Question

An organic compound \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}\) is found to be optically active. Which of the following is correct structure of the given compound? (a) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHCHO}\) (b) \(\mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{3}\) (c) \(\mathrm{CH}_{3} \mathrm{COCH}_{2} \mathrm{CH}_{3}\) (d) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CHO}\)

Short answer

The correct structure is (b) \( \mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}( ext{OH}) \mathrm{CH}_{3} \).

Step-by-step solution

Understand the Properties of the Compound

We know that the compound \( \mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O} \) is optically active. Optical activity implies the presence of a chiral center, which is a carbon atom with four different groups attached to it.

Analyze Each Structure for Chirality

Evaluate the structures for the presence of a chiral center. A chiral center is a carbon atom bonded to four different atoms or groups.1. \( \left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHCHO} \) - The carbon atom in the "CHO" group is bonded to two hydrogen atoms, so no chiral center exists.2. \( \mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{3} \) - The third carbon atom forms a chiral center, as it is attached to \(-OH\), \(-CH_3\), \(-CH=CH_2\), and a hydrogen atom.3. \( \mathrm{CH}_{3} \mathrm{COCH}_{2} \mathrm{CH}_{3} \) - This molecule lacks a chiral center because all carbon atoms are bonded to the same or similar groups.4. \( \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CHO} \) - The carbon atoms in the chain have either equivalent substituents or hydrogen bonds, thus eliminating the potential for chirality.

Choose the Correct Structure

Based on the presence of a chiral center, option (b) \( \mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{3} \) has a chiral center on the third carbon atom, satisfying the criteria of being optically active.

Key concepts

Optical Activity

Optical activity is a fascinating property observed in certain compounds that allows them to rotate plane-polarized light. This property stems from the asymmetry in the molecule, typically due to a specific arrangement of atoms around a central carbon atom. When an organic compound such as our example, \( \mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O} \), exhibits this behavior, it is often attributed to the presence of a chiral center within the structure. This inherent asymmetry results in the compound having non-superimposable mirror images, much like one's left and right hands.
The extent to which a substance can rotate light is measured using a polarimeter. This characteristic turning of light distinguishes optically active compounds from those that do not exhibit such properties, known as optically inactive. Notably, optical activity is a key indicator in determining the presence of chirality within organic molecules.

Chiral Center

A chiral center, sometimes referred to as a stereocenter, is a single carbon atom within a molecule bonded to four distinct atoms or groups. The unique arrangement around this carbon atom is what confers the property of chirality to the compound. In our problem, option (b) \( \mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{3} \) exhibits a chiral center:

• The third carbon atom is bonded to an \(-OH\) group, a \(-CH_3\), a \(-CH=CH_2\), and a hydrogen atom.
• This diverse bonding ensures no two groups around the carbon are the same, creating a non-superimposable mirror image, which is the hallmark of chirality.

Identifying a chiral center in organic compounds is crucial for understanding their optical activity and plays a significant role in the chemical behavior and interactions of the compound in various biological systems.

Organic Compounds

Organic compounds are the backbone of organic chemistry, represented primarily by carbon-containing molecules. These compounds form the basis of all life on Earth and are defined by their complex structures and variegated functionality.
One primary feature of organic compounds is the presence of carbon atoms bonded to other carbon atoms or different elements such as hydrogen, oxygen, nitrogen, and more. They exhibit a wide range of properties based on the functional groups attached and their structural configuration. For example, the variety of functional groups such as alcohols, alkenes, or aldehydes significantly influences the chemical properties of the organic compound.
Special attention is given to understanding functional groups because they dictate the molecule's reactivity and interactions. In our compound \( \mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O} \), it showcases a particular arrangement of atoms that leads to the creation of a chiral center, and thus, it becomes optically active. Understanding the structural intricacies of organic compounds is key in fields like pharmaceuticals and materials science, where the exact nature of the compound can greatly impact its effectiveness and use.