Question

Diborane, \(\mathrm{B}_{2} \mathrm{H}_{6}\), is a highly unstable compound that reacts explosively with oxygen. Ethane, \(\mathrm{C}_{2} \mathrm{H}_{6}\), combines with oxygen only at elevated temperatures. Explain the differences in these two compounds.

Short answer

The reactivity differences between diborane (B2H6) and ethane (C2H6) with oxygen can be attributed to their molecular structures, bond energies, and electron distributions. Diborane has an electron-deficient system with weaker three-center, two-electron bonds, making it highly unstable and prone to explosive reactions with oxygen. In contrast, ethane has a stable electron configuration with stronger single covalent bonds, requiring elevated temperatures and higher activation energy for a reaction with oxygen to occur.

Step-by-step solution

Analyze the molecular structures and bonding in Diborane and Ethane

: Diborane has an unusual structure with two bridging hydrogen atoms connecting the two boron atoms, which leads to three-center, two-electron bonds in addition to usual two-center, two-electron bonds between boron and terminal hydrogen atoms. This results in an electron-deficient system. In contrast, ethane has single covalent bonds between carbon and hydrogen and also between the two carbon atoms. The carbons are sp3-hybridized, and all the orbitals are filled with paired electrons, leading to a stable electron configuration.

Compare the bond energies

: The three-center, two-electron bonds in diborane have weaker bond strengths compared to the single covalent bonds between carbon and hydrogen atoms in ethane. As a result, diborane is more prone to reactions than ethane, as it requires less energy to break the bonds and form new ones during a reaction.

Determine the stability based on electron distribution

: Diborane is an electron-deficient system, making it highly unstable and susceptible to reactions. The electron deficiency causes diborane to readily accept electrons from other compounds, such as oxygen, leading to an explosive reaction as diborane tries to fill its electron-deficient orbitals. On the other hand, ethane has a stable electron configuration with no electron deficiency. Ethane can react with oxygen, but the reaction is much slower and requires elevated temperatures. The higher temperature provides the necessary activation energy to initiate the reaction between ethane and oxygen. #Conclusion#: The differences in the reactivity of diborane and ethane with oxygen can be explained by their molecular structures, bond energies, and electron distributions. Diborane's electron-deficient system, weaker bond strength and unstable structure make it highly reactive and result in it reacting explosively with oxygen. Whereas, ethane's stable electron configuration, stronger covalent bonds, and requirement for higher activation energy results in a slower reaction at elevated temperatures.

Key concepts

Diborane

Diborane is a compound described by the chemical formula \(\mathrm{B}_{2} \mathrm{H}_{6}\). It is known for its unusual molecular structure and high reactivity with oxygen. The structure of diborane is quite unique due to its triangular formation involving boron and hydrogen atoms. Two bridging hydrogens connect the two boron atoms, forming three-center, two-electron (3c-2e) bonds. This means that two electrons are shared across three atoms, a feature that contributes significantly to its instability. The terminal hydrogen atoms are bonded to boron with two-center, two-electron bonds, similar to conventional single covalent bonds. However, diborane's 3c-2e bonds introduce an electron-deficient nature, which makes the compound prone to accept electrons from other substances, such as oxygen, instigating highly energetic reactions.

Ethane

Ethane, represented by \(\mathrm{C}_{2} \mathrm{H}_{6}\), is a simple hydrocarbon but much less reactive compared to diborane. Its structure is composed entirely of single covalent bonds. Each carbon atom forms covalent bonds with three hydrogen atoms and one carbon atom, resulting in stable sp3 hybridization. This hybridization ensures that all the bonding orbitals in ethane are filled with paired electrons, leading to minimal chemical reactivity at room temperature. Unlike diborane, ethane does not easily react with oxygen unless additional energy is provided, such as through heating. This energy is needed to break the strong carbon-hydrogen and carbon-carbon bonds before any significant reaction with oxygen can occur.

Molecular Structure

The molecular structure of a compound greatly influences its chemical reactivity. For diborane, the special arrangement of its boron and hydrogen atoms results in a structure where electron sharing is not conventional, making it electron-deficient and therefore more reactive. The unusual bridging hydrogens lead to a structure where bonds are weaker and more susceptible to breaking.

In contrast, ethane has a simple and straightforward structure. Each atom in ethane achieves a stable electronic configuration by sharing electrons, creating strong conventional single covalent bonds. The carbon atoms in ethane exhibit \(sp^3\) hybridization, forming a tetrahedral geometry, which is typical for saturated hydrocarbons. This regular arrangement and electron pairing provide ethane with a robust and stable structure, making it significantly less reactive than diborane.

Bond Energy

Bond energy refers to the strength of a bond, or the amount of energy required to break it. In diborane, the three-center, two-electron bonds are weaker compared to traditional covalent bonds because the electrons are spread across multiple atoms. This type of bonding requires less energy to break, making diborane considerably more reactive as less energy is needed to initiate a reaction.

On the other hand, the covalent bonds in ethane are robust and require a substantial amount of energy to break. Both carbon-hydrogen and carbon-carbon bonds possess high bond energies, contributing to ethane's thermal stability. Since high energy is needed to disrupt these bonds, ethane reacts only under conditions where additional thermal energy is provided, unlike diborane which reacts readily.

Electron Deficiency

Electron deficiency is a condition where a molecule does not have enough electrons to form stable bonds. Diborane is a classic example of an electron-deficient compound due to its 3c-2e bonds, which feature fewer electrons than atoms involved. This deficiency means diborane can act as an electron acceptor, explaining its tendency to react explosively with electron-rich molecules like oxygen.

In contrast, ethane does not exhibit electron deficiency. Each of its atoms achieves a full valence shell through shared electron pairs, resulting in a complete and stable electron configuration. With no electron deficiency, ethane does not seek out additional electrons, thus explaining its relative lack of reactivity under standard conditions. It requires higher temperatures to exceed the activation energy needed for reactions, reflecting its thermodynamically stable nature.