Q.Compare the relative stability of the following species and indicate their magnetic properties: $O_2$, $O_2^+$, $O_2^-$ (superoxide), $O_2^{2-}$ (peroxide).

Concept: Bond Order and Stability

Stability increases with bond order, calculated from molecular orbital theory as $\text{BO} = \frac{1}{2}(n_b - n_a)$, where $n_b$ and $n_a$ are bonding and antibonding electrons. Species with unpaired electrons are paramagnetic; all paired means diamagnetic.

Molecular orbital filling for oxygen species:

The $O_2$ configuration ends at $\pi_{2p}^*$ orbitals. Adding or removing electrons changes the antibonding occupancy:

Why Bond Order Governs Stability

The strength of a chemical bond—and therefore the stability of a molecule—depends on how many electrons occupy bonding versus antibonding orbitals. Bond order quantifies this balance:

A higher bond order means more net bonding character, a shorter and stronger bond, and greater stability. When we add or remove electrons from $O_2$, we change the bond order and thus the relative stability.

Magnetism follows directly from electron configuration: any species with unpaired electrons is paramagnetic (attracted to a magnetic field), while species with all electrons paired are diamagnetic.

Molecular Orbital Configuration of Oxygen Species

Oxygen ($Z = 8$) has 16 electrons in $O_2$. The molecular orbital diagram for second-period homonuclear diatomics places orbitals in this order:

For our purposes, focus on the valence electrons (the inner $\sigma_{1s}$, $\sigma^*_{1s}$, $\sigma_{2s}$, $\sigma^*_{2s}$ are filled and cancel out):

Valence MO filling for $O_2$ (12 valence electrons):

The two electrons in the degenerate $\pi^*$ orbitals remain unpaired (Hund's rule).

Now let's analyze each species systematically.

1. $O_2$ (neutral oxygen molecule)

Total valence electrons: 12

Configuration: \sigma_{2p_z}^2 \, \pi_{2p_x}^2 \, \pi_{2p_y}^2 \, \pi^*_{2p_x}^1 \, \pi^*_{2p_y}^1

• Bonding electrons: $2 + 2 + 2 = 6$
• Antibonding electrons: $1 + 1 = 2$

Magnetic property: Two unpaired electrons → paramagnetic

2. $O_2^+$ (dioxygen cation)

Total valence electrons: 11 (one electron removed from $O_2$)

The electron is removed from the highest-energy occupied orbital, a $\pi^*$ orbital:

Configuration: \sigma_{2p_z}^2 \, \pi_{2p_x}^2 \, \pi_{2p_y}^2 \, \pi^*_{2p_x}^1 \, \pi^*_{2p_y}^0

• Bonding electrons: 6
• Antibonding electrons: 1

Magnetic property: One unpaired electron → paramagnetic

3. $O_2^-$ (superoxide ion)

Total valence electrons: 13 (one electron added to $O_2$)

The extra electron goes into a $\pi^*$ orbital:

Configuration: \sigma_{2p_z}^2 \, \pi_{2p_x}^2 \, \pi_{2p_y}^2 \, \pi^*_{2p_x}^2 \, \pi^*_{2p_y}^1

• Bonding electrons: 6
• Antibonding electrons: 3 …