Animated Solution for Chemistry - Organic Chemistry: Racemic mixture is formed by mixing two

Imagine you are standing in a laboratory with two identical-looking beakers. One contains the $d$-enantiomer of a chiral compound, and the other contains its exact mirror image, the $l$-enantiomer.

Today, we are going to witness the magic that happens when these two opposites are mixed together. This is the fascinating world of stereochemistry, where geometry dictates physical reality.

Before we mix them, let's understand what we are dealing with. Enantiomers are molecules that are non-superimposable mirror images of each other.

Just like your left and right hands, they look identical but cannot be perfectly aligned on top of one another. For a molecule to exhibit this property, it must possess at least one chiral carbon—a carbon atom attached to four different groups.

Now, there is a catch. If we mix these two beakers in just any random ratio, we won't get our desired result.

To create a true racemic mixture, we must mix them in an exact fifty-fifty, equimolar proportion. This means the number of $d$-molecules must perfectly equal the number of $l$-molecules.

When these two enantiomers combine in equal amounts, something beautiful happens. One molecule tries to rotate plane-polarized light to the right, while its mirror image rotates it equally to the left.

Because they are present in equal numbers, their optical rotations perfectly cancel each other out. The net optical rotation becomes exactly $0^{\circ }$.

This phenomenon, where two separate molecules cancel each other's optical activity, is known as external compensation. As a result, the final racemic mixture is completely optically inactive.

So, what is our final takeaway? A racemic mixture is not just any random combination of isomers.

It is specifically formed by mixing two enantiomers with a chiral carbon in equal proportions. Therefore, the correct choice is Option (d).

As you master this concept, take a moment to think about meso compounds. They are also optically inactive, but their inactivity arises from internal compensation within a single molecule.

Always remember this critical difference between external and internal compensation. It is a favorite concept for competitive exams and will serve you well in your chemistry journey!