Problem 11 - A Complete Resource Book in Chemistry for JEE Main

Question

In diborane, the two \(\mathrm{H}-\mathrm{B}-\mathrm{H}\) angles are nearly (a) \(60^{\circ}, 120^{\circ}\) (b) \(95^{\circ}, 150^{\circ}\) (c) \(95^{\circ}, 120^{\circ}\) (d) \(120^{\circ}, 180^{\circ}\)

Step-by-Step Solution

Answer

The two \(\text{H}-\text{B}-\text{H}\) angles in diborane are \(95^{\circ}\) and \(120^{\circ}\). So, the correct answer is (c).

Step 1: Identify the Structure of Diborane

Diborane, with the chemical formula \(\text{B}_2\text{H}_6\), consists of two boron atoms and six hydrogen atoms. The molecule has a bridged structure with two bridging hydrogen atoms between the boron atoms.

Step 2: Determine the Types of \/H-B-H\/ Angles in Diborane

In the diborane molecule, two types of \( \text{H}-\text{B}-\text{H} \) bond angles exist. These angles are created by the terminal hydrogen atoms and the bridging hydrogen atoms.

Step 3: Understand the Bridging Hydrogen Angles

In the diborane structure, the \( \text{H}-\text{B}-\text{H} \) angle involving the bridging hydrogen atoms is approximately \(95^{\circ}\). This is due to the unique 3-center, 2-electron bond formed by the bridging hydrogens.

Step 4: Analyze the Terminal Hydrogen Angles

The \( \text{H}-\text{B}-\text{H} \) angle involving the terminal hydrogen atoms is around \(120^{\circ}\). This is due to the planar, sp2 hybridization of the boron atoms.

Step 5: Compare with the Given Options

Among the options, \(95^{\circ}\) and \(120^{\circ}\) fit the bond angles in diborane's structure, matching the angles described in the unique bridged and terminal positions.

Key Concepts

Bridging Hydrogen

Diborane, or \(\text{B}_2\text{H}_6\), has an intriguing structure that boasts two bridging hydrogen atoms. These hydrogen atoms have a unique role in connecting the two boron atoms. Unlike typical hydrogen bonds that directly connect one atom to another, bridging hydrogens form a bridge between two boron atoms.

These hydrogen atoms lie in a position where they can simultaneously bond to two atoms, creating a less common bonding environment. This unique feature plays a crucial role in the stability and geometry of diborane. The position of the bridging hydrogens results in distinct bond angles that are not commonly found in simpler hydrogen-containing molecules.

In diborane, the bond between the bridging hydrogen atoms and the boron atoms is least intuitive. The angle is approximately \(95^\circ\), distinct from typical angles found in simpler molecules due to the unique bridging structure. This angle reflects the shared nature of hydrogen atoms that "bridge" the gap between the two boron atoms, thus stabilising the overall structure.

3-center 2-electron bond

A fascinating aspect of diborane's structure is the presence of a 3-center, 2-electron bond, often abbreviated as 3c-2e bond. This might sound complex, but it's essentially a type of bond where three atoms share two electrons.

In the context of diborane, this involves two boron atoms and one hydrogen atom. Usually, bonds form between two atoms sharing a pair of electrons, but here it's a bit different. The hydrogen in diborane doesn’t fully belong to just one boron but rather forms a link between the two, using a single pair of electrons.

This type of bonding leads to the peculiar angle of \(95^\circ\) we discussed earlier. It enables the unusual structural integrity of diborane, as two boron atoms are able to share one pair of electrons via a common hydrogen. This allows for a stable yet highly reactive compound, contributing to its interesting chemical properties.

sp2 Hybridization

In diborane's structure, sp2 hybridization occurs when boron atoms form planar bonds with terminal hydrogen atoms. This type of hybridization means that one s orbital and two p orbitals hybridize to form three sp2 hybrid orbitals.

These hybrid orbitals organize themselves in a trigonal planar geometry, which leads to an angle of \(120^\circ\) between the terminal \( \text{H}-\text{B}-\text{H} \) bonds. This configuration is a result of the planar orientation and spacing of electrons around the boron atom. It minimizes repulsion and stabilizes the structure in a flat plane.

The sp2 hybridization is pivotal because it explains the planar nature of the diborane where terminal hydrogens reside. This aspect works harmoniously with the bridging setup, creating a complex, yet balanced, molecular structure. This hybridization contributes to the overall reactivity and distinctive bond angles seen in diborane.