Problem 189 - A Complete Resource Book in Chemistry for JEE Main

Question

The number of stereo isomers possible for a compound of the molecular formula [2009] \(\mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}(\mathrm{OH})-\mathrm{Me}\) is: (a) 2 (b) 4 (c) 6 (d) 3

Step-by-Step Solution

Answer

The compound has 4 stereoisomers.

Step 1: Identify Chiral Centers and Double Bonds

First, examine the compound: \(\mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}(\mathrm{OH})-\mathrm{Me}\). Identify that there is one double bond (\(\mathrm{CH}=\mathrm{CH}\)), which can show cis-trans isomerism, and one chiral center on the carbon with the \(-\mathrm{OH}\) group attached.

Step 2: Determine Stereoisomer Types

The compound can exhibit two types of stereoisomerism: geometrical isomerism (cis-trans) due to the double bond, and optical isomerism due to the chiral center.

Step 3: Calculate Geometrical Isomers

The double bond (\(\mathrm{CH}=\mathrm{CH}\)) can have two geometrical isomers: one cis (or Z) and one trans (or E). Thus, there are 2 possibilities due to the double bond.

Step 4: Calculate Optical Isomers

The chiral center can lead to two optical isomers (enantiomers), which are mirror images of each other. Thus, there are 2 possibilities due to the chiral center.

Step 5: Combine Stereoisomers

When combining both types of isomerism (geometrical and optical) that are independent of each other, multiply the number of geometrical isomers by the number of optical isomers: \[ 2 \text{ (geometrical)} \times 2 \text{ (optical)} = 4 \text{ stereoisomers} \]

Key Concepts

Geometrical Isomerism

Geometrical isomerism, also known as cis-trans isomerism, happens in compounds with double bonds. This type of isomerism is important because double bonds prevent the rotation around the bond axis, causing different spatial arrangements of the groups attached to the double-bonded carbons.
For example, in the compound \( \mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}(\mathrm{OH})-\mathrm{Me} \), the double bond between the second and third carbons allows for two configurations:

• Cis (Z) Isomer: The substituents like methyl (-CH₃) and hydroxyl (-OH) groups can be on the same side.
• Trans (E) Isomer: The substituents are on opposite sides of the double bond.

These arrangements lead to the two possible geometrical isomers, emphasizing that the difference in spatial orientation can result in unique physical and chemical properties.

Optical Isomerism

Optical isomerism occurs when a molecule has a chiral center, resulting in non-superimposable mirror images called enantiomers. To understand optical isomerism, it's essential to become familiar with terms like 'chiral' and 'achiral.'
A chiral molecule is one that cannot be superimposed on its mirror image. It's like comparing your left and right hands, which are mirror images but not identical.

• Enantiomers: These are the pairs of optical isomers that are mirror images of each other.
• Chiral Center: An atom, often carbon, with four different substituents attached.

In our compound, \( \mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}(\mathrm{OH})-\mathrm{Me} \), the carbon bonded to the hydroxyl group is chiral. This chirality allows the molecule to rotate plane-polarized light, resulting in optical activity, which is central to the concept of optical isomerism.

Chiral Centers

Chiral centers, often found in organic compounds, are crucial to understanding optical activity and isomerism. A chiral center usually contains a carbon atom bonded to four different atoms or groups.
Identifying chiral centers:

• The carbon must be attached to four distinct groups.
• No element or group should be repeated among these four attachments.
• If the carbon has a double or triple bond, it cannot be a chiral center because it would not have four different groups directly attached.

In the compound \( \mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}(\mathrm{OH})-\mathrm{Me} \), the highlighted carbon with the hydroxyl group is a chiral center because it is connected to groups like hydroxyl (-OH), hydrogen (-H), a methyl group (-CH₃), and the continuation of the carbon chain.
Recognizing chiral centers helps predict the number of optical isomers, as each chiral center contributes to the potential diversity of these isomers.