Indicate the trend in increasing bond length for molecular oxygen, the peroxide ion and superoxide ion. (a) \(\mathrm{O}_{2}^{2 \cdot}>\mathrm{O}_{2}>\mathrm{O}^{2-}\) (b) \(\mathrm{O}_{2}^{2 \cdot}>\mathrm{O}_{2}^{-}>\mathrm{O}_{2}\) (c) \(\mathrm{O}_{2}>\mathrm{O}_{2}^{-}>\mathrm{O}_{2}^{\frac{2}{2}}\) (d) \(\mathrm{O}_{2}>\mathrm{O}_{2}^{2}>\mathrm{O}^{2-}\)

Molecular Orbital Theory (MOT) provides an advanced explanation of how atoms combine to form molecules through the combination of their atomic orbitals.

In MOT, atomic orbitals overlap to create molecule-specific orbitals known as molecular orbitals. These are classified as bonding orbitals, which lower the energy of the system, and antibonding orbitals, which raise it. When two atoms bond, their electrons occupy the lowest available molecular orbitals, usually starting with the bonding ones.

Bond order is a crucial concept in MOT and it represents the strength and stability of a bond. It can be calculated by subtracting the number of electrons in antibonding orbitals from the number of electrons in bonding orbitals and then dividing by two. A higher bond order signifies a stronger, shorter bond, while a lower bond order indicates a weaker, longer bond.

Using MOT, we can understand that molecular oxygen, with a bond order of 2, has a shorter bond length compared to the superoxide and peroxide ions, with bond orders of 1.5 and 1, respectively.

Chemical bonding is the force that holds atoms together in molecules and compounds. Bonds form when atoms share or transfer electrons to achieve stability, typically through a full outer electron shell.

There are several types of chemical bonds, including ionic, covalent, and metallic bonds. Covalent bonds involve the sharing of electron pairs between atoms. These bonds can be single, double, or triple, depending on the number of shared electron pairs.

In the context of our exercise, we focus on covalent bonding within oxygen-containing species. The nature of these covalent bonds changes due to the addition of electrons in the case of the peroxide and superoxide ions, making the bonds weaker and, consequently, longer than in molecular oxygen.

Oxyanions are negative ions containing oxygen and at least one other element. Their structure is determined by their charge and the number of oxygen atoms present.

The peroxide (O2^2-) and superoxide (O2^-) ions are examples of oxyanions. Peroxide has each oxygen atom with a single electron from the bonding pair, resulting in a longer bond length due to the repulsion between the electron pairs.

Superoxide Ions

In contrast, the superoxide ion has an additional unpaired electron that adds to the repelling force but also contributes to bond strength, leaving it in a state between a single and double bond. The structure of oxyanions affects their properties, such as reactivity, bond lengths, and bond angles. Understanding the structure of these ions from a molecular orbital perspective is key to explaining their physical and chemical behavior.