Problem 6 - A Complete Resource Book in Chemistry for JEE Main

Question

The number of optically active isomers of tartaric acid is CC(O)C(=O)O (a) 2 (b) 3 (c) 4 (d) 1

Step-by-Step Solution

Answer

(b) 3

Step 1: Understand the Compound

Tartaric acid is a molecule with two chiral centers. This means each chiral center can have two possible configurations (R or S), creating stereoisomers.

Step 2: Calculate Total Stereoisomers

For a molecule with two chiral centers, the maximum number of stereoisomers is given by the formula \(2^n\), where \(n\) is the number of chiral centers. Hence, for tartaric acid, the total number of stereoisomers is \(2^2 = 4\).

Step 3: Identify Optically Active Isomers

Not all stereoisomers are optically active. We need to exclude the meso compound, which is achiral despite having chiral centers due to internal symmetry. Tartaric acid has one meso form, reducing the number of optically active isomers.

Step 4: Count the Optically Active Isomers

Subtract the one meso form from the total of four stereoisomers. This leaves us with 3 optically active isomers. Thus, there are 3 optically active isomers of tartaric acid.

Key Concepts

Chiral Centers

Chiral centers play a vital role in the study of optical isomerism. A chiral center is typically a carbon atom bonded to four different groups or atoms. This unique arrangement makes the carbon asymmetrical, leading to the possibility of non-superimposable mirror images. These mirror images are known as enantiomers.

• Enantiomers are a pair of stereoisomers that are mirror images.
• They possess identical physical and chemical properties but differ in the way they interact with polarized light.

Chiral centers are essential because they introduce the concept of chirality into molecules, which is the key to understanding optical isomerism. In the case of tartaric acid, the presence of two chiral centers leads to the formation of various stereoisomers, each with different properties.

Tartaric Acid Stereoisomers

Tartaric acid is an excellent example of a compound with multiple stereoisomers due to its two chiral centers. As explained in the solution, the maximum number of stereoisomers for a compound is calculated using the formula \(2^n\). Here, \(n\) is the number of chiral centers.

• This formula gives us \(2^2 = 4\) stereoisomers for tartaric acid.
• These stereoisomers include different combinations of (R) and (S) configurations at the chiral centers.

The presence of these configurations is what gives rise to the characteristic properties of each stereoisomer. Notably, tartaric acid includes both chiral forms (optically active) and a meso form (inactive), contributing to its rich isomeric diversity.

Meso Compounds

One intriguing aspect of stereochemistry is the existence of meso compounds. Meso compounds are achiral, despite having multiple chiral centers. This may sound contradictory, but the presence of a plane of symmetry within the molecule allows for superimposition on its mirror image, resulting in an achiral molecule.

• Meso compounds appear in molecules with two or more chiral centers but are optically inactive.
• The internal symmetry cancels out any optical activity.

In the specific case of tartaric acid, one of the four possible stereoisomers is a meso compound. This unique form reduces the optical activity of the overall mixture, as it does not rotate plane-polarized light. Recognizing a meso compound is crucial for understanding why not all stereoisomers in a molecule contribute to optical activity.