Problem 3 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following boron compounds is optically active? (a) boron anhydride (b) sodium tetraborate (c) borosalicylic acid (d) boron trifluoride

Step-by-Step Solution

Answer

Borosalicylic acid is optically active.

Step 1: Understand Optical Activity

A molecule is optically active if it can rotate plane-polarized light. This typically happens if the molecule is chiral, meaning it lacks an internal plane of symmetry and has non-superimposable mirror images.

Step 2: Examine Boron Anhydride

Boron anhydride is another name for boric oxide (B\(_2\)O\(_3\)). It is a symmetric, non-chiral compound, thus it is not optically active.

Step 3: Examine Sodium Tetraborate

Sodium tetraborate, commonly known as borax, is a symmetric compound. It does not have a chiral center; therefore, it is not optically active.

Step 4: Examine Boron Trifluoride

Boron trifluoride (BF\(_3\)) is a symmetric, planar structure without chiral centers, hence it is not optically active.

Step 5: Examine Borosalicylic Acid

Borosalicylic acid can be chiral because it might have a structure that is asymmetric, meaning it can lack a plane of symmetry and potentially exhibit optical activity. A detailed examination shows this is indeed possible with borosalicylic acid.

Step 6: Conclude

Among the listed compounds, borosalicylic acid is the only one that can potentially have the structure and asymmetry required for optical activity.

Key Concepts

Chiral Molecules

Chiral molecules are fascinating entities in chemistry that exhibit the property of chirality, which is fundamental to optical activity. A chiral molecule is like your left and right hand. Just as these hands mirror each other yet cannot be perfectly aligned when overlaid, chiral molecules have a special quality.
Chirality arises when a molecule has a center, often a carbon atom, bonded to four different groups. This arrangement creates a unique, asymmetric structure. The molecule will typically exhibit two forms, called enantiomers, which are non-superimposable mirror images of each other.

• "Chiral center" - the atom, usually carbon, that determines chirality based on bonding to four unique groups.
• "Enantiomers" - the pair of mirror-image forms that a chiral molecule can exist in.

Recognizing chirality in molecules implies recognizing potential optical activity, which means the molecule can rotate plane-polarized light, much like we derived from examining borosalicylic acid in the exercise.

Plane of Symmetry

The concept of a plane of symmetry is a simple yet powerful tool to determine whether a molecule is chiral or achiral. A plane of symmetry means there is a mirror-like division across the molecule such that one half of the molecule is a mirror image of the other half.
A molecule that has any plane of symmetry is termed achiral and does not exhibit optical activity because it does not yield non-superimposable mirror images.

• "Achiral" - molecules with a plane of symmetry, lacking the capability to display optical activity.
• The presence of symmetry usually implies a uniform distribution of atoms across the molecule, as seen in structures like boron trifluoride (BF\(_3\)) and sodium tetraborate, making them optically inactive.

Chiral molecules, however, break free from this symmetry, like how borosalicylic acid may potentially lack symmetry, thus can exhibit optical activity.

Non-superimposable Mirror Images

A defining characteristic of chiral molecules is that they have non-superimposable mirror images. Imagine looking in a mirror. The reflection you see mimics your appearance but can't be perfectly lined up on top of your real self; this feature similarly defines chiral molecules.
For a real-life molecular example, consider how both enantiomers of a chiral molecule are like mirrored twins; equal in form but opposite in orientation. These enantiomers have identical physical attributes, such as boiling points, yet they interact differently in biological systems, a reason why optical activity is significant.

• Non-superimposability ensures that the two mirror images (enantiomers) of a chiral molecule cannot be aligned to match perfectly.
• This property is an excellent determinant of a molecule's capability to rotate plane-polarized light, making it imperative for optically active compounds, like potentially with borosalicylic acid in our exercise.

Recognizing this concept can be integral for students trying to identify optically active compounds just based on their structural details.