Problem 105 - A Complete Resource Book in Chemistry for JEE Main

Question

How many optically active stereoisomers are possible for butan-2, 3 -diol? (a) 1 (b) 2 (c) 3 (d) 4

Step-by-Step Solution

Answer

There are 3 optically active stereoisomers for butan-2,3-diol.

Step 1: Understanding Stereochemistry

A molecule is optically active if it has one or more chiral centers and is non-superimposable on its mirror image. Butan-2,3-diol has two chiral centers at the 2nd and 3rd carbon atoms since both carbons are attached to four different groups.

Step 2: Counting Chiral Centers

Identify the chiral centers in butan-2,3-diol. Each chiral center can have two configurations (R or S). Butan-2,3-diol has two chiral centers.

Step 3: Calculating Maximum Number of Stereoisomers

The maximum number of stereoisomers for a compound is given by the formula \[ 2^n \] where \( n \) is the number of chiral centers. For butan-2,3-diol, \( n = 2 \), so the maximum number of stereoisomers is \[ 2^2 = 4. \]

Step 4: Considering Mesomers

Some of these stereoisomers may actually be meso forms. A meso compound has an internal plane of symmetry and is not optically active. In butan-2,3-diol, one of the forms is meso, which reduces the number of optically active stereoisomers.

Step 5: Calculating Optically Active Stereoisomers

Subtract the meso form from the total number of stereoisomers to find the optically active ones. Given that there is 1 meso form, the number of optically active stereoisomers is \[ 4 - 1 = 3. \]

Step 6: Answer Verification

Verify the calculation step by step. Two chiral centers lead to \( 2^2 = 4 \) stereoisomers, one of which is meso, resulting in 3 optically active stereoisomers.

Key Concepts

Chiral Centers

A chiral center in a molecule is a carbon atom bonded to four different groups. This unique arrangement means the molecule can have non-superimposable mirror images, known as enantiomers. In butan-2,3-diol, the 2nd and 3rd carbon atoms are such chiral centers. These carbons each have distinct groups attached, making them centers of chirality.
Recognizing chiral centers is essential because they determine if a molecule can exist in different spatial arrangements. Each chiral center contributes to the molecule's ability to display optical activity. In simpler terms, chiral centers are the reason a molecule like butan-2,3-diol can potentially rotate plane-polarized light.
To identify a chiral center, look for a central carbon with four varied groups in its immediate alternative structural representation. A lack of a symmetry plane that would make the molecule superimposable on its mirror image confirms its chirality.

Optically Active Stereoisomers

Optically active stereoisomers are molecules that can rotate the plane of polarized light. This property arises due to molecules having chiral centers that are asymmetrically arranged. When a molecule, such as butan-2,3-diol, contains two chiral centers, it can form multiple stereoisomers.
To determine the number of possible stereoisomers, use the formula \( 2^n \), where \( n \) is the number of chiral centers. For two chiral centers as in butan-2,3-diol, the calculation goes as follows: \( 2^2 = 4 \). This suggests that four stereoisomers can potentially be formed.
However, not all stereoisomers are optically active, as some may be symmetrical and cancel out optical activity, leading to the presence of meso forms. Thus, the real number of optically active forms could be less depending on the presence of such forms.

Meso Compounds

Meso compounds are unique in stereochemistry due to their internal symmetry. Despite having chiral centers, a meso compound is not optically active because it possesses an internal plane that creates a mirror symmetry.
This symmetry causes the chiral centers' effects to balance out, making the compound superimposable on its mirror image. In the case of butan-2,3-diol, one of the possible four stereoisomers is a meso compound. This means that although initially there are four potential stereoisomers, only three are optically active due to one being meso.
Understanding meso compounds help in identifying the true number of optically active stereoisomers versus the purely possible ones, by acknowledging the crucial role symmetry plays in eliminating optical activity in these compounds.