Question

(a) What does the term paramagnetism mean? (b) How can one determine experimentally whether a substance is paramagnetic? (c) Which of the following ions would you expect to be paramagnetic: \(\mathrm{O}_{2}^{+}, \mathrm{N}_{2}^{2-}, \mathrm{Li}_{2}^{+}, \mathrm{O}_{2}{ }^{2-}\) ? For those ions that are paramagnetic, determine the number of unpaired electrons.

Short answer

Paramagnetism is a form of magnetism where certain atoms or ions are attracted into the magnetic field due to the presence of unpaired electrons. Experimentally, the Gouy method can be used to determine if a substance is paramagnetic. Among the given ions, \(\mathrm{O}_{2}^{+}\) and \(\mathrm{Li}_{2}^{+}\) are paramagnetic with one unpaired electron each, while \(\mathrm{N}_{2}^{2-}\) and \(\mathrm{O}_{2}{ }^{2-}\) are not paramagnetic as they have no unpaired electrons.

Step-by-step solution

(Answer to Part A: Define Paramagnetism)

Paramagnetism is a form of magnetism where certain atoms or ions are attracted into the magnetic field due to the presence of unpaired electrons in their atomic or molecular orbitals. When the substance is placed into an external magnetic field, these unpaired electrons align with the magnetic field, and the substance exhibits a net magnetic moment.

(Answer to Part B: Determine Experimentally Whether a Substance is Paramagnetic)

One common method to determine if a substance is paramagnetic experimentally is by using the Gouy method. In this method, a sample of the substance in question is placed between the poles of a strong electromagnet. The change in the magnetic field caused by the introduction of the substance into the magnetic field is measured. If there is a positive change in the magnetic field, i.e., an increase, then the substance is considered paramagnetic. If there is a negative change in the magnetic field, i.e., a decrease, then the substance is considered diamagnetic.

(Answer to Part C: Determine the Paramagnetism of the Given Ions and Unpaired Electrons)

First, let's find the electronic configurations of each ion: 1. \(\mathrm{O}_{2}^{+}\): - Oxygen has 8 electrons, and the diatomic molecule \(\mathrm{O}_{2}\) has 16 electrons. \(\mathrm{O}_{2}^{+}\) has 15 electrons. - Its molecular orbital configuration is: \(\sigma_{1s}^2, \sigma_{1s*}^2, \sigma_{2s}^2, \sigma_{2s*}^2, \sigma_{2p}^2, \pi_{2p}^4, \pi_{2p*}^1\). - There is one unpaired electron in the \(\pi_{2p*}\) orbital. 2. \(\mathrm{N}_{2}^{2-}\): - Nitrogen has 7 electrons, and the diatomic molecule \(\mathrm{N}_{2}\) has 14 electrons. \(\mathrm{N}_{2}^{2-}\) has 16 electrons. - Its molecular orbital configuration is: \(\sigma_{1s}^2, \sigma_{1s*}^2, \sigma_{2s}^2, \sigma_{2s*}^2, \sigma_{2p}^2, \pi_{2p}^4, \pi_{2p*}^2\). - There are no unpaired electrons. 3. \(\mathrm{Li}_{2}^{+}\): - Lithium has 3 electrons, and the diatomic molecule \(\mathrm{Li}_{2}\) has 6 electrons. \(\mathrm{Li}_{2}^{+}\) has 5 electrons. - Its molecular orbital configuration is: \(\sigma_{1s}^2, \sigma_{1s*}^2, \sigma_{2s}^1\). - There is one unpaired electron in the \(\sigma_{2s}\) orbital. 4. \(\mathrm{O}_{2}^{2-}\): - As mentioned earlier, the diatomic molecule \(\mathrm{O}_{2}\) has 16 electrons. \(\mathrm{O}_{2}^{2-}\) has 18 electrons. - Its molecular orbital configuration is: \(\sigma_{1s}^2, \sigma_{1s*}^2, \sigma_{2s}^2, \sigma_{2s*}^2, \sigma_{2p}^2, \pi_{2p}^4, \pi_{2p*}^4\). - There are no unpaired electrons. Based on the molecular orbital configurations and unpaired electrons, we can conclude that \(\mathrm{O}_{2}^{+}\) and \(\mathrm{Li}_{2}^{+}\) are paramagnetic, while \(\mathrm{N}_{2}^{2-}\) and \(\mathrm{O}_{2}{ }^{2-}\) are not. The number of unpaired electrons in \(\mathrm{O}_{2}^{+}\) is 1, and the number of unpaired electrons in \(\mathrm{Li}_{2}^{+}\) is also 1.

Key concepts

Molecular Orbital Theory

Molecular Orbital (MO) Theory offers a comprehensive explanation of how electrons are distributed in a molecule's atomic orbitals. It plays a critical role in determining the magnetic properties of molecules by demonstrating the presence or absence of unpaired electrons.

MO theory posits that atomic orbitals combine to form molecular orbitals that are spread over the entire molecule. These MOs are of two types: bonding and antibonding orbitals. Bonding orbitals are lower in energy, leading to a stable molecule, while antibonding orbitals are higher in energy and may contain unpaired electrons if occupied.

For example, take the ion \(\mathrm{O}_{2}^{+}\), which has one unpaired electron. MO theory explains this by the filling up of molecular orbitals: the last electron resides in an antibonding orbital that is typically higher in energy than the rest. Hence, molecular orbitals not only explain the structure and bond order of molecules and ions but also their magnetic properties.

Magnetic Properties of Ions

The magnetic properties of ions are fundamentally influenced by the arrangement of their electrons, specifically whether they possess unpaired electrons. Ions with unpaired electrons exhibit paramagnetism because unpaired electrons have intrinsic magnetic moments that align with an external magnetic field, causing attraction.

Contrarily, ions with all paired electrons are diamagnetic because paired electrons have opposite spins that cancel out their magnetic moments, leading to a net zero moment. As elucidated in the solution, ions such as \(\mathrm{O}_{2}^{+}\) and \(\mathrm{Li}_{2}^{+}\) which have unpaired electrons, are paramagnetic. On the other hand, \(\mathrm{N}_{2}^{2-}\) and \(\mathrm{O}_{2}^{2-}\), with all electrons paired, are classified as diamagnetic. This magnetic behavior significantly impacts how ions interact with magnetic fields, thus influencing experiments and applications that utilize magnetic properties.

Gouy Method

The Gouy method is an experimental technique to measure the magnetic susceptibilities of substances, which directly relates to their magnetism. This practical approach helps determine whether a substance is paramagnetic or diamagnetic.

In this method, a substance is suspended between the poles of a magnet, where a change in the weight of the substance is observed. If the weight appears to increase, it indicates that the substance is paramagnetic, as it's pulled towards the magnetic field. Conversely, a decrease in weight suggests diamagnetism, as the substance is repelled by the field.

The beauty of the Gouy method lies in its simplicity and its ability to provide quantitative data about a sample's magnetic properties. It commonly uses a balance to detect small changes in weight, which correspond to changes in the magnetic field caused by the substance’s presence. It's a powerful tool for verifying the magnetic behavior predicted by molecular orbital theory and the electron configurations of ions.