Problem 43 - A Complete Resource Book in Chemistry for JEE Main

Question

An organic molecule necessarily shows optical activity if it (a) contains asymmetric carbon atoms (b) is non-planar (c) is non-superimposable on its mirror image (d) is superimposable on its mirror image

Step-by-Step Solution

Answer

(c) is non-superimposable on its mirror image.

Step 1: Understanding Optical Activity

Optical activity refers to a property of a molecule that allows it to rotate the plane of polarized light. This usually occurs when a molecule is chiral, meaning it has a non-superimposable mirror image.

Step 2: Explore Options

We will evaluate each option to understand which condition guarantees optical activity. (a) Contains asymmetric carbon atoms: Asymmetric carbon, also called a chiral center, might lead to optical activity if the molecule is overall chiral. (b) Is non-planar: Being non-planar alone does not guarantee optical activity. (c) Is non-superimposable on its mirror image: By definition, this is a characteristic of chirality, which leads to optical activity. (d) Is superimposable on its mirror image: This describes an achiral molecule, which does not exhibit optical activity.

Step 3: Identify Correct Answer

Option (c) 'is non-superimposable on its mirror image' describes a chiral molecule, which is essential for a molecule to be optically active. Therefore, this option satisfies the requirement for optical activity.

Key Concepts

Chiral Molecules

To understand why a molecule might be optically active, it's crucial to talk about chiral molecules. A chiral molecule is one that cannot be superimposed on its mirror image. This means that if you imagine flipping it like you would flip your hand from left to right, the mirror image will not match the original one.

Chirality induces optical activity because of this non-superimposable nature, leading each chiral molecule to exist in two distinct forms known as enantiomers. Enantiomers are mirror images of each other and have distinct properties, particularly in interacting with plane-polarized light. One common example of chirality in daily life is found in your hands; they are essentially mirror images and not superimposable.

• Unique structure makes them appear 'left' or 'right-handed'
• Interact differently with light or other chiral molecules
• Essential for understanding optical activity in chemistry

Recognizing chiral molecules involves identifying features that make these molecules unique, such as their mirror image relationship which leads to their fascinating optical properties.

Asymmetric Carbon Atoms

An important feature in many chiral molecules is the presence of asymmetric carbon atoms. An asymmetric carbon atom is typically bonded to four different atoms or groups. Because of this variability, these carbon atoms act as chiral centers and are responsible for the molecule's overall chirality.

The concept of asymmetric carbon is straightforward once you visualize it. Imagine a central carbon atom bonded to four unique substituents. No matter how you rotate these bonds, the overall structure remains asymmetric, contributing to the molecule's chirality.

• Central to forming chiral molecules
• Always bonded to four different groups/atoms
• Causes molecule to potentially have two enantiomers

The presence of an asymmetric carbon atom suggests that a molecule could be chiral, although the entire molecule must combine these centers properly to exhibit optical activity.

Non-superimposable Mirror Image

The concept of a non-superimposable mirror image is foundational in explaining chirality. When a molecule and its mirror image cannot be placed on top of each other perfectly, they are considered non-superimposable.

This feature of non-superimposability is a defining characteristic of chiral molecules. It enables them to have two enantiomers with different behaviors in chemical reactions and interactions with light. Optical isomers are often referred to this way because their distinct interactions with polarized light lead to observable optical activity.

• Means each enantiomer will interact differently with other molecules
• Ensures distinct rotation of plane-polarized light
• Crucial in identifying chiral compounds

By understanding non-superimposable mirror images, it becomes easier to identify chiral molecules, thereby understanding which molecules can be optically active.