Question

Construct approximate MO diagrams for \(\left[\mathrm{O}_{2}\right]^{-}\) and \(\left[\mathrm{O}_{2}\right]^{2-}\) and confirm that \(\left[\mathrm{O}_{2}\right]^{-}\) is paramagnetic, while \(\left[\mathrm{O}_{2}\right]^{2-}\) is diamagnetic.

Short answer

0_{2}^{-} is paramagnetic with one unpaired electron, while
0_{2}^{2-} is diamagnetic with all electrons paired.

Step-by-step solution

Determine the Total Electrons

For
0_{2}^{-}, start with molecular oxygen,
0_{2}, which has 16 electrons (8 from each oxygen). The extra negative charge adds one electron, giving a total of 17 electrons. For
0_{2}^{2-},
0_{2} again starts with 16 electrons, and the two extra negative charges add two electrons, resulting in a total of 18 electrons.

Construct the MO Diagram for
0_{2} \(^{-}\)

Molecular oxygen
0_{2} has the following MO configuration: \[(\sigma_{1s})^{2}(\sigma_{1s}^*)^{2}(\sigma_{2s})^{2}(\sigma_{2s}^*)^{2}(\sigma_{2p_{z}})^{2}(\pi_{2p_{x}})^{2}(\pi_{2p_{y}})^{2}(\pi_{2p_{x}^*})^{1}\]Adding the extra electron to
0_{2}^{-} gives:\[(\pi_{2p_{x}^*})^{1}(\pi_{2p_{y}^*})^{1}\]The remaining configuration stays the same.Since there is an unpaired electron,
0_{2}^{-} is paramagnetic.

Construct the MO Diagram for
0_{2} \(^{2-}\)

Using the same base MO configuration as
0_{2}, for
0_{2}^{2-} add two electrons to the antibonding \(\pi^*\) orbitals:\[(\pi_{2p_{x}^*})^{2}(\pi_{2p_{y}^*})^{2}\]The entire configuration becomes:\[(\sigma_{1s})^{2}(\sigma_{1s}^*)^{2}(\sigma_{2s})^{2}(\sigma_{2s}^*)^{2}(\sigma_{2p_{z}})^{2}(\pi_{2p_{x}})^{2}(\pi_{2p_{y}})^{2}(\pi_{2p_{x}^*})^{2}(\pi_{2p_{y}^*})^{2}\]With all electrons paired,
0_{2}^{2-} is diamagnetic.

Key concepts

Paramagnetism

Paramagnetism is the property of a material to be attracted to a magnetic field. This occurs due to the presence of unpaired electrons in the material's atomic or molecular structure. Let’s break it down further by focusing on molecular orbital theory, which is crucial for understanding paramagnetism.Molecular orbitals (MOs) are formed when atomic orbitals combine. The number of MOs formed equals the number of atomic orbitals combined. Electrons in a molecule fill these orbitals according to specific rules, similar to how they fill atomic orbitals. Electrons will fill the lowest energy orbitals first, following Hund's rule and the Pauli exclusion principle.In paramagnetic substances, like the superoxide ion \( ext{O}_{2}^{-}\), the molecular orbitals contain unpaired electrons. For \( ext{O}_{2}^{-}\), the molecular orbital configuration ends with partially filled antibonding π* orbitals:

• \((\pi_{2p_x^*})^1(\pi_{2p_y^*})^1\)

Since the \(\pi_{2p_x^*}\) and \(\pi_{2p_y^*}\) orbitals contain unpaired electrons, molecular oxygen in this state exhibits paramagnetism. These unpaired electrons align their spins with an external magnetic field, resulting in the characteristic attraction of paramagnetic materials.

Diamagnetism

Diamagnetism is another magnetic property that occurs in materials where all of the electrons are paired. Unlike paramagnetic materials, diamagnetic substances are slightly repelled by a magnetic field. This occurs because, in the presence of a magnetic field, the paired electrons in atoms or molecules create tiny loops of current, resisting the influence of the magnetic field.In the context of molecular orbital theory, a molecule is diamagnetic when all of its molecular orbitals are completely filled with paired electrons. For instance, the peroxide ion \( ext{O}_{2}^{2-}\) is diamagnetic. Its molecular orbital configuration is such that the \(\pi^*\) antibonding orbitals are fully occupied:

• \((\pi_{2p_x^*})^2(\pi_{2p_y^*})^2\)

Here, each antibonding orbital has a pair of electrons, resulting in all electrons being paired up in their respective orbitals. As a result, \( ext{O}_{2}^{2-}\) does not have any net magnetic moment and is diamagnetic. It is this electron pairing that leads to the slight repulsion from a magnetic field generally observed in diamagnetic materials.

Oxygen Ion Electron Configuration

The electron configuration of ions, especially those of oxygen species, is essential for predicting and understanding their magnetic properties. It primarily involves considering the number of electrons and determining how these electrons are arranged in molecular orbitals.Starting with neutral molecular oxygen \(\text{O}_{2}\), it has 16 electrons derived from 8 electrons contributed by each oxygen atom. The electronic configuration is given as:

• \((\sigma_{1s})^2(\sigma_{1s}^*)^2(\sigma_{2s})^2(\sigma_{2s}^*)^2(\sigma_{2p_z})^2(\pi_{2p_x})^2(\pi_{2p_y})^2\)

When the molecule gains electrons, forming ions such as \(\text{O}_{2}^{-}\) and \(\text{O}_{2}^{2-}\), these extra electrons occupy the next available molecular orbitals, which are antibonding \(\pi^*\) orbitals.

• For \(\text{O}_{2}^{-}\), adding one electron results in: \((\pi_{2p_x^*})^1(\pi_{2p_y^*})^1\)
• For \(\text{O}_{2}^{2-}\), adding two electrons results in a completely filled configuration: \((\pi_{2p_x^*})^2(\pi_{2p_y^*})^2\)

The knowledge of electron configurations is crucial for discussing the magnetic behavior and chemical properties of such ions, illustrating how changes in electron count and arrangement due to ion formation can significantly alter physical properties like magnetism.