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 with a value of 3.

Step-by-step solution

Understanding Bond Order

Bond order is a concept that tells us the number of chemical bonds between a pair of atoms. It is calculated as: \[ \text{Bond Order} = \frac{1}{2} (\text{number of electrons in bonding orbitals} - \text{number of electrons in antibonding orbitals}) \] This formula allows us to figure out the stability of a molecule.

Calculate Bond Order for N2

The electron configuration for \(\mathrm{N}_{2}\) in terms of molecular orbitals is \((\sigma_{1s})^2 (\sigma_{1s}^*)^2 (\sigma_{2s})^2 (\sigma_{2s}^*)^2 (\pi_{2p_x})^2 (\pi_{2p_y})^2 (\sigma_{2p_z})^2\). There are a total of 10 electrons in bonding orbitals and 4 in antibonding. Thus, \[ \text{Bond Order} = \frac{1}{2} (10-4) = 3 \].

Calculate Bond Order for O2

For \(\mathrm{O}_{2}\), the electron configuration is \((\sigma_{1s})^2 (\sigma_{1s}^*)^2 (\sigma_{2s})^2 (\sigma_{2s}^*)^2 (\sigma_{2p_z})^2 (\pi_{2p_x})^2 (\pi_{2p_y})^2 (\pi_{2p_x}^*)^1 (\pi_{2p_y}^*)^1\). It consists of 10 bonding electrons and 6 antibonding electrons, which gives us \[ \text{Bond Order} = \frac{1}{2} (10-6) = 2 \].

Calculate Bond Order for He2

The molecular orbital configuration for \(\mathrm{He}_{2}\) is \((\sigma_{1s})^2 (\sigma_{1s}^*)^2\). It has 2 bonding electrons and 2 antibonding electrons, leading to \[ \text{Bond Order} = \frac{1}{2} (2-2) = 0 \]. Thus, \(\mathrm{He}_{2}\) is not a stable molecule.

Calculate Bond Order for H2

For \(\mathrm{H}_{2}\), the configuration is \((\sigma_{1s})^2\). There are 2 bonding electrons and 0 antibonding electrons, resulting in \[ \text{Bond Order} = \frac{1}{2} (2-0) = 1 \].

Compare Bond Orders

Now, compare the bond orders: \(\mathrm{N}_{2}\) 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. \(\mathrm{N}_{2}\) has the highest bond order of 3.

Key concepts

Molecular Orbitals

In chemistry, molecular orbitals are regions in a molecule where electrons are likely to be found. These orbitals form when atomic orbitals combine as atoms bond together. Molecular orbital theory offers a better understanding of how molecules bind than simpler models like valence bond theory.
The bonding and antibonding orbitals are key to understanding bond order. **Bonding orbitals** contribute to holding two atoms together because they enhance electron density between the atomic nuclei. Meanwhile, **antibonding orbitals** can destabilize a molecule because they reduce electron density between nuclei.

• If there are more electrons in bonding orbitals, the bond order increases, indicating a stronger bond.
• Conversely, more electrons in antibonding orbitals decrease bond order, potentially weakening the bond or leading to molecular instability.

Molecular orbitals are often represented in diagrams that order them by energy levels, making it easier to visualize which molecular orbitals participate in bonding or antibonding.

Chemical Stability

Chemical stability in a molecule is often related to its bond order. The **bond order** is a predictor of how strong or stable a chemical bond is. Stability indicates that a molecule is less reactive and more likely to maintain its structure under different environmental conditions.

• A higher bond order typically suggests increased stability because it means more electrons are participating actively in bonding.
• A bond order of zero indicates that the molecule doesn't form a stable bond and, therefore, likely won't exist under normal conditions.

In comparing different molecules like nitrogen ( \( \mathrm{N}_{2} \)), oxygen ( \( \mathrm{O}_{2} \)), helium ( \( \mathrm{He}_{2} \)), and hydrogen ( \( \mathrm{H}_{2} \)), it's clear that nitrogen's bond order of 3 suggests it's very stable. Nitrogen molecules have a triple bond, making them among the strongest bonds known.

Electron Configuration

Electron configuration in molecules refers to how electrons are distributed across molecular orbitals. Understanding electron configuration is crucial for predicting bond order and hence the stability of the molecule.
When electrons fill the orbitals, they do so according to their **energy levels**, filling lower-energy orbitals first which are generally bonding orbitals. This distribution can be observed in the molecular orbital diagrams.

• **For nitrogen ( \( \mathrm{N}_{2} \))**, its configuration shows 10 electrons in bonding orbitals and 4 in antibonding, yielding a bond order of 3.
• **For oxygen ( \( \mathrm{O}_{2} \))**, there are 10 bonding electrons and 6 antibonding, which gives a bond order of 2.
• **For helium ( \( \mathrm{He}_{2} \))**, its configuration results in equal numbers of bonding and antibonding electrons, giving a bond order of 0, and thus, it doesn't exist as a stable molecule.
• **For hydrogen ( \( \mathrm{H}_{2} \))**, with 2 bonding electrons and no antibonding, the bond order is 1.

By examining these electron configurations, one can visualize and understand the molecular stability, formation, and interactions.