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

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

Step 1: Determine the Number of Chiral Centers

To find the number of optically active stereoisomers, we must first determine the number of chiral centers in butan-2,3-diol. A chiral center is a carbon atom that has four different groups attached to it. In butan-2,3-diol, the structure is CH3-CHOH-CHOH-CH3. Each of the two central carbon atoms (C2 and C3) is attached to four different groups: a hydrogen atom, a hydroxyl group (-OH), a methyl group (CH3), and the rest of the molecule. Therefore, there are 2 chiral centers in butan-2,3-diol.

Step 2: Calculate Possible Stereoisomers

The formula to calculate the maximum number of stereoisomers is 2^n, where n is the number of chiral centers. Since butan-2,3-diol has 2 chiral centers (as found in Step 1), the maximum number of stereoisomers is 2^2 = 4.

Step 3: Identify Optically Active Stereoisomers

Optically active stereoisomers are those that rotate plane-polarized light. They come in enantiomeric pairs, which are nonsuperimposable mirror images of each other. Since the calculation in Step 2 gives 4 stereoisomers, they can exist as two pairs of enantiomers, resulting in 2 optically active stereoisomers.

Key Concepts

Chiral Centers

In organic chemistry, a chiral center is a crucial concept for identifying the potential optical activity of a compound. A chiral center, also known as a stereocenter, is typically a carbon atom bearing four distinct substituents. This distinct arrangement creates a situation where the molecule can exist in two non-superimposable mirror images, known as enantiomers.
In the case of butan-2,3-diol, the structure features two chiral centers at the second and third carbon atoms. Here is how it breaks down:

• At the second carbon (C2), the substituents are a hydrogen atom, a hydroxyl group (-OH), a methyl group (CH3), and the rest of the molecule.
• Similarly, the third carbon (C3) has the same four different groups attached.

The presence of these chiral centers is fundamental to the molecule's ability to exhibit optical activity, as they introduce the element of chirality required for stereoisomerism.

Stereoisomers Calculation

Once the number of chiral centers is determined, calculating the total number of possible stereoisomers becomes straightforward. The formula used is 2ⁿ, where n is the number of chiral centers.
For butan-2,3-diol, having two chiral centers means we apply the formula as follows:

• Number of chiral centers, n = 2
• Maximum stereoisomers = 2² = 4

These four stereoisomers include both optically active and inactive forms. It's essential to understand this calculation, as it lays the groundwork for exploring more complex stereochemical relationships in organic molecules.

Enantiomers

Enantiomers are a type of stereoisomer that are especially important in understanding optical activity. They are non-superimposable mirror images of each other, much like left and right hands. Each enantiomer in a pair will rotate plane-polarized light in opposite directions, a property termed optical activity.
In the context of butan-2,3-diol, with four stereoisomers calculated, these can be paired into enantiomers. Since each pair consists of two enantiomers, the enantiomeric pairs are responsible for the optical activity observed in these molecules. Here are the key characteristics of enantiomers:

• Identical physical properties (melting point, boiling point, etc.) except for their interaction with plane-polarized light and chiral environments.
• One enantiomer will rotate polarized light clockwise (dextrorotatory), while the other will rotate it counterclockwise (levorotatory).

Recognizing how enantiomers relate to stereochemistry and optical activity is crucial for tackling problems involving chiral molecules.

Butan-2,3-diol

Butan-2,3-diol is a simple organic molecule that serves as an excellent example for studying chirality and stereochemistry. The molecule has the formula CH3-CHOH-CHOH-CH3. This particular compound is noteworthy because it includes two adjacent chiral centers, making it capable of forming multiple stereoisomers.
Here are some essential aspects:

• It contains two hydroxyl groups (-OH) attached to the second and third carbon atoms, which contribute significantly to its reactivity and solubility properties.
• The presence of two chiral centers allows the molecule to form four stereoisomers, including two pairs of enantiomers.
• Understanding the structure of butan-2,3-diol provides insight into how molecular chirality affects physical and chemical properties.

Studying butan-2,3-diol's stereochemistry can deepen comprehension of key concepts in organic chemistry, particularly those related to optical activity and the behavior of stereoisomers.