Problem 149 - A Complete Resource Book in Chemistry for JEE Main

Question

Match the following Column-I (a) \(\mathrm{CH}_{3} \mathrm{CHDT}\) (b) \(\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{CH}(\mathrm{OH}) \mathrm{C}_{2} \mathrm{H}_{5}\) (c) \(\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{3}\) (d) Column-II (p) No optical isomer (q) Two optical isomers (r) Four optical isomers (s) Three optical isomers (t) Two asymmetric carbon atoms.

Step-by-Step Solution

Answer

(a) matches (q), (b) matches (r) and (t), (c) matches (s).

Step 1: Analyze Compound (a)

Compound (a) is \(\mathrm{CH}_{3} \mathrm{CHDT}\). This compound has only one carbon atom bonded to four different groups: H, D, T, and CH₃. Since it contains one asymmetric carbon, it can exhibit optical isomerism, leading to **two optical isomers**.

Step 2: Analyze Compound (b)

Compound (b) is \(\mathrm{CH}_{3} \mathrm{CH(OH)CH(OH)C}_{2} \mathrm{H}_{5}\). This molecule has two chiral centers, which are the two \(\mathrm{-CH(OH)-}\) groups. According to the formula \(2^n\) where \(n\) is the number of chiral centers, this compound can have four stereoisomers, thus **four optical isomers**.

Step 3: Analyze Compound (c)

Compound (c) is \(\mathrm{CH}_{3} \mathrm{CH(OH)CH(OH)CH}_{3}\). It also has two asymmetric carbon atoms (those attached to the hydroxyl groups). Similar to compound (b), it can have \(2^2 = 4\) stereoisomers. However, it’s a symmetric molecule (meso) which reduces the number of optical isomers to **three optical isomers**.

Step 4: Conclusion and Matching

- **(a)** corresponds to two optical isomers: (q). - **(b)** corresponds to four optical isomers and has two asymmetric carbon atoms: (r) and (t). - **(c)** corresponds to three optical isomers: (s).

Key Concepts

Chiral Centers

Chiral centers are crucial when studying molecules with optical isomerism. A chiral center, also known as a stereocenter, is an atom that is bonded to four different groups or atoms. This creates an asymmetry within the molecule, which allows it to have non-superimposable mirror images, much like left and right hands.

When a molecule contains one or more chiral centers, it can exist as different stereoisomers. Each of these isomers has a unique three-dimensional arrangement of the atoms around the chiral center, often leading to significant differences in their chemical and physical properties.

• Molecules with one chiral center can have two enantiomers (mirror images).
• Molecules with multiple chiral centers can have several stereoisomers, not all of which are necessarily optical isomers.

Understanding chiral centers helps us predict the number of optical isomers a molecule can have, utilizing the formula \(2^n\), where \(n\) is the number of chiral centers.

Asymmetric Carbon

An asymmetric carbon atom, a specific type of chiral center, is a carbon atom that is bonded to four different atoms or groups of atoms. This unique bonding is what grants the molecule its chiral nature, creating potential for optical isomerism.

The presence of an asymmetric carbon is essential for a molecule to exhibit chirality. Molecules with asymmetric carbon atoms can have pairs of enantiomers, which are non-superimposable mirror images of each other, akin to a left-handed and right-handed glove. The discovery of asymmetric carbon was significant as it laid the foundation for stereochemistry - the study of different spatial arrangements of atoms. Here are a few key points about asymmetric carbon:

• It generates optical activity in a compound, allowing it to rotate plane-polarized light.
• It is a pivotal component in the field of pharmaceuticals, where different enantiomers can have drastically different effects.

Stereoisomers

Stereoisomers are a fascinating aspect of chemistry, referring to compounds with the same structural formula but different spatial arrangements of atoms. This difference in spatial configuration can result in varying properties, despite the structural formula being identical.

Stereoisomers include both enantiomers and diastereomers. Here's a breakdown:

• Enantiomers: These are mirror-image stereoisomers that cannot be superimposed on one another, like a person's left and right hand.
• Diastereomers: These are stereoisomers not related by mirror symmetry, often having more than one chiral center, and exhibiting different physical properties.

In molecules with two or more chiral centers, understanding stereoisomers becomes crucial as the number of potential isomers multiplies, often shown by the formula \(2^n\), where \(n\) is the number of chiral centers.

Meso Compounds

Meso compounds are an intriguing subtype of stereoisomers that defy the typical expectations of molecules with multiple chiral centers. Despite having chiral centers, meso compounds are achiral overall due to an internal plane of symmetry.

This symmetry makes it such that the molecule cannot exhibit optical activity, meaning it doesn't rotate plane-polarized light, setting it apart from other molecules with chiral centers. Here are a few distinguishing features of meso compounds:

• They contain two or more asymmetric carbon atoms.
• They have an internal plane of symmetry, resulting in superimposable mirror images.
• They significantly reduce the expected number of optical isomers due to this symmetry.

The concept of meso compounds highlights how even within the realm of chiral centers, symmetry plays a crucial role in the behavior of molecules.