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) 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

(a) Diborane has a more complex structure than ethane, with boron atoms connected by a bridging hydrogen atom forming a 3-center-2-electron (3C-2E) bond and two other hydrogen atoms connected to each boron atom. Diborane has a trigonal planar arrangement around each boron atom with bond angles of roughly 120 degrees, while ethane has a tetrahedral arrangement with bond angles of 109.5 degrees. (b) The geometry of diborane arises due to the electronic configuration of boron, which can accommodate only 6 electrons in its valence shell. The formation of 3C-2E bonds with bridging hydrogen atoms allows each boron atom to achieve an electron count of six. The trigonal planar arrangement around each boron atom minimizes electron pair repulsion. (c) In diborane, the term "hydridic" refers to the behavior of hydrogen atoms participating in the 3C-2E bonds, as they donate their lone pair of electrons to bond with boron atoms, acquiring a partial negative charge similar to that of a hydride ion (H-).

Step-by-step solution

Comparing the structures of diborane and ethane

Ethane, C2H6, has a simple structure with each carbon atom bonded to 3 hydrogen atoms and the two carbon atoms connected by a single bond. This arrangement gives each carbon atom a tetrahedral arrangement with bond angles of 109.5 degrees. Diborane, B2H6, has a more complex structure. It consists of two boron atoms with a bridging hydrogen atom between them and two other hydrogen atoms connected to each boron atom. The boron-hydrogen-boron bridge is represented by the 3-center-2-electron (3C-2E) bond formed by the sharing of two electrons between three atoms. This type of bond is called a 'banana bond' in diborane. In contrast to ethane, diborane has a trigonal planar arrangement around each boron atom with bond angles of roughly 120 degrees.

Explaining the geometry of diborane

The geometry of diborane is the result of the electronic configuration of boron. Boron has three valence electrons, so it can form three single bonds, but it can only accommodate 6 electrons in its valence shell. In diborane, each boron atom forms a single bond with two terminal hydrogen atoms, which contributes two bonding pairs of electrons (4 electrons). To complete the octet rule, the bridging hydrogen atom must share its two electrons with both boron atoms simultaneously, forming the 3C-2E bond. This arrangement enables each boron atom to achieve an electron count of six. The trigonal planar arrangement around each boron atom minimizes electron pair repulsion, leading to the observed geometry of diborane.

Understanding the term "hydridic"

In the context of diborane, the term "hydridic" refers to the behavior of hydrogen atoms participating in the 3C-2E bonds. In these bonds, hydrogen behaves as a hydride ion (H-) because it donates its lone pair of electrons to the bonding interaction with the two boron atoms. This donation of the electron pair leads to a partial negative charge on the hydrogen atom, resembling the negative charge on a hydride ion. In summary, diborane has a different structure from ethane due to the electronic configuration of boron, which leads to the formation of 3C-2E bonds. The hydrogen atoms involved in these bonds are described as "hydridic" because they participate in bonding by donating their lone pair of electrons, acquiring a partial negative charge.

Key concepts

Diborane

Diborane, with the chemical formula \( ext{B}_2 ext{H}_6\), stands out for its unique structure. Unlike a traditional molecule structure, diborane features what is known as a 3-center, 2-electron (3C-2E) bond. These bonds, often called "banana bonds", involve two boron atoms sharing electrons with three hydrogen atoms. Each boron atom in diborane is bonded to two terminal hydrogen atoms and shares electrons with a bridging hydrogen atom.
This creates a trigonal planar geometry around each boron atom, with bond angles that deviate from standard tetrahedral angles due to this unique arrangement. The formation of these "banana bonds" is integral to ensuring that both boron atoms achieve an electron count sufficient for stability, despite not fulfilling the traditional octet rule.

Ethane

Ethane, represented chemically as \( ext{C}_2 ext{H}_6\), exhibits a classic organic structure known as a single covalent bond between two carbon atoms. Each carbon atom in ethane is linked to three hydrogen atoms, leading to a

• tetrahedral geometry
• 109.5-degree bond angles

The simple structure of ethane exemplifies conventional covalent bonding where each bond consists of two electrons shared by atoms. Furthermore, this structure of ethane demonstrates the octet rule, with the carbon atoms achieving a stable electron arrangement by sharing electrons in such a way that they each complete an octet. Due to its straightforward bonding and tetrahedral structure, ethane contrasts sharply with the more complex diborane.

Banana Bonds

"Banana bonds" is a term often used to describe the unique type of bonding found in diborane. In the 3-center, 2-electron bonds, a pair of electrons is shared between three atoms. To visualize, imagine a bridge where two towers (boron atoms) are connected by a string (electron pair) that loops through an anchor (hydrogen atom) in the middle. This unusual bond is necessary because boron does not have enough valence electrons to form "normal" double bonds.

• Allows boron to reach a stable state with fewer electrons
• Forms a bridge-like structure between atoms

The naming as "banana bonds" comes from the arcuate shape of the electron cloud in this bonding mode, resembling a banana. These bonds highlight boron's ability to form stable compounds even when it doesn't achieve a full octet, showcasing adaptability in bonding.

Electron Configuration

Understanding electron configuration is essential when discussing structures like diborane. Boron, in its ground state, has the electron configuration \([1s^2 2s^2 2p^1]\). With only three valence electrons, boron can form three covalent bonds, reflecting its place in the periodic table. However, this also means boron has fewer electrons available for bonding than carbon does.
In diborane:

• Each boron atom can only share three pairs of electrons
• The molecule relies on banana bonds to complete the electron arrangement

By utilizing the three-center bonds, diborane adjusts to compensate for this deficiency. Electron configuration directly influences the structures molecules can form. In ethane, carbon's electron configuration \([1s^2 2s^2 2p^2]\) allows for a fuller bonding complement. Each carbon can form four single bonds, adhering to the octet rule. The differences in electron configurations help explain why diborane and ethane have such different structures and bonding styles.