Question

An organic compound \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}\) is found to be optically active. Which of the following could it be? (ISM Dhanbad 94 ) (1) \(\mathrm{CII}_{3} \mathrm{COCII}_{2} \mathrm{CII}_{3}\) (2) \(\mathrm{CII}_{3} \mathrm{CH}_{2} \mathrm{CII}_{2} \mathrm{CIIO}\) (3) \(\left(\mathrm{CII}_{3}\right)_{2} \mathrm{CII}\) CIIO (4) \(\mathrm{CII}_{2}=\mathrm{CII} \mathrm{CH}(\mathrm{OII}) \mathrm{CH}_{3}\)

Short answer

Option 4 (\text{CH}_2=\text{CHCH}(\text{OH})\text{CH}_3) is the optically active compound.

Step-by-step solution

Identify the Molecular Formula

Given an organic compound with the molecular formula \(\text{C}_4\text{H}_8\text{O}\), match the molecular formulas of each provided compound to confirm they align. All options should represent \(\text{C}_4\text{H}_8\text{O}\).

Check for Optically Active Compounds

An optically active compound must have a chiral center. A chiral center is a carbon atom that is attached to four different groups. Inspect each of the given structures to identify if they contain a chiral center.

Analyze Option 1

The molecular formula for \(\text{CH}_3\text{COCH}_2\text{CH}_3\) does not align with \(\text{C}_4\text{H}_8\text{O}\), making it incorrect.

Analyze Option 2

The molecular formula for \(\text{CH}_3\text{CH}_2\text{CH}_2\text{CHO}\) aligns with \(\text{C}_4\text{H}_8\text{O}\), but it does not contain a chiral center because the carbon atoms are not attached to four different groups.

Analyze Option 3

The molecular formula for \(\text{(CH}_3)_2\text{CHCHO}\) aligns with \(\text{C}_4\text{H}_8\text{O}\), however, it also does not contain a chiral center.

Analyze Option 4

The molecular formula for \(\text{CH}_2=\text{CHCH}(\text{OH})\text{CH}_3\) aligns with \(\text{C}_4\text{H}_8\text{O}\) and contains a chiral center at the carbon bonded to \(\text{-CH}_2\), \(\text{-CH}_3\), \(\text{-OH}\), and \(\text{-CH}=\text{CH}_2\). This makes it optically active.

Key concepts

Chiral Center Identification

In organic chemistry, identifying a chiral center is essential for determining optical activity. A chiral center, or an asymmetric carbon, is a carbon atom that is connected to four different groups or atoms. This unique structure makes the molecule non-superimposable on its mirror image. Imagine your hands: no matter how you turn them, the left hand cannot be perfectly overlaid on the right hand. That's exactly the kind of non-superimposability we're talking about with chiral centers.
When identifying chiral centers, look at each carbon atom in the molecule. Ask yourself if the carbon is bonded to four different substituents. If yes, you have a chiral center. This chiral center is what makes the molecule potentially optically active.
Let's take a closer look at some key points:

• A chiral center must be a carbon atom.
• It must be bonded to four different groups.
• Absence of chiral centers means the molecule cannot be optically active.

Molecular Formula Analysis

The molecular formula of a compound gives us a snapshot of the elements and their quantities that make up the molecule. In this exercise, we are provided with the molecular formula \(\text{C}_4\text{H}_8\text{O}\). Analyzing this formula is our first step.
Here’s how you can analyze a molecular formula:

• Confirm the number of carbon, hydrogen, and oxygen atoms.
• Compare this with the given options to filter out incorrect structures.

For example, the structure \(\text{CH}_3\text{COCH}_2\text{CH}_3\) doesn't match \(\text{C}_4\text{H}_8\text{O}\). It's critical to match each element to ensure we are working with the correct compound.
This step helps us eliminate options that do not fit the molecular formula, streamlining the identification process for optically active compounds.

Optically Active Compounds

Optically active compounds are those that can rotate plane-polarized light. This property stems from the presence of chiral centers within the molecular structure. A molecule without chiral centers cannot be optically active. Let's review how to identify optically active compounds step-by-step:

• Ensure the molecular formula fits the given requirements.
• Identify any chiral centers within the molecule.
• Verify that there is at least one carbon atom attached to four distinct groups.

From the provided exercise options, we found that the molecular formula \(\text{CH}_2=\text{CHCH}(\text{OH})\text{CH}_3\) aligns with \(\text{C}_4\text{H}_8\text{O}\) and contains a chiral center at the carbon bonded to \-CH_2\, \-CH_3\, \-OH\, and \-CH=CH_2\. This makes the compound optically active.
So, whenever you are asked to determine if a compound is optically active, remember to:# Check the molecular formula. # Identify chiral centers. # Confirm optical activity through the presence of these chiral centers.