Question

Which of the following is incorrect with regard to the structure of diborane? (a) Two bridged hydrogen atoms lie above and below the plane. (b) The sp \(^{3}\) - hybrid orbitals of the boron atoms have one electron each. (c) The terminal hydrogen atoms and boron atoms lie in a plane. (d) Four terminal hydrogen atoms and two bridged |hydrogen atoms.

Short answer

Option (b) is incorrect; not all sp³ orbitals have one electron each.

Step-by-step solution

Understand the Properties of Diborane

Diborane, B2H6, is a molecule that consists of two boron atoms and six hydrogen atoms. The structure involves a pair of three-center, two-electron bonds, known as banana bonds, where the bridged hydrogen atoms play a crucial role.

Analyze the Bridged Hydrogen Atoms

The two bridged hydrogen atoms are positioned in such a way that they lie above and below the plane formed by the boron atoms and the terminal hydrogen atoms. This is consistent with option (a).

Examine the Boron Atom Hybridization

In diborane, each boron atom is sp³ hybridized. One of the sp³ hybrid orbitals on each boron atom forms a sigma bond with a terminal hydrogen. The remaining electrons in the boron atom participate in forming the three-center, two-electron bonds with the bridged hydrogens.

Inspect the Plane Formation

The four terminal hydrogen atoms and the two boron atoms do indeed lie in the same plane, establishing a plane of symmetry in the molecule as stated in option (c).

Count the Hydrogen Atoms

Diborane consists of four terminal hydrogen atoms and two bridged hydrogen atoms, which matches the description given in option (d).

Identify the Incorrect Statement

Option (b) states that the sp³ hybrid orbitals of boron atoms have one electron each. However, not all sp³ orbitals have one electron each; some are involved in bridging bonds that share two electrons between three atoms. Therefore, option (b) is incorrect.

Key concepts

Banana Bonds

Diborane, a compound with the formula \(B_2H_6\), is famous for its unusual bonding, prominently featuring "banana bonds". These bonds are a kind of three-center two-electron bond that occurs between two boron atoms and a hydrogen atom that acts as a bridge. These bonds are shaped like a banana, hence their name. Unlike typical covalent bonds where electrons are shared between two atoms, banana bonds allow for electron sharing among three atoms. This electron sharing forms a stable structure despite the presence of fewer electrons for bonding.

• The name comes from the curved shape of the bond.
• Essential for stabilizing diborane’s structure.

Understanding banana bonds is fundamental to grasping how diborane maintains its structure against the odds of conventional bonding rules. The concept of a three-center bond is different from traditional bonding, creating a unique set of chemical properties.

Boron Hybridization

In diborane, the boron atoms undergo sp³ hybridization, which is crucial for the formation of its peculiar structure. Each boron atom forms four sp³ hybrid orbitals. However, it doesn't complete an octet by itself, which is typically the aim in conventional molecules. Key Points about Boron's Hybridization:

• Each B atom uses its sp³ orbitals to form bonds with hydrogen atoms.
• Some of these hybrid orbitals are involved in banana bonds, allowing electron-sharing with hydrogen bridges.
• This hybridization doesn't entirely follow the typical rules due to the formation of three-center bonds.

This hybridization results in each boron atom engaging in both bridging (involving shared orbitals) and terminal bonding with hydrogen atoms, enabling diborane to adopt its stable structure despite having fewer solitary electrons available than usual.

Three-center two-electron bonds

The concept of three-center two-electron bonds (3c-2e) is central to understanding compounds like diborane. This bond type describes the unique way electrons are shared among three atoms instead of the usual two. In diborane, this unique bond exists between the two boron atoms and the hydrogen atom acting as a bridge. This form of bonding is challenging to visualize but can be understood as a shared cloud of electrons providing stability and strength through this bridge. Important Aspects of 3c-2e Bonds:

• Involves three atomic centers sharing two electrons.
• Contributes to the flexibility and strength of the bond.
• Essentially creates "half-bonds" between the participating atoms.

This allows for some unusual properties in the molecule, like the stability of diborane with fewer electrons than expected for its bonds and an ability to form structures that are not typically seen in traditional chemistry.

Hydrogen Positioning

Hydrogen positioning in diborane plays a significant role in its molecular structure and stability. In diborane, four terminal hydrogens and two hydrogen atoms serve as bridges. The bridged hydrogens are distinguished by their position as they lie above and below the plane of the boron atoms. Details on Hydrogen Positioning:

• Four terminal hydrogens lie in the same plane as the borons.
• The two bridged hydrogens form the unique banana bonds with the boron atoms.
• This arrangement allows for the characteristic three-dimensional shape of diborane.

By being positioned above and below, the bridged hydrogens play a pivotal part in stabilizing the entire structure by distributing electron density across the molecule uniformly. This positioning contributes to the overall symmetry and balance, thereby enhancing the molecule's stability despite its unconventional bonding methods.