Question

Compare the relative bond orders of the following species and indicate their magnetic properties (i.e. diamagnetic or paramagnetic): \(\mathrm{O}_{2}, \mathrm{O}_{2}^{+}, \mathrm{O}_{2}^{-}\) (superoxide ion) \(, \mathrm{O}_{2}^{2-}\) (peroxide ion).

Short answer

Bond orders: \(\text{O}_2^+ > \text{O}_2 > \text{O}_2^- > \text{O}_2^{2-}\); \(\text{O}_2\), \(\text{O}_2^+\), \(\text{O}_2^-\) are paramagnetic, \(\text{O}_2^{2-}\) is diamagnetic.

Step-by-step solution

Determine Bond Order Formula

The bond order can be calculated using the formula: \[ \text{Bond Order} = \frac{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}{2} \] Determine the number of bonding and antibonding electrons for each \(\text{O}_2 \) species.

Analyze Each Species

Analyze the electron configurations of the following: - \(\text{O}_2\): Standard electron configuration has 12 bonding and 8 antibonding electrons.- \(\text{O}_2^+\): Loss of 1 electron (from antibonding orbital) results in 12 bonding and 7 antibonding.- \(\text{O}_2^-\): Gain of 1 electron (into antibonding orbital) gives 12 bonding and 9 antibonding.- \(\text{O}_2^{2-}\): Gain of 2 electrons (both into antibonding orbitals) results in 12 bonding and 10 antibonding.

Calculate Bond Orders

Calculate the bond order for each species:\(\text{O}_2\): \[ \text{Bond Order} = \frac{12 - 8}{2} = 2 \]\(\text{O}_2^+\): \[ \text{Bond Order} = \frac{12 - 7}{2} = 2.5 \]\(\text{O}_2^-\): \[ \text{Bond Order} = \frac{12 - 9}{2} = 1.5 \]\(\text{O}_2^{2-}\): \[ \text{Bond Order} = \frac{12 - 10}{2} = 1 \]

Determine Magnetic Properties

Determine the magnetic properties based on unpaired electrons.- \(\text{O}_2\): Has 2 unpaired electrons; thus, paramagnetic.- \(\text{O}_2^+\): Has 1 unpaired electron; thus, paramagnetic.- \(\text{O}_2^-\): Has 1 unpaired electron; thus, paramagnetic.- \(\text{O}_2^{2-}\): No unpaired electrons; thus, diamagnetic.

Key concepts

Magnetic Properties

Magnetic properties of a molecule relate to its behavior in the presence of a magnetic field.
Molecules can be classified as either **paramagnetic** or **diamagnetic** based on the presence of unpaired electrons in their electron configuration.

• **Paramagnetic** substances have unpaired electrons, which cause them to be attracted to magnetic fields.
• **Diamagnetic** substances, on the other hand, have no unpaired electrons, and are slightly repelled by magnetic fields.

Understanding magnetic properties helps in the analysis of how molecules will interact with external magnetic forces. This concept is especially useful in fields like chemistry and physics when determining the structural and reactive capabilities of molecules.

Diamagnetic

A **diamagnetic** molecule has all its electrons paired. This complete pairing leads to no net magnetic moment, meaning the molecule does not have a natural external magnetic field.
Consequently, diamagnetic substances are slightly repelled by a magnetic field.

• For example, in the species \(O_2^{2-}\), when an additional electron alters the electron configuration such that all orbitals contain paired electrons, the molecule becomes diamagnetic.
• Since there are no unpaired electrons, \(O_2^{2-}\) exhibits diamagnetism.

The presence or absence of unpaired electrons is essential for predicting whether a molecule is diamagnetic or paramagnetic.

Paramagnetic

**Paramagnetic** molecules contain one or more unpaired electrons. These unpaired electrons impart a magnetic moment to the molecule, making it attracted to an external magnetic field.
This attraction to magnetic fields occurs because unpaired electrons create a net magnetic moment.

• For instance, molecules like \(\mathrm{O}_2\) and \(\mathrm{O}_2^+\) have unpaired electrons. \(\mathrm{O}_2\) specifically has two unpaired electrons.
• \(\mathrm{O}_2^-\) gains an additional electron into an antibonding orbital, resulting in one unpaired electron. Thus, it also remains paramagnetic.

The presence of these unpaired electrons is what differentiates paramagnetic molecules from diamagnetic ones. Understanding whether a molecule is paramagnetic can help predict its behavior in magnetic fields.

Electron Configuration

Electron configuration refers to the arrangement of electrons in the orbitals of an atom or molecule. This configuration plays a critical role in determining many chemical properties, including reactivity, color, and magnetism.

• By identifying how these electrons are distributed among the different atomic or molecular orbitals, one can deduce whether there are any unpaired electrons.
• For example, in molecular oxygen \(\mathrm{O}_2\), the electron configuration includes two unpaired electrons in the antibonding molecular orbitals, which leads to its paramagnetic nature.
• In ions such as \(\mathrm{O}_2^+\) or \(\mathrm{O}_2^-\), gaining or losing electrons alters the electron configuration and thus affects the molecule's magnetic properties.

Understanding electron configuration is crucial for chemistry students as it forms the basis for predicting and explaining the magnetic and bonding characteristics of molecules and ions.