Problem 153 - A Complete Resource Book in Chemistry for JEE Main

Question

In the following questions two statements (Assertion) (A) and Reason (R) are given. Mark (a) If both \(\mathrm{A}\) and \(\mathrm{R}\) are correct and \(\mathrm{R}\) is the correct explanation of \(\mathrm{A}\). (b) If both A and \(R\) are correct but \(R\) is not the correct expalnation of \(\mathrm{A}\). (c) \(\mathrm{A}\) is true but \(\mathrm{R}\) is false. (d) \(\mathrm{A}\) is false but \(\mathrm{R}\) is true. (e) \(\mathrm{A}\) and \(\mathrm{R}\) both are false. (Assertion): An optically active molecule must be asymmetric. (Reason): Asymmetric molecules will have nonsuperposable mirror image.

Step-by-Step Solution

Answer

Option (a) is correct: both A and R are correct and R is the correct explanation of A.

Step 1: Analyze the Assertion (A)

The assertion states that an optically active molecule must be asymmetric. This implies that for a molecule to show optical activity, it must lack symmetry. Typically, asymmetry in a molecule is due to a chiral center, which can lead to optical activity. Thus, this statement is generally true when referring to purely organic molecules.

Step 2: Analyze the Reason (R)

The reason provided states that asymmetric molecules will have nonsuperposable mirror images. Bringing to mind the concept of chirality, a molecule that is asymmetric would indeed have a nonsuperposable mirror image, akin to your left hand being a nonsuperposable mirror image of your right hand. This statement is true as it is a fundamental property of chiral molecules.

Step 3: Determine the Relationship between A and R

Now, we need to establish the connection between the assertion and the reason. Since having a nonsuperposable mirror image is precisely what defines optical activity due to molecular asymmetry, the reason directly explains why the assertion is true. Therefore, the reason (R) is both true and the correct explanation for the assertion (A).

Key Concepts

Chirality

Chirality is a fascinating concept that plays a crucial role in understanding optical activity in molecules. It's derived from the Greek word 'cheir', meaning hand, ingeniously reflecting how chiral objects, like our hands, are mirror images but are not superposable. This inability to superpose a molecule and its mirror image is the essence of chirality.
When a molecule is chiral, it will have an enantiomer, which is essentially its non-superposable mirror image. Enantiomers often exhibit different behaviors, especially in biological systems, due to their 3D spatial arrangement interacting uniquely with other chiral substances.
Some key points to understand about chirality include:

• Chiral molecules will rotate plane-polarized light, a phenomenon directly linked to optical activity.
• The presence of chiral centers is a necessary condition for a molecule to be chiral, although not sufficient on its own.
• Chirality is an important factor in the design of many pharmaceuticals, where one enantiomer may be beneficial, while the other could be inactive or even harmful.

Asymmetry in molecules

Asymmetry in molecules is critical to understanding why certain molecules exhibit optical activity. Symmetry can be found in molecules with superposable mirror images; however, asymmetrical molecules lack this property.
Optical activity originates from this asymmetrical nature, as these molecules are unable to overlap perfectly with their mirror images. The key principle here is that the lack of symmetry allows for the possibility of rotation of plane-polarized light when it passes through the molecule. An asymmetric molecule typically has:

• An irregular spatial arrangement of atoms.
• Significant implications for the molecule’s physical and chemical properties, such as its reactivity and interaction with other molecules.
• Potential to show optical isomerism, where the isomers differ in the way they interact with polarized light.

Understanding molecular asymmetry is, therefore, vital in fields such as stereochemistry and material science, where the three-dimensional arrangement of atoms greatly influences functionality.

Chiral center

The concept of a chiral center is integral to discussions about molecular chirality and asymmetry. Typically, a chiral center is a carbon atom bonded to four different atoms or groups, creating a site of asymmetry within the molecule.
Such chiral centers are the primary reason a molecule can have enantiomers. The presence of just one chiral center is enough for the entire molecule to be chiral, although in more complex molecules, there can be multiple chiral centers.
Features of chiral centers include:

• They are the main contributors to a molecule’s 3D structure, influencing its interaction with light.
• Chiral centers can exist in two configurations, often denoted as R (rectus) and S (sinister), based on priority rules in the Cahn-Ingold-Prelog system.
• While crucial, a chiral center alone doesn’t guarantee optical activity—other symmetry elements may negate chirality in some cases.

In practical applications, identifying and manipulating chiral centers is crucial in fields like pharmacology and organic chemistry, where they can profoundly affect a molecule's behavior and utility.