Question

(a) How does the structure of diborane \(\left(\mathrm{B}_{2} \mathrm{H}_{6}\right)\) differ from that of ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right) ?\) (b) By using concepts discussed in Chapter 8 , explain why diborane adopts the geometry that it does. (c) What is the significance of the statement that the hydrogen atoms in diborane are described as hydridic?

Short answer

The structure of diborane (B2H6) consists of two boron atoms bonded to four terminal hydrogen atoms and two bridging hydrogen atoms, with a 3-center-2-electron bond (banana bond) involving the bridging hydrogens, resulting in a planar D2h symmetry. In contrast, ethane (C2H6) has two carbon atoms bonded to six hydrogen atoms, with sp^3 hybridization and a staggered conformation (D3d symmetry). Diborane adopts this geometry due to the electron deficiency in boron atoms, which leads to the formation of 3-center-2-electron bonds. The term "hydridic" signifies that the hydrogen atoms in diborane can behave as hydrides and participate in unique bonding interactions not observed in hydrocarbons like ethane.

Step-by-step solution

Describe the molecular structure and geometry of diborane and ethane

Diborane (B2H6): The structure of diborane consists of two boron atoms covalently bonded to four terminal hydrogen atoms and two bridging hydrogen atoms. The molecule has a 3-center-2-electron (3c2e) bond, also known as a banana bond, involving the bridging hydrogens, making it electron-deficient. This results in a geometry classified as a planar D2h symmetry. Ethane (C2H6): In ethane, there are two carbon atoms bonded to each other, with each carbon atom also bonded to three hydrogen atoms by single covalent bonds. This results in a σ-framework where each carbon atom uses sp^3 hybridization to form four σ-bonds. The geometry is a staggered conformation (D3d symmetry) with the H-C-H bond angle 109.5°.

Explain why diborane adopts its specific geometry

Using concepts from Chapter 8, we can reason that diborane adopts its specific geometry due to the electron deficiency in boron atoms, which have only three valence electrons. This means that boron cannot form the standard four σ-bonds to achieve an octet of electrons, like carbon does in ethane. Instead, the boron atom forms three σ-bonds, with the two terminal hydrogens and one bridging hydrogen. The 3-center-2-electron bond (banana bond) allows the electrons to be shared between three atoms (the two boron atoms and the bridging hydrogen atom), which helps to stabilize the structure considering the electron deficiency in boron.

Explain the significance of the term "hydridic" for hydrogen atoms in diborane

The term "hydridic" refers to the nature of the hydrogen atoms in diborane, which behave as hydrides. This means that they can behave as a donor and carry a partial negative charge (δ−) while being bound to the electron-deficient boron atom, which holds a partial positive charge (δ+). The fact that the hydrogen atoms in diborane are described as hydridic signifies their ability to participate in unique bonding interactions, such as the 3-center-2-electron bonds, which are not observed in hydrocarbons like ethane.

Key concepts

3-center-2-electron bond

One of the distinctive features of diborane's structure is the existence of the 3-center-2-electron (3c2e) bond. Also known colloquially as a 'banana bond', this type of bonding isn't seen in typical organic compounds like ethane. In a 3c2e bond, two electrons are shared among three atoms: two boron atoms and one bridging hydrogen atom. The electrons in this bond are delocalized and serve to stabilize the molecule despite its apparent electron deficiency.

This allows for electron-rich regions to complement the electron-poor boron centers. The 'banana' nickname comes from the curved shape of the bond's electron density, resembling a banana. A great way to visualize this bond is to imagine a banana hugging both sides of the boron atoms, with the hydrogen atom at the center.

Molecular geometry

The molecular geometry of a compound defines the three-dimensional arrangement of its atoms. For diborane, the geometry is quite unconventional compared to ethane. While ethane boasts a tetrahedral shape around each carbon with sp^3 hybridization, diborane features a mixed arrangement: four terminal hydrogens form a tetrahedral shape around the boron atoms, and two bridging hydrogens lie above and below the plane formed by the borons.

The molecular geometry of diborane is described as having a planar D2h symmetry which is peculiar given that each boron is involved in three σ-bonds and one 3c2e bond. This structure contrasts starkly with the staggered conformation of ethane and serves as a fascinating example of the diversity of geometric forms that molecules can adopt.

Hydridic hydrogen atoms

Hydrogen atoms in diborane are unique in their hydridic nature. Unlike in hydrocarbons where hydrogen atoms are typically in a protic state, in diborane they function as hydrides. A hydridic hydrogen carries a partial negative charge (indicated as δ−) because it is bonded to a less electronegative boron atom.

This ability of hydrogen to manifest as a hydride has significant implications for the chemical properties and reactivity of diborane. It particularly influences its ability to form bonds where the hydrogen atom acts as an electron pair donor—a key aspect that differentiates the bonding in diborane from that in more common hydrocarbons.

Electron deficiency

Electron deficiency occurs when an atom in a molecule does not have a complete octet of electrons in its valence shell. In the context of diborane, the boron atoms are electron deficient, each having only three valence electrons. Consequently, boron cannot form the 'standard' four bonds that would typically fulfill the octet rule, as carbon does in ethane.

Hence, diborane's unique bonding structure, including the 3c2e bonds, compensates for this electron deficiency. The bridging hydrogen atoms share their electrons with two boron atoms, thereby providing a sort of 'electron-sharing network' that partially mitigates the electron shortfall in the boron atoms.

sp^3 hybridization

sp^3 hybridization is a concept that describes the merging of one s-orbital and three p-orbitals in an atom to form four equivalent hybrid orbitals, which are oriented tetrahedrally. Ethane is the classic example of a molecule utilizing sp^3 hybridization. Each carbon atom in ethane uses the four sp^3 hybrid orbitals to form sigma bonds with three hydrogen atoms and one bond with the other carbon atom, resulting in the stable and tetrahedral geometry.

While the terminal hydrogen atoms in diborane are associated with sp^3 hybridized boron atoms, the overall molecule doesn't have sp^3 hybridization for boron because the bridging hydrogens are involved in different bonding—specifically the 3c2e bonds. Thus, diborane showcases how variations in hybridization can lead to vastly different molecular structures.