HCl to cis-2-butene, the planar nature of the carbocation intermediate allows for attack from either side, forming both enantiomers of 2-chlorobutane in equal amounts.

Conclusion

When both enantiomers are present in equal amounts, they form a racemic mixture, which is not optically active as the rotation of plane-polarized light by one enantiomer is canceled by the other.

Key concepts

Chirality

Chirality is a property of a molecule that makes it non-superimposable on its mirror image. Imagine your hands; they are mirror images but cannot be perfectly aligned regardless of how you position them. This is very similar to what happens with chiral molecules. For a molecule to be chiral, it must have a chiral center, which is typically a carbon atom bonded to four different substituents.
A chiral molecule does not have an internal plane of symmetry and can exist in two different forms, known as enantiomers.
This structural uniqueness is what allows chiral molecules to rotate plane-polarized light, a key factor in making a substance optically active.

Enantiomers

Enantiomers are pairs of molecules that are non-superimposable mirror images of each other. They play a critical role in the field of stereochemistry. These two distinct forms have identical physical and chemical properties in an achiral environment but differ in how they interact with other chiral substances.
One of the most striking features of enantiomers is their ability to rotate plane-polarized light in opposite directions. One enantiomer will rotate light in a clockwise direction, while its mirror image will rotate light counterclockwise. This is what's known as optical activity. However, if they are present in equal amounts, their effects on light cancel out, making the mixture non-optically active.
This scenario occurs in a racemic mixture, which explains why some reactions yield products that appear to be optically inactive even when chiral centers are present.

Racemic Mixture

A racemic mixture is a blend of equal amounts of two enantiomers. As a result, their abilities to rotate plane-polarized light cancel each other out, resulting in a mixture that appears optically inactive. This can easily confuse those trying to identify the chirality of the components involved.
In chemical reactions, such as the electrophilic addition of \( ext{HCl} \) to \( ext{cis-2-butene} \), racemic mixtures often form due to how molecules interact at the microscopic level.
During such reactions, intermediates form without bias to either enantiomer, leading to the creation of equal amounts of each enantiomer, making the entire mixture racemic and ultimately optically inactive.

Electrophilic Addition

Electrophilic addition is a common reaction mechanism in organic chemistry where an electrophile reacts with a molecule possessing a double bond. This reaction involves the addition of atoms to a carbon-carbon double bond and plays a significant role in forming products like 2-chlorobutane from cis-2-butene.
The reaction usually proceeds through a carbocation intermediate, which is an electron-deficient species and allows for attack from either side of the molecule. This makes it possible for two enantiomers to form.
As a result, a racemic mixture is often obtained when the product is chiral, explaining the lack of optical activity in such reactions. Understanding the mechanism helps in predicting the outcomes and characteristics of the products formed, including their optical properties.