Question

Compare the relative stability of these species and indicate their magnetic properties (that is, diamagnetic or paramagnetic): \(\mathrm{O}_{2}, \mathrm{O}_{2}^{+}, \mathrm{O}_{2}^{-}\) (superoxide ion), \(\mathrm{O}_{2}^{2-}\) (peroxide ion).

Short answer

In decreasing order of stability: \(O2+ > O2 > O2- > O2^{2-}\) . Only peroxide ion is diamagnetic whereas all other ions along with neutral O2 are paramagnetic.

Step-by-step solution

Determine the Total Number of Electrons

First calculate the total number of electrons for each species: O2 has 16 electrons (8 from each oxygen atom), O2+ has 15 electrons (one electron has been removed), O2- has 17 electrons (one electron has been added) and O2^{2-} has 18 electrons (two electrons have been added).

Fill the Molecular Orbitals

Using the molecular orbital diagram for Oxygen, fill the molecular orbitals according to the aufbau principle (from lowest to highest energy) and the Pauli Exclusion Principle (each orbital can hold a maximum of two electrons of opposite spin).

Calculate Bond Order and Determine Magnetic Property

For each species, calculate the bond order as (number of electrons in bonding orbitals - number of electrons in anti-bonding orbitals) / 2. A higher bond order suggests greater stability. For the magnetic properties, if all electrons are paired, the molecule is diamagnetic; if there are unpaired electrons, the molecule is paramagnetic.

Apply the Principles

The bond order of O2 is 2, making it very stable. Because there are two unpaired electrons in its π* orbitals, it is paramagnetic. The bond order in O2+ is 2.5 and is the most stable ion because it has the highest bond order. It is also paramagnetic because it has one unpaired electron. The bond order in O2- is 1.5, and it is paramagnetic because it has one unpaired electron. Lastly, O2^{2-}(peroxide ion) has a bond order of 1 and is diamagnetic because it has no unpaired electrons. Hence in decreasing order of stability: \(O2+ > O2 > O2- > O2^{2-}\) . Only peroxide ion is diamagnetic whereas all other ions along with neutral O2 are paramagnetic.

Key concepts

Diamagnetic

Diamagnetic substances are those that do not have any unpaired electrons in their molecular orbitals. This lack of unpaired electrons means that diamagnetic substances do not generate a net magnetic field. As a result, when exposed to a magnetic field, they are slightly repelled rather than attracted.

In the context of the oxygen species from the exercise, only the peroxide ion \( \mathrm{O}_2^{2-} \) is diamagnetic. This is because it has all paired electrons within its molecular orbitals. Let's look at the molecular orbital diagram for the peroxide ion: it fills up the \( \sigma \) and \( \pi \) bonding orbitals completely with paired electrons. There are no electrons in the antibonding \( \pi^* \) orbitals, resulting in a bond order of 1 and no unpaired electrons.

• All electrons in \( \mathrm{O}_2^{2-} \) are paired.
• No induced magnetic field in the presence of an external magnetic field.
• Only the peroxide ion among the provided oxygen species is diamagnetic.

Paramagnetic

Paramagnetic substances have at least one unpaired electron in their molecular orbitals. This presence of unpaired electrons gives rise to a net magnetic moment, which allows these substances to be attracted to magnetic fields.

Molecular oxygen (\( \mathrm{O}_2 \)), superoxide ion (\( \mathrm{O}_2^- \)), and \( \mathrm{O}_2^+ \) are examples of paramagnetic species. Let's consider their electronic configuration:

• \( \mathrm{O}_2 \): Has two unpaired electrons in the \( \pi^* \) antibonding orbitals.
• \( \mathrm{O}_2^- \): Adds an electron that results in one unpaired electron in the \( \pi^* \) orbitals.
• \( \mathrm{O}_2^+ \): Removes an electron, leaving one unpaired electron in the \( \pi^* \) orbitals.

These unpaired electrons make these species noticeable in magnetic fields, classifying them as paramagnetic.
This means, if you were to place any of these molecules in a magnetic field, they would be attracted to it due to their net magnetic moment.

Bond Order

Bond order is a concept used to predict the stability of a molecule. It is calculated using the formula:\[\text{Bond Order} = \frac{\text{Number of electrons in bonding orbitals} - \text{Number of electrons in antibonding orbitals}}{2}\]This measure tells us how strongly atoms in a molecule are bonded together.

For our oxygen species:

• \( \mathrm{O}_2 \): Bond order of 2, indicating a double bond.
• \( \mathrm{O}_2^+ \): Bond order of 2.5, indicates this is the most stable species.
• \( \mathrm{O}_2^- \): Bond order of 1.5, intermediate stability.
• \( \mathrm{O}_2^{2-} \): Bond order of 1, the least stable among the species provided.

In essence, a higher bond order corresponds to greater stability of the molecule. Thus, \( \mathrm{O}_2^+ \) with the highest bond order is the most stable, while \( \mathrm{O}_2^{2-} \) with the lowest bond order is the least stable.

Oxygen Species

The oxygen species we are examining include the dioxygen molecule and its various ionic forms. Each of these forms has different properties including stability and magnetism, and these differences arise from the varying electron arrangements in their molecular orbitals.

• \( \mathrm{O}_2 \) (Dioxygen): A stable molecule with a bond order of 2 and paramagnetic properties due to two unpaired electrons.
• \( \mathrm{O}_2^+ \) (Cation): The most stable ion with a bond order of 2.5. It is paramagnetic with one unpaired electron.
• \( \mathrm{O}_2^- \) (Superoxide ion): Less stable than \( \mathrm{O}_2 \) with a bond order of 1.5 and paramagnetic properties due to one unpaired electron.
• \( \mathrm{O}_2^{2-} \) (Peroxide ion): The least stable, having a bond order of 1, and is diamagnetic because all electrons are paired.

Understanding these species involves recognizing how electrons distribute in their molecular orbitals, which affects both their chemical bonding and magnetic behavior.