Question

(a) What does the term diamagnetism mean? (b) How does a diamagnetic substance respond to a magnetic field? (c) Which of the following ions would you expect to be diamagnetic: \(\mathrm{N}_{2}{ }^{2-}, \mathrm{O}_{2}{ }^{2-}, \mathrm{Be}_{2}{ }^{2+}, \mathrm{C}_{2}{ }^{-}\)?

Short answer

(a) Diamagnetism is a property of materials with no net magnetic moments due to paired electrons with opposite magnetic moments, effectively canceling each other out. (b) A diamagnetic substance, when exposed to an external magnetic field, develops a weak induced magnetic field in the opposite direction, causing the substance to be weakly repelled by the magnetic field. (c) Among the given ions, \(\mathrm{N}_{2}{ }^{2-}\) and \(\mathrm{Be}_{2}{ }^{2+}\) are expected to be diamagnetic, as they have no unpaired electrons.

Step-by-step solution

Understanding Diamagnetism

Diamagnetism is a property of materials that do not have any net magnetic moments in the absence of an external magnetic field. This occurs because the individual magnetic moments of the electrons in the material are paired, with each electron's magnetic moment being canceled by another electron with an opposite magnetic moment. Therefore, diamagnetic substances do not have any unpaired electrons.

Diamagnetic Response to Magnetic Field

When a diamagnetic substance is exposed to an external magnetic field, it tends to develop an induced magnetic field in the opposite direction. This weak induced magnetic field is caused by the substance's electrons rearranging their orbits slightly, and the material as a whole becomes weakly repelled by the external magnetic field. This repulsion causes diamagnetic substances to be pushed away from a magnetic field, demonstrating that they are inherently repelled by magnetic fields.

Determining Diamagnetic Ions

To determine whether an ion is diamagnetic, we can analyze its molecular orbital diagram or determine the number of unpaired electrons in the ion. If there are no unpaired electrons, then the ion is diamagnetic. This occurs when all electrons are paired, and their individual magnetic moments are canceled out by each other.

Identifying Diamagnetic Ions

Using the information provided about diamagnetism, we can now determine which of the given ions are expected to be diamagnetic: $\mathrm{N}_{2}{ }^{2-}, \mathrm{O}_{2}{ }^{2-}, \mathrm{Be}_{2}{ }^{2+}, \mathrm{C}_{2}{ }^{-}$. - \(\mathrm{N}_{2}{ }^{2-}\): Nitrogen has 7 electrons, and this ion has an additional 2, giving it a total of 16 electrons. These 16 electrons fill the molecular orbitals, resulting in no unpaired electrons. Thus, it is diamagnetic. - \(\mathrm{O}_{2}{ }^{2-}\): Oxygen has 8 electrons, and this ion also has an additional 2, totaling 18 electrons. Oxygen's molecular orbital diagram results in two unpaired electrons, making it paramagnetic and not diamagnetic. - \(\mathrm{Be}_{2}{ }^{2+}\): Beryllium has 4 electrons, and this ion has 2 fewer, resulting in 2 electrons. These 2 electrons are paired in the molecular orbital, making it diamagnetic. - \(\mathrm{C}_{2}{ }^{-}\): Carbon has 6 electrons, and this ion has 1 additional electron, giving a total of 13 electrons. This configuration results in one unpaired electron in the molecular orbital diagram, making it paramagnetic and not diamagnetic. To conclude, the diamagnetic ions from the given list are \(\mathrm{N}_{2}{ }^{2-}\) and \(\mathrm{Be}_{2}{ }^{2+}\).

Key concepts

Molecular Orbital Theory

Molecular Orbital (MO) Theory is a sophisticated way of explaining the electronic structure of molecules. Unlike the Lewis structure approach, which shows electron pairs as localized bonds between specific atoms, MO theory describes how atomic orbitals can combine to create molecular orbitals that extend over the entire molecule.

These molecular orbitals can be bonding, anti-bonding, or non-bonding, with bonding orbitals having a lower energy and stabilizing effect on the molecule, while anti-bonding orbitals have higher energy and can destabilize the molecule if they contain electrons.

Understanding Electron Configuration in MO Theory

Electrons in molecules fill the molecular orbitals starting with the lowest energy orbitals, much like they fill atomic orbitals in an atom. A key factor in determining the magnetic properties of the molecule is the presence of unpaired electrons within these molecular orbitals. MO theory also takes into account the Pauli Exclusion Principle and Hund's Rule in arranging the electrons for optimized stability.

Role in Determining Magnetic Properties

By using MO diagrams, we can predict the magnetic behavior of the molecule: if all electrons are paired, the molecule is diamagnetic; if one or more electrons are unpaired, the molecule is paramagnetic. This conceptual framework allows chemists to understand and predict how substances will interact with magnetic fields, which is crucial for materials science and applications such as MRI in medicine.

Paramagnetic and Diamagnetic Substances

Understanding the concepts of paramagnetism and diamagnetism requires a grasp of the underlying electron configurations within substances. In diamagnetism, all electrons in the substance are paired, and when diamagnetic materials are introduced into a magnetic field, they produce an induced magnetic field in the opposite direction, exhibiting repulsion from the external magnetic field.

Paramagnetic substances, on the other hand, have one or more unpaired electrons and are attracted to magnetic fields. This behavior is due to the magnetic moments of unpaired electrons aligning with the magnetic field, resulting in a net magnetic attraction.

Induced Magnetic Fields

While the repulsion or attraction is generally weak, especially in diamagnetic substances, it still can be observed with strong magnets or sensitive instruments. In the case of diamagnetic substances, the induced magnetic field is often too weak to feel by hand, but it is significant enough to be measured and utilized in scientific applications.

Magnetic Properties of Ions

The magnetic properties of ions are influenced by their electronic configuration, specifically by the presence or absence of unpaired electrons in the molecular orbital structure. Ions with paired electrons, as in the case of diamagnetic ions, resist the external magnetic field and are weakly repelled.

The molecular orbital theory comes into play when predicting these properties as it allows chemists to determine whether the electrons in an ion are paired or unpaired by analyzing its electronic structure based on MO diagrams. For instance, ions derived from transition metals often have unpaired electrons, resulting in various magnetic behaviors depending on the exact electronic configuration.

Importance of Electron Pairing in Magnetic Behavior

The interactions between ions with different magnetic properties are essential in numerous chemical processes, such as the formation of coordination compounds. Understanding these properties not only aids in the prediction of how substances will behave around magnets but also influences how they might interact with each other at the molecular level, which has implications in fields ranging from pharmacology to nanotechnology.