Question

Describe the structure of diborane \(\left(\mathrm{B}_{2} \mathrm{H}_{6}\right)\), and explain why the bridging \(\mathrm{B}-\mathrm{H}\) bonds are longer than the terminal \(\mathrm{B}-\mathrm{H}\) bonds.

Short answer

Bridging \(\text{B}-\text{H}\) bonds are longer due to 3-center 2-electron bonding.

Step-by-step solution

Understanding Diborane

Diborane is a compound consisting of two boron atoms and six hydrogen atoms. Its molecular formula is \( ext{B}_2 ext{H}_6\). The structure includes four terminal hydrogen atoms, each bonded to one boron atom, and two bridging hydrogen atoms that connect the two boron atoms.

Identifying Types of Bonds

In diborane, there are two types of \( ext{B}- ext{H}\) bonds: terminal \( ext{B}- ext{H}\) bonds and bridging \( ext{B}- ext{H}\) bonds. Each boron atom forms three bonds: two terminal bonds with hydrogen and one bridging bond with a hydrogen that is shared between both boron atoms.

Analyzing Terminal B-H Bonds

The terminal \( ext{B}- ext{H}\) bonds involve a direct one-to-one bonding between a boron atom and a hydrogen atom. These are regular covalent bonds where two electrons are shared between the boron and hydrogen.

Analyzing Bridging B-H Bonds

Bridging \( ext{B}- ext{H}\) bonds are a unique feature of diborane. They are known as three-center two-electron (3c-2e) bonds. In this setup, two electrons are shared between three atoms: two boron atoms and one hydrogen atom.

Comparing Bond Lengths

The bridging \( ext{B}- ext{H}\) bonds are longer than the terminal \( ext{B}- ext{H}\) bonds. This is because in a bridging bond, the electron density that bonds the atoms is spread over three atoms instead of two, making the bond less localized and therefore longer.

Conclusion

The structure of diborane can be described as having four terminal hydrogen atoms with short covalent \( ext{B}- ext{H}\) bonds, and two hydrogen atoms that form longer, more delocalized 3c-2e bonds with the boron atoms.

Key concepts

Bridging B-H Bonds

In the structure of diborane, the bridging B-H bonds are quite fascinating due to their unusual bond configuration. Instead of a standard two-atom, two-electron bond, bridging bonds involve three atoms and two electrons. These bonds connect two boron atoms to a single hydrogen atom, forming a unique triangular structure. As a result, each hydrogen atom in the bridge shares its electrons unequally between the two boron atoms.

This sharing of electrons across three atoms creates what's known as a three-center two-electron (3c-2e) bond. The electron density in such bonds is spread out or delocalized over all three atoms, which results in these bonds being longer than typical B-H bonds. Since the electron cloud is spread out, the interaction is weaker and causes a physical lengthening of the bond. This lengthening is a key characteristic of bridging B-H bonds in diborane, distinguishing them from regular terminal bonds.

Terminal B-H Bonds

The terminal B-H bonds in diborane are straightforward and easier to understand compared to their bridging counterparts. Each boron atom is connected to two terminal hydrogen atoms through standard covalent bonds, where one hydrogen atom shares a pair of electrons directly with one boron atom. These bonds are typical two-electron, two-atom bonds, well-known in chemistry as simple sigma bonds.

The focus here is on the direct electron sharing between the hydrogen and the boron, which allows these bonds to be short and strong. Since there's no need to stretch out the electron cloud over more than two atoms, the bond length is minimized, leading to stronger and more concentrated bonding compared to the bridging B-H bonds. The typical strength and compact nature of these bonds explain why they are shorter in length.

Three-center two-electron bonds

Three-center two-electron (3c-2e) bonds form the cornerstone of what makes diborane unique. Normally, electron pairs form bonds between just two atoms. However, in 3c-2e bonds, the same pair of electrons are shared among three atoms: specifically, two boron atoms and one bridging hydrogen atom in the case of diborane.

The electron pair is not localized between two atoms, but instead spreads over three. This delocalization lowers the electron pair's potential energy, allowing diborane to exist as a stable molecule despite having fewer electrons than traditional bonding would suggest. This type of bond is less direct and covers more spatial territory, which accounts for the weakened bond strength and increased length compared to standard B-H bonds.

The presence of these unique bonds explains many of the intriguing properties of diborane, including its bonding anomalies and its overall molecular stability despite an apparent deficiency of electrons for conventional bonding.