Question

The number of three-centre-two-electron bond(s) present in diborane molecule is
A. 1
B. 2
C. 4
D. 6

Answer 1

Hint: The knowledge of molecular bonding and three-centre-two-electron bond is required to solve this question. A three-centre-two-electron bond or 3c-2e bond is an electron-deficient bond in which three atoms share two electrons. These bonds are generally weaker in comparison to the $\sigma$-bond.

Complete step by step answer:
Consider the electronic configuration of boron: $\text{1}{\text{s}}^{\text{2}}\text{2}{\text{s}}^{\text{2}}\text{2}{\text{p}}^{\text{1}}$. After hybridization of the atomic orbitals, three $$\text{s}{\text{p}}^{\text{2}}$$ hybrid orbitals are obtained which contain one electron each, combine with the s-orbital of three hydrogen atoms to form three covalent bonds. But this does not satisfy the octet of boron and it is still desperate for bonds. In this situation, two boron hydride molecules form a dimer called “diborane” or ${\text{B}}_{\text{2}}{\text{H}}_{\text{6}}$.
To understand the formation of the 3c-2e bonds, each boron atom would use two of its three $$\text{s}{\text{p}}^{\text{2}}$$ hybrid orbitals and two electrons to form terminal B-H bonds. Each B-atom is now left with one electron and one molecular orbital. So, one 1s orbital from each H-atom with one electron and two $$\text{s}{\text{p}}^{\text{2}}$$ hybrid orbital from each boron atom form two 3c-2e bridge bonds to make the stable diborane molecule. Thus, the octet of boron is full-filled in this way.

The correct answer is option (B).

Note:
 The concept of 3c-2e bonds with three centres and two electrons can be thought of in terms of resonance, where the two electrons are delocalized over three centres.
There is a huge category of boron compounds formed as a result of 3c-2e bonds and those are known as “boranes”, diborane being the simplest borane.