Problem 200 - A Complete Resource Book in Chemistry for JEE Main

Question

The structure of diborane \(\left(\mathrm{B}_{2} \mathrm{H}_{6}\right)\) contains (a) four \(2 \mathrm{c}-2 \mathrm{e}\) bonds and two \(3 \mathrm{c}-2 \mathrm{e}\) bonds (b) two \(2 \mathrm{c}-2 \mathrm{e}\) bonds and four \(3 \mathrm{c}-2 \mathrm{e}\) bonds (c) two \(2 \mathrm{c}-\) ee bonds and two \(3 \mathrm{c}-3 \mathrm{e}\) bonds (d) four \(2 \mathrm{c}\)-2e bonds and four \(3 \mathrm{c}-2 \mathrm{e}\) bonds

Step-by-Step Solution

Answer

(a) Diborane contains four 2c-2e bonds and two 3c-2e bonds.

Step 1: Understand the Problem

We need to determine which type of chemical bonds are present in diborane \(\left(\mathrm{B}_{2} \mathrm{H}_{6}\right)\). The options give us different configurations of 2-center-2-electron and 3-center-2-electron bonds.

Step 2: Identify Diborane's Bonding

Diborane, \(\mathrm{B}_2\mathrm{H}_6\), is made of two boron atoms and six hydrogen atoms. It is known for having both regular two-center and unusual three-center bonds. The \(3\mathrm{c}-2\mathrm{e}\) bridges are a key feature.

Step 3: Analyze Boron-Hydrogen Bonds

In diborane, four terminal hydrogen atoms form standard \(2\mathrm{c}-2\mathrm{e}\) bonds with two borons. The two bridging hydrogen atoms are connected uniquely in \(3\mathrm{c}-2\mathrm{e}\) bonds that involve both borons and a hydrogen atom, also called banana bonds.

Step 4: Determine Correct Option

The structure of diborane includes four \(2\mathrm{c}-2\mathrm{e}\) and two \(3\mathrm{c}-2\mathrm{e}\) bonds. Thus, the correct answer is option (a).

Key Concepts

2-center-2-electron bonds

A 2-center-2-electron bond, often abbreviated as 2c-2e, is the type of bond most commonly found in chemical compounds. In such a bond, two electrons are shared between two atomic centers, typically seen in simple covalent and ionic connections. In the case of diborane \( (\mathrm{B}_{2} \mathrm{H}_{6}) \), four out of its six hydrogen atoms each form a 2c-2e bond with one of the boron atoms. These bonds are similar to the regular single bonds you might find in a molecule like methane \( (\mathrm{CH}_4) \). Here, each hydrogen shares its single electron with boron, resulting in a pair of electrons that hold the two atoms together. This sharing creates a strong, stable linkage characterized by a clear understanding in typical chemistry courses and textbooks.
Understanding this bond is not complicated; it forms the foundation of what is generally known as a single bond, and its mechanics are straightforward since two electrons are involved in directly bonding the two atoms together in a linear arrangement.

3-center-2-electron bonds

The 3-center-2-electron (3c-2e) bond is a less conventional bond that plays a unique role in the structure of diborane \((\mathrm{B}_{2} \mathrm{H}_{6})\). This bond involves three atoms sharing only two electrons. In diborane, this unusual bonding occurs between the two boron atoms and a bridging hydrogen atom. Instead of a linear single bond as in 2c-2e bonds, these form what are often visually represented as 'banana bonds' due to the curved shape of the electron cloud.

• The three atoms that participate include the two boron atoms and one bridging hydrogen atom.
• These bonds are crucial for the stable geometry of diborane because they allow the molecule to exist without the normally supposed additional electrons usually needed for bonding.
• The electrons in such a bond are less localized compared to regular two-electron bonds, contributing to unique bonding characteristics.

Commonly, students find these bonds fascinating because they defy conventional bonding rules by using only two electrons to stabilize three atoms, showcasing the flexibility and diversity of chemical bonding.

Chemical bonding in diborane

Diborane \((\mathrm{B}_{2} \mathrm{H}_{6})\) is a fascinating molecule because of its distinct combination of bond types, setting it apart from more conventional molecules. The molecule consists of two boron atoms which are bridged by hydrogen atoms, resulting in a compact and unusual structure. The structure of diborane can be seen as a mix of two regular 2-center-2-electron bonds with four hydrogen atoms and two bridge motions involving the 3-center-2-electron bonds with the two remaining hydrogen atoms.

This results in a configuration where:

• Four terminal hydrogen atoms are bound directly to boron atoms, each forming 2c-2e bonds.
• Two hydrogen atoms serve as bridges, linking both boron atoms through 3c-2e bonds (banana bonds).

The overall arrangement of these bonds forms a symmetric shape and contributes to the stability and reactivity of diborane, which is utilized in many chemical reactions and as a reagent in organic synthesis. This dual bonding nature of diborane not only intrigues chemists but also provides profound insights into the variations of atomic interactions beyond conventional definitions, expanding our comprehension of atomic connectivity.