Question

The simple valence bond picture of \(\mathrm{O}_{2}\) does not agree with the molecular orbital view. Compare these two theories with regard to the peroxide ion, \(\mathbf{O}_{2}^{2-}\) (a) Draw an electron dot structure for \(\mathrm{O}_{2}^{2-}\). What is the bond order of the ion? (b) Write the molecular orbital electron configuration for O \(_{2}^{2-} .\) What is the bond order based on this approach? (c) Do the two theories of bonding lead to the same magnetic character and bond order for \(\mathbf{O}_{2}^{2-} ?\)

Short answer

Both theories give a bond order of 1 for \(\mathrm{O}_{2}^{2-}\), but only MO theory predicts diamagnetism.

Step-by-step solution

Electron Dot Structure for Peroxide Ion

To find the electron dot structure for \(\mathrm{O}_{2}^{2-}\), start by counting the total number of valence electrons. Each oxygen atom contributes 6 electrons, leading to a total of 12 electrons for two oxygens. The \(2-\) charge adds 2 more electrons, giving a total of 14 valence electrons.Distribute these electrons to form a stable structure. A single bond between the oxygens will utilize 2 electrons: \({\cdot\cdot\cdot\cdot\cdot\cdot}\mathrm{O}-\mathrm{O}{\cdot\cdot\cdot\cdot\cdot\cdot}\). Each oxygen should have 8 electrons around it for a full octet. This structure reflects a single bond in the peroxide ion. Therefore, the bond order is 1.

Molecular Orbital Configuration for Peroxide Ion

Write down the molecular orbital (MO) electronic configuration for \(\mathrm{O}_{2}^{2-}\). We start with the standard electron configuration for \(\mathrm{O}_{2}\): \(\sigma_{1s}^{2}\sigma^{*}_{1s}^{2}\sigma_{2s}^{2}\sigma^{*}_{2s}^{2}\sigma_{2p_z}^{2}\pi_{2p_x}^{2}\pi_{2p_y}^{2}\pi^{*}_{2p_x}^{1}\pi^{*}_{2p_y}^{1}\).The peroxide ion, \(\mathrm{O}_{2}^{2-}\), has 2 additional electrons compared to \(\mathrm{O}_{2}\), filling the \(\pi^{*}_{2p}\) orbitals completely: \(\sigma_{1s}^{2}\sigma^{*}_{1s}^{2}\sigma_{2s}^{2}\sigma^{*}_{2s}^{2}\sigma_{2p_z}^{2}\pi_{2p_x}^{2}\pi_{2p_y}^{2}\pi^{*}_{2p_x}^{2}\pi^{*}_{2p_y}^{2}\).To find the bond order, apply the formula: \(\text{Bond Order} = [\text{(Number of electrons in bonding MOs)} - \text{(Number of electrons in antibonding MOs)}]/2\). In this case, the bond order is \((8 - 6)/2 = 1\).

Compare Bonding Theories

Both the Lewis structure and the molecular orbital theory predict the same bond order of 1 for \(\mathrm{O}_{2}^{2-}\). However, the magnetic character differs. From the MO theory, all electrons in \(\mathrm{O}_{2}^{2-}\) are paired, suggesting that it is diamagnetic. The Lewis structure does not inherently describe magnetic properties, focusing instead on electron pairs and bonds.

Key concepts

Valence Bond Theory

Valence bond (VB) theory offers a straightforward and intuitive approach to understanding chemical bonding. It focuses on how atomic orbitals overlap to form bonds. In the case of the peroxide ion, \(\text{O}_2^{2-}\), VB theory uses electron dot structures to represent valence electrons. This visual method highlights how atoms achieve stable configurations by sharing electrons.
When drawing the electron dot structure for \(\text{O}_2^{2-}\), each oxygen atom contributes 6 valence electrons. The additional \(2^-\) charge adds 2 more electrons to the overall valence pool, summing it up to 14 valence electrons. The electrons are shared between the two oxygen atoms, forming a single bond and resulting in each oxygen atom holding a full octet. Thus, in this picture, the bond order for \(\text{O}_2^{2-}\) is determined to be 1.
This theory has some limitations. It doesn't extensively delve into molecular magnetic properties or the nature of individual electron distributions across molecular orbits. Its simplistic visual approach can overlook some complex scenarios that other models cover, particularly when it comes to delocalized electrons.

Molecular Orbital Theory

Molecular orbital (MO) theory provides a more comprehensive vision of chemical bonding by considering the entire molecule, not just individual atom overlaps. It explains how atomic orbitals blend to form molecular orbitals that cover the whole molecule, influencing its electronic structure and properties.
For the peroxide ion \(\text{O}_2^{2-}\), the MO configuration is built starting from \(\text{O}_2\). This involves the filling up of \(\pi^*_{2p}\) molecular orbital levels after adding the extra 2 electrons to \(\text{O}_2^{2-}\). The configuration follows this order: \(\sigma_{1s}^2\sigma^*_{1s}^2\sigma_{2s}^2\sigma^*_{2s}^2\sigma_{2p_z}^2\pi_{2p_x}^2\pi_{2p_y}^2\pi^*_{2p_x}^2\pi^*_{2p_y}^2\).
The bond order calculation here is achieved by noting the difference in electron numbers in bonding and antibonding molecular orbitals. This formula: \[\text{Bond Order} = \frac{\text{(Number of electrons in bonding MOs)} - \text{(Number of electrons in antibonding MOs)}}{2}\] results in a bond order of 1, equivalent to what is derived via valence bond theory.
Moreover, MO theory uniquely explains magnetic properties. Since all electrons are paired in \(\text{O}_2^{2-}\), it is classified as diamagnetic, indicating its non-response to magnetic fields. This is a distinct advantage where MO theory adds deeper insights, over VB theory, into the magnetic behavior of molecules.

Peroxide Ion

The peroxide ion, represented as \(\text{O}_2^{2-}\), is a fascinating example of how different bonding theories can provide varied insights into the same molecular entity. Known for its reactive properties, the peroxide ion is comprised of two oxygen atoms each contributing 6 electrons, plus an additional 2 electrons due to its \(2^-\) charge.
In both valence bond and molecular orbital theories, \(\text{O}_2^{2-}\) presents a bond order of 1. This single bond character arises as each bonding method suggests a similar conclusion about the shared electron cloud between the oxygen atoms.
However, the peroxide ion is more than just its bond order. Its role in redox reactions and its behavior under various conditions, such as in aqueous solutions, make it a fundamental component in fields ranging from industrial bleaches to potential energy storage systems.
Understanding \(\text{O}_2^{2-}\) through diverse theoretical frameworks equips students and chemists with a well-rounded view of chemical bonding. This also helps in predicting molecular properties and reactivity patterns effectively.