Question

\(\mathrm{O}_{2}^{2+}\) has a bond order of: (a) 1 (b) 2 (c) 3 (d) 4

Short answer

The bond order of \( \mathrm{O}_{2}^{2+} \) is 3.

Step-by-step solution

Understand Bond Order Formula

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 allows us to determine the stability and strength of a bond in a molecule.

Determine Electron Configuration

For \(\mathrm{O}_2\), the electron configuration in molecular orbitals is \((\sigma_{1s})^2(\sigma^*_{1s})^2(\sigma_{2s})^2(\sigma^*_{2s})^2(\sigma_{2p_z})^2(\pi_{2p_x})^2(\pi_{2p_y})^2(\pi^*_{2p_x})^1(\pi^*_{2p_y})^1\). For \(\mathrm{O}_{2}^{2+}\), remove 2 electrons from the antibonding orbitals, resulting in \((\pi^*_{2p_x})^0(\pi^*_{2p_y})^0\).

Count Bonding and Antibonding Electrons

In \(\mathrm{O}_{2}^{2+}\), the total number of bonding electrons is 8 and antibonding electrons is 2. This is because the antibonding orbitals \((\pi^*_{2p_x})\) and \((\pi^*_{2p_y})\) now have no electrons.

Calculate Bond Order

Using the bond order formula: \[ \text{Bond Order} = \frac{1}{2} (8 - 2) = \frac{1}{2} \times 6 = 3 \]. Thus, the bond order of \(\mathrm{O}_{2}^{2+}\) is 3.

Key concepts

Molecular Orbital Theory

The molecular orbital theory is a crucial concept in understanding how atoms combine to form molecules. Unlike the valence bond theory, which focuses on localized electron pairs, molecular orbital theory considers electrons as delocalized over the entire molecule. This gives us a comprehensive picture of the electron distribution. In this theory, atomic orbitals mix to form molecular orbitals, which can be of two types: bonding and antibonding.

• Bonding orbitals: These are lower in energy than the original atomic orbitals and result from constructive interference of the electron waves. Electrons in these orbitals increase the stability of a molecule.
• Antibonding orbitals: Higher in energy, these come from destructive interference, and electrons here decrease stability.

Molecular orbital theory provides a more precise prediction of molecular properties like bond order, stability, magnetic behavior, and electronic structure. It is especially useful in explaining the properties of molecules like Oxygen (O₂), which have unpaired electrons!

Bonding and Antibonding Electrons

Electrons can occupy two primary types of molecular orbitals: bonding and antibonding. The electron count in these orbitals determines if a molecule is stable or not. Bonding Electrons: These reside in molecular orbitals where electrons contribute to bond formation. By being in these orbitals, they help lower the overall energy of the molecule, and this results in a stronger bond. For example, in an oxygen molecule (O₂), electrons in (\(\sigma_{2p_z}\)) and (\(\pi_{2p}\)) orbitals provide the bonding interactions. Antibonding Electrons: Electrons in antibonding molecular orbitals are opposite. They have a destabilizing effect, as they reside in higher-energy orbitals marked with an asterisk (\(\sigma^*\) or \(\pi^*\)). These electrons counteract the stabilizing effect of bonding electrons, weakening the bond within a molecule. In the case of \(\mathrm{O}_{2}^{2+}\), removing antibonding electrons helps in strengthening the bond, increasing the bond order.

Oxygen Molecule

Oxygen (O₂) is a fascinating molecule often serving as a classic example illustrating molecular orbital theory. In its stable form, oxygen comprises a mix of bonding and antibonding molecular orbitals contributing to its overall electron configuration.The usual electron configuration for an oxygen molecule is \((\sigma_{1s})^2(\sigma^*_{1s})^2(\sigma_{2s})^2(\sigma^*_{2s})^2(\sigma_{2p_z})^2(\pi_{2p_x})^2(\pi_{2p_y})^2(\pi^*_{2p_x})^1(\pi^*_{2p_y})^1\).When examining the \(\mathrm{O}_{2}^{2+}\) ion, two electrons are removed from the antibonding orbitals (\(\pi^*\)), resulting in a higher bond order. This modification illustrates how molecular orbital theory is used to understand and predict the behavior of diatomic molecules. Notably, it clarifies why the removal of electrons from antibonding orbitals results in a stronger and more stable bond. Furthermore, Oxygen's paramagnetic nature is explained by the presence of unpaired electrons in the \(\pi^*\) orbitals, a reality properly accounted for by the molecular orbital framework.