Question

Which of the following has the highest bond order? (a) \(\mathrm{N}_{2}\) (b) \(\mathrm{O}_{2}\) (c) \(\mathrm{He}_{2}\) (d) \(\mathrm{H}_{2}\)

Short answer

\(\mathrm{N}_{2}\) has the highest bond order.

Step-by-step solution

Review Bond Order Formula

The bond order is calculated using the formula: \( \text{Bond Order} = \frac{1}{2} (\text{Number of bonding electrons} - \text{Number of antibonding electrons}) \). This formula helps in determining the stability of a molecule.

Analyze \(\mathrm{N}_{2}\)

For \(\mathrm{N}_{2}\), the electronic configuration in molecular orbital terms is \((\sigma_{1s})^2(\sigma^{*}_{1s})^2(\sigma_{2s})^2(\sigma^{*}_{2s})^2(\pi_{2p})^4(\sigma_{2p})^2\). The number of bonding electrons is 10 and antibonding electrons is 4. The bond order is \(\frac{1}{2} (10 - 4) = 3\).

Analyze \(\mathrm{O}_{2}\)

For \(\mathrm{O}_{2}\), the molecular electronic configuration is \((\sigma_{1s})^2(\sigma^{*}_{1s})^2(\sigma_{2s})^2(\sigma^{*}_{2s})^2(\sigma_{2p})^2(\pi_{2p})^4(\pi^{*}_{2p})^2\). The number of bonding electrons is 10 and antibonding electrons is 6. The bond order is \(\frac{1}{2} (10 - 6) = 2\).

Analyze \(\mathrm{He}_{2}\)

For \(\mathrm{He}_{2}\), the molecular electronic configuration is \((\sigma_{1s})^2(\sigma^{*}_{1s})^2\). The number of bonding electrons is 2 and antibonding electrons is 2. The bond order is \(\frac{1}{2} (2 - 2) = 0\). \(\mathrm{He}_{2}\) does not have a stable bond.

Analyze \(\mathrm{H}_{2}\)

For \(\mathrm{H}_{2}\), the molecular electronic configuration is \((\sigma_{1s})^2\). The number of bonding electrons is 2 and antibonding electrons is 0. The bond order is \(\frac{1}{2} (2 - 0) = 1\).

Compare Bond Orders

Summarizing each molecule's bond order: \(\mathrm{N}_{2}\) has a bond order of 3, \(\mathrm{O}_{2}\) has a bond order of 2, \(\mathrm{He}_{2}\) has a bond order of 0, and \(\mathrm{H}_{2}\) has a bond order of 1. The highest bond order is associated with \(\mathrm{N}_{2}\).

Key concepts

Molecular Orbital Theory

Molecular Orbital Theory is a way of understanding how electrons are distributed in molecules. Instead of focusing on individual atoms, this theory takes into account the entire molecule. Through Molecular Orbital Theory (MO Theory), atomic orbitals combine to create molecular orbitals that are spread over the entire molecule. Two main types of molecular orbitals form:

• Bonding orbitals: These result from constructive interaction between atomic orbitals. Electrons in these orbitals add stability to a molecule.
• Antibonding orbitals: These result from destructive interaction. Electrons in antibonding orbitals make a molecule less stable.

Each molecular orbital can hold up to two electrons. The arrangement and number of electrons in these orbitals help determine molecular stability and properties, such as bond order.

Bonding and Antibonding Electrons

Within the framework of Molecular Orbital Theory, electrons are divided into bonding and antibonding categories, and this division plays a crucial role in determining the bond order of a molecule.

• Bonding Electrons: Reside in molecular orbitals formed by constructive interference. These electrons help hold the two nuclei of a molecule together, supporting stability.
• Antibonding Electrons: Found in orbitals that are the product of destructive interference. They work against the stability, acting like a force that tries to pull the nuclei apart.

To calculate the bond order, we use the difference between these two types of electrons. The formula is: \[\text{Bond Order} = \frac{1}{2} (\text{Number of bonding electrons} - \text{Number of antibonding electrons})\]A higher bond order indicates more bonding interactions than antibonding, leading to increased molecular stability.

Stability of Molecules

The stability of a molecule is closely related to its bond order and how it's affected by electrons occupying different molecular orbitals. A higher bond order generally signifies a more stable molecule due to more effective bonding between atoms. This increased stability is due to:

• Lower Energy: Bonding orbitals are typically lower in energy than antibonding orbitals. Thus, molecules with more electrons in bonding orbitals are more stable.
• Nuclear Attraction: Greater bond order means more electrons are acting to draw atomic nuclei together, increasing binding strength.

In practical terms, molecules like \( \text{N}_2 \) showcase high bond orders (3 in this case), indicating robust stability where the nitrogen atoms are tightly bonded together. Conversely, molecules like \( \text{He}_2 \) with a bond order of 0 don't form stable bonds, as forces preferring disassembly overpower any constructing forces.