Question

Which of the following species has unpaired electrons? (a) \(\mathrm{N}_{2}\) (b) \(\mathrm{F}_{2}\) (c) \(\mathrm{O}_{2}^{-}\) (d) \(\mathrm{O}_{2}^{2-}\)

Short answer

\(\mathrm{O}_{2}^{-}\) and \(\mathrm{O}_{2}^{2-}\) have unpaired electrons.

Step-by-step solution

Recall molecular orbital (MO) theory for diatomic molecules

Remember that according to MO theory, electrons in diatomic molecules fill the molecular orbitals with lower energy first. Bonding orbitals are lower in energy compared to antibonding orbitals. Also, remember Hund's rule, which states that electrons fill degenerate orbitals singly before pairing up.

Determine electron configurations using MO diagrams

Draw the MO diagrams for N2, F2, O2-, and O22-. Count the electrons for each molecule and fill the molecular orbitals from lowest to highest energy, taking into account the 2s-2p orbital mixing which occurs in molecules with Z<8 (such as N2 and F2), and doesn't occur in molecules with Z>=8 (such as O2, O2-, and O22-).

Identify unpaired electrons

Examine the electron configurations in the molecular orbitals you've drawn to identify if there are any unpaired electrons.O2 and O2- have unpaired electrons in the π* antibonding orbitals, while N2 and F2 have all electrons paired.

Choose the correct option(s)

Based on the number of unpaired electrons, select which species have them. Only O2 and O2- will have unpaired electrons, making (c) \(\mathrm{O}_{2}^{-}\) and (d) \(\mathrm{O}_{2}^{2-}\) the correct answers.

Key concepts

Unpaired Electrons

Unpaired electrons are those electrons in an atom or molecule that are not part of a pair. In molecular orbitals, paired electrons usually occupy the lowest energy levels first due to their tendency to stabilize a molecule.

For example, when determining which diatomic species has unpaired electrons, one needs to examine the electron configuration within molecular orbitals. Unpaired electrons can significantly influence the magnetic and chemical properties of a molecule, often making the molecule paramagnetic—meaning it has an attraction to magnetic fields. An important take-home point is that species with unpaired electrons exhibit different physical properties, like magnetism, compared to those without.

MO Diagrams

Molecular orbital (MO) diagrams are visual representations used in molecular orbital theory to illustrate the bonding between atoms. They show the relative energy levels of the molecular orbitals and which orbitals electrons occupy in a molecule.

Creating an MO diagram involves placing the atomic orbitals at the sides and the molecular orbitals in the middle, with the bonding orbitals being lower in energy than the antibonding orbitals. When filling these molecular orbitals with the corresponding number of electrons, one must follow the principles of the Aufbau principle, Pauli exclusion principle, and Hund's rule. Each molecular orbital can hold a maximum of two electrons, with opposite spins.

Bonding and Antibonding Orbitals

Bonding and antibonding orbitals are two types of molecular orbitals that form when atomic orbitals overlap in the process of molecule formation.

Bonding Orbitals

Bonding orbitals are lower in energy and result from the constructive interference between atomic orbitals. They serve to hold two atoms together, thus stabilizing the molecule.

Antibonding Orbitals

On the other hand, antibonding orbitals are higher in energy and result from destructive interference. They can destabilize the molecule as they possess enough energy to potentially break bonds when occupied by electrons. Normally, electrons will fill the lower energy bonding orbitals before occupying the antibonding ones.

Hund's Rule

Hund's rule is a principle that guides the filling of electrons into molecular orbitals. It states that electrons will fill degenerate (equal-in-energy) orbitals singly first, and only pair up when no empty degenerate orbitals are available.

This rule ensures the minimization of electron-electron repulsions within an atom or molecule, as placing an electron in an already occupied orbital increases the repulsion between the electrons. Therefore, by distributing unpaired electrons evenly before starting to pair them, the molecule achieves a lower energy state. It is particularly important when interpreting MO diagrams, as it helps determine the correct number of unpaired electrons and the species' magnetic properties.