Problem 114 - Advanced Problems in Organic Chemistry for Competitive Examinations

Question

The number of stereoisomers possible for a compound of the molecular formula \(\mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}(\mathrm{OH})-\mathrm{Me}\) is (a) 2 (b) 4 (c) 6 (d) 3

Step-by-Step Solution

Answer

The number of stereoisomers is 4.

Step 1: Identify Types of Stereoisomerism

The given compound can exhibit stereoisomerism due to the presence of a double bond (cis-trans isomerism) and a chiral center, represented by the carbon bonding to the OH group and the Me (methyl group). A double bond exhibits cis-trans isomerism, and a chiral center can exhibit enantiomerism.

Step 2: Determine Number of Geometric Isomers

The double bond between C2 and C3 allows for cis-trans (or E-Z) isomerism. Therefore, there are 2 possibilities for geometric isomers: either one cis and one trans configuration or one E and one Z configuration.

Step 3: Determine Number of Optical Isomers

The chiral carbon (C4) bonded to the OH and the Me groups introduces chirality into the compound. A single chiral center generally leads to 2 enantiomers or optical isomers.

Step 4: Calculate Total Number of Stereoisomers

The total number of stereoisomers is determined by the product of the number of geometric isomers and the number of optical isomers. Number of geometric isomers = 2 (cis-trans or E-Z) Number of optical isomers = 2 (enantiomers) Total number of stereoisomers = 2 * 2 = 4.

Key Concepts

Geometric Isomers

Geometric isomers arise due to the restricted rotation around double bonds. In our compound, the double bond located between the carbon atoms at positions C2 and C3 leads to two different possible configurations: cis and trans.

• Cis isomer - Both groups of interest (like the methyl group and the rest of the chain) are on the same side of the double bond.
• Trans isomer - The groups of interest are on opposite sides of the double bond.

This type of isomerism is also known as cis-trans isomerism or E-Z isomerism. This concept exists because double bonds restrict rotation, unlike single bonds, which allows these differences to occur.
In summary, the compound has 2 geometric isomers, owing to the double bond between C2 and C3.

Optical Isomers

Optical isomers, or enantiomers, are mirror images of each other but are non-superimposable. They usually occur due to the presence of a chiral center in a molecule.
In our molecule, the carbon atom at position C4 acts as a chiral center because it is bonded to four different atoms or groups: a hydroxyl group (OH), a methyl group (Me), a hydrogen atom, and a part of the carbon chain.
The presence of a chiral center usually means the molecule can form two enantiomers, each being a non-superimposable mirror image of the other. These enantiomers also rotate plane-polarized light in different directions - one to the right (dextrorotatory) and one to the left (levorotatory).
Thus, our compound exhibits two optical isomers due to the chiral center at C4.

Chiral Center

A chiral center is typically a carbon atom that is attached to four distinct groups or atoms. It creates stereoisomerism by creating two forms (enantiomers) that are mirror images.
In our exercise's molecular structure, the key chiral center is located at the fourth carbon atom. This carbon is bonded to the following groups:

• Hydroxyl group (OH)
• Methyl group (Me)
• Hydrogen atom (H)
• Rest of the carbon chain

This diversity in attachments makes the carbon in question chiral, contributing two stereoisomers (optical isomers).
The reason behind this is that light can interact differently with each isomer due to the unique way each isomer twists the light - a clear mark of the presence of a chiral center.