Problem 77 - Chemistry The Central Science

Question

(a) How does the structure of diborane \(\left(\mathrm{B}_{2} \mathrm{H}_{6}\right)\) differ from that of ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right) ?(\mathbf{b})\) 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"?

Step-by-Step Solution

Answer

The structure of diborane (B2H6) differs from that of ethane (C2H6) in that two hydrogen atoms bridge between both boron atoms, forming a planar arrangement with 3c-2e bonds, while ethane has a direct carbon-carbon bond with a 2c-2e single bond. Diborane adopts its unique geometry due to its electron-deficient nature, which results in the formation of 3c-2e bonds with bridging hydrogen atoms, stabilizing the molecule. The term "hydridic" hydrogen atoms in diborane signifies their role in the unusual 3c-2e bonds and their more negative charge, which plays a crucial role in the reactivity, stability, and properties of diborane and related compounds.

Step 1: Describe the structure of diborane

To answer part (a), we need to know the molecular structure of diborane and how it differs from that of ethane. Diborane is a compound consisting of 2 boron atoms and 6 hydrogen atoms. The structure of diborane can be represented as the following: Boron atoms are bridged by two hydrogen atoms, while each boron is also bonded to two additional hydrogen atoms, forming a planar arrangement. The two boron atoms are connected by two bridging hydrogen atoms that participate in electron-deficient, three-center two-electron (3c-2e) bonds.

Step 2: Describe the structure of ethane

Ethane is a compound composed of two carbon atoms connected by a single bond and 6 hydrogen atoms bonded to the carbon atoms. Its structure is as follows: Each carbon atom is bonded to 3 hydrogen atoms in a tetrahedral geometry, with the H-C-H bond angle being approximately 109.5°. The carbon-carbon bond is a conventional two-center two-electron (2c-2e) single bond.

Step 3: Compare the structures of diborane and ethane

Diborane and ethane both possess 2 central atoms (B and C, respectively) in their structures. However, the structures differ in the following aspects. 1. In diborane, two hydrogen atoms bridge between both boron atoms, forming a planar arrangement with 3c-2e bonds. In ethane, there is a direct carbon-carbon bond with a 2c-2e single bond. 2. The bond angles in diborane are different from those of ethane. The bond angle around boron in diborane is approximately 120°, while the H-C-H bond angle in ethane is approximately 109.5°.

Step 4: Explain why diborane adopts its geometry

In answer to part (b), diborane adopts its unique geometry due to its electron-deficient nature. Boron atoms in diborane have only three valence electrons, which means they cannot form conventional 2c-2e bonds with all hydrogen atoms. As a result, the 3c-2e bonds with bridging hydrogen atoms are formed, which allow boron to accommodate fewer than an octet of electrons in its valence shell. This is a type of multicenter bonding that stabilizes the molecule.

Step 5: Discuss the significance of "hydridic" hydrogen atoms

In response to part (c), when hydrogen atoms in diborane are referred to as "hydridic," it signifies their role in the unusual 3c-2e bonds. These "hydridic" hydrogen atoms have a more negative charge than those in typical covalently bonded hydrogen atoms, thus they have a greater tendency to donate electrons. This characteristic of hydridic hydrogen plays a crucial role in the reactivity, stability, and properties of diborane and related compounds.

Key Concepts

Electron-Deficient Bonding

Diborane (\(\mathrm{B}_2\mathrm{H}_6\)) stands out due to its unique electron-deficient bonding. Unlike typical molecules such as ethane (\(\mathrm{C}_2\mathrm{H}_6\)), where there are enough electrons to satisfy the octet rule for each atom, diborane is different. Boron, naturally, has only three valence electrons. This limitation means that diborane cannot form enough conventional 2-center 2-electron (2c-2e) bonds to satisfy the octet rule for both boron centers.

To overcome this deficit of electrons, diborane forms a specific type of bond known as a 3-center 2-electron bond. This type of bond is less common but provides structural stability to electron-deficient compounds like diborane.

• Improves molecular stability despite fewer electrons.
• Allows the involvement of three atoms sharing two electrons.
• Results in an unusual but stable molecular formation.

The electron-deficient bonding in diborane opens up unique pathways for bonding, breaking away from the conventional rules that most molecules adhere to.

Three-Center Two-Electron Bonds

A pivotal aspect of diborane's structure involves the three-center two-electron bonds, often abbreviated as 3c-2e bonds. In these bonds, two electrons are shared across three atoms rather than just two. This configuration arises when an electron-deficient element like boron needs to form stable structures with insufficient electrons.

In diborane:

• Two boron atoms and two bridging hydrogen atoms form the core bonds.
• The 3c-2e bonds consist of one pair of electrons, typically contributed by the hydrogen, that are spread over these three atoms.
• These bonds result in a sort of triangle, with the hydrogen atoms acting as bridges.

This type of bonding is crucial because it alleviates the electron deficiency while maintaining the integrity and stability of the molecule.

It is also a hallmark of other boron-hydrogen compounds, underlining the fascinating ways non-metal elements adapt their bonding mechanisms to account for electron shortage.

Hydridic Hydrogen Atoms

The hydrogen atoms in diborane also exhibit a distinct behavior, being referred to as "hydridic." This term hints at their role within the diborane structure and their unusual electron distribution. In general chemistry, hydrogen typically participates as a positively charged ion when bonded. However, in diborane, these hydrogen atoms carry a partial negative charge derived from their role in the 3-center 2-electron bonds.

Characteristics of hydridic hydrogen atoms include:

• A tendency to hold on to electrons more strongly compared to regular hydrogen atoms in typical covalent bonds.
• A negative polarization, in contrast to the usual positive charge in other chemical contexts.
• Contributing to the stability and reactivity of diborane by acting as electron donors.

This hydridic nature is significant because it indicates that the hydrogen atoms in diborane can act as electron sources, influencing the reactivity patterns of the molecule. It also points to intricate electronic interactions that are not seen in many other simple hydrides.