Problem 158 - A Complete Resource Book in Chemistry for JEE Main

Question

Select the correct statements about diborane: (a) \(\mathrm{H}_{\mathrm{b}} \ldots . \mathrm{B} \ldots . \mathrm{H}_{\mathrm{b}}\) bond angle is \(122^{\circ}\) (b) All hydrogens in \(\mathrm{B}_{2} \mathrm{H}_{6}\) lie in the same plane (c) \(\mathrm{B}_{2} \mathrm{H}_{6}\) has three centered bond (d) Each boron atom lies in sp \(^{3}\) hybrid state

Step-by-Step Solution

Answer

Correct statements are (c) and (d).

Step 1: Understanding Diborane Structure

Diborane (_2H_6) is a compound with a unique structure featuring two boron atoms and six hydrogen atoms. It is important to understand this to identify the validity of the statements.

Step 2: Analyzing Statement (a)

Statement (a) claims the bond angle at hydrogen bridge atoms (H_b...B...H_b) is 122 degrees. However, in diborane, the angle formed between bridging hydrogen atoms and the connected boron atoms is approximately 97 degrees. Thus, this statement is incorrect.

Step 3: Analyzing Statement (b)

Statement (b) suggests all hydrogen atoms in B_2H_6 lie in the same plane. In reality, diborane has a three-dimensional structure where the two bridging hydrogens do not lie in the same plane as the other four terminal hydrogen atoms. Thus, this statement is incorrect.

Step 4: Analyzing Statement (c)

Statement (c) says B_2H_6 has three-centered bonds. Diborane is known for its three-center, two-electron (3c-2e) bonds, particularly in the B-H-B bridge. Therefore, this statement is correct.

Step 5: Analyzing Statement (d)

Statement (d) claims each boron atom is in an sp^3 hybrid state. In diborane, each boron atom forms bonds using sp^3 hybridization to accommodate its bonding structure. Thus, this statement is correct.

Key Concepts

Molecular structure

Diborane, with the formula \( \text{B}_2\text{H}_6 \), consists of two boron atoms and six hydrogen atoms. It exhibits an intriguing three-dimensional structure that is distinct from many other covalent molecules. At the core, the two boron atoms are connected by a pair of hydrogen atoms, known as bridging hydrogens. These bridge-forming hydrogen atoms are an essential feature of diborane, giving it a distinctive look.

• The molecule is non-planar, meaning the hydrogens are not all in a single plane.
• Four of the hydrogens (terminal hydrogens) are bonded directly to the boron atoms.
• The remaining two hydrogens (bridging hydrogens) form a bond between the boron atoms.

This setup leads to interesting bonding arrangements, including unusual bond angles and electron sharing mechanisms.

Three-center bonds

In diborane's structure, the existence of three-center, two-electron (or 3c-2e) bonds is pivotal. This type of bonding is somewhat unconventional compared to typical two-center, two-electron bonds. In diborane, such bonds occur particularly in the B-H-B bridge.

• A three-center bond involves three atoms sharing two electrons.
• The bridging hydrogens are involved in such bonds between the two boron atoms.

These bridge bonds are crucial for connecting the boron atoms, providing a stable yet unique configuration. Essentially, the three-center bonds are a key to understanding why diborane's structure is considered remarkable.

Hybridization

To comprehend diborane's structure further, grasping the concept of hybridization is essential. In the case of diborane, the boron atoms exhibit \( sp^3 \) hybridization, although it may appear non-standard due to the molecule's shape. Here's how it works:

• Each boron atom forms four hybrid orbitals, aligning with \( sp^3 \) hybridization.
• These hybrid orbitals accommodate bonding with both terminal and bridging hydrogens.

Despite the unconventional appearance, this hybridization facilitates the formation of the necessary bonds, enabling the unique bonding found in diborane.

Bond angles

Bond angles in diborane are intriguing, contributing to its notable geometry. A common misconception is that the B-H-B bridging bond angle is 122 degrees. However, this angle is actually closer to 97 degrees.

• This smaller angle is due to the three-dimensional arrangement of atoms.
• It allows for a stable, yet compact, alignment of the bridging hydrogens.

Being aware of the accurate bond angles not only provides insight into the physical structure of diborane but also enhances understanding of its electronic distribution and molecular interactions.