Problem 77 - Chemistry The Central Science

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: \(N_{2}^{2-}, \mathrm{O}_{2}^{2-}, \mathrm{Be}_{2}^{2+}, \mathrm{C}_{2}^{-} ?\)

Step-by-Step Solution

Answer

(a) Diamagnetism is a property of materials that causes them to be repelled by an external magnetic field due to the opposition of their magnetic dipoles. (b) A diamagnetic substance creates an induced magnetic field that opposes the external field when exposed to a magnetic field, resulting in repulsion from the magnetic field. (c) The diamagnetic ions among the given options are \(N_{2}^{2-}, \mathrm{O}_{2}^{2-}, \mathrm{Be}_{2}^{2+}\) since they have all their electrons paired up in their electron configurations.

Step 1: Define Diamagnetism

Diamagnetism is a property of materials that causes them to be repelled by an external magnetic field. This phenomenon occurs when the magnetic dipoles within the material are oriented in such a way that they oppose the applied magnetic field.

Step 2: Describe the Response of Diamagnetic Substances to a Magnetic Field

When a diamagnetic substance is exposed to a magnetic field, the magnetic dipoles within the material align in opposition to the applied field. This causes the material to create an induced magnetic field that opposes the external field. As a result, the diamagnetic substance is repelled from the magnetic field.

Step 3: Determine the Diamagnetic Ions Based on Electron Configurations

To identify whether an ion is diamagnetic, we need to examine its electron configuration and look for any unpaired electrons. Diamagnetic ions have all of their electrons paired up. Let's look at the electron configurations of each ion to determine if they are likely to be diamagnetic. 1. \(N_{2}^{2-}\): Nitrogen has an electron configuration of \(1s^2\ 2s^2\ 2p^3\). With the added 2 electrons, the configuration becomes \(1s^2\ 2s^2\ 2p^5\). All electrons are paired, so this ion is diamagnetic. 2. \(O_{2}^{2-}\): Oxygen has an electron configuration of \(1s^2\ 2s^2\ 2p^4\). With the added 2 electrons, the configuration becomes \(1s^2\ 2s^2\ 2p^6\). All electrons are paired, so this ion is diamagnetic. 3. \(Be_{2}^{2+}\): Beryllium has an electron configuration of \(1s^2\ 2s^2\). With the loss of 2 electrons, the configuration becomes \(1s^2\). All electrons are paired, so this ion is diamagnetic. 4. \(C_{2}^{-}\): Carbon has an electron configuration of \(1s^2\ 2s^2\ 2p^2\). With the added 1 electron, the configuration becomes \(1s^2\ 2s^2\ 2p^3\). One electron remains unpaired, so this ion is not diamagnetic. In conclusion, the following ions are expected to be diamagnetic: \(N_{2}^{2-}, \mathrm{O}_{2}^{2-}, \mathrm{Be}_{2}^{2+}\).

Key Concepts

Magnetic Field

A magnetic field is a fundamental aspect of physics, involved in everything from everyday compasses to advanced medical imaging technologies. It is essentially a vector field that describes the magnetic force on moving charges, like electrons.

Magnetic fields are produced by electric currents, which can be macroscopic, like the flow of electricity in a wire, or microscopic, such as the movement of electrons in atomic orbits. The strength of a magnetic field is measured in Tesla (T), and its direction is the one that a magnetic north pole would point to within the field.

When materials interact with a magnetic field, we observe magnetic properties such as diamagnetism, paramagnetism, and ferromagnetism. Diamagnetic materials, like the ones mentioned in the exercise, are unique because they develop an induced magnetic field in a direction opposite to the applied magnetic field, thus experiencing a repelling force.

Electron Configurations

Electron configurations are at the heart of understanding an atom's chemical properties, including how it reacts in a magnetic field. In simplest terms, an electron configuration is a distribution of electrons of an atom or molecule in atomic or molecular orbitals.

For atoms, electrons fill orbitals in a way that minimizes the energy of the atom, following the Pauli exclusion principle and Hund's rule. These rules dictate that each orbital can hold a maximum of two electrons with opposite spins, and that single electrons with the same spin must occupy each equal-energy orbital before doubling up.

Electron configurations can predict magnetic properties; for diamagnetism, we look for atoms or ions where all the electrons are paired. These pairings lead to a cancellation of magnetic moments, which is why diamagnetic substances are repelled by magnetic fields, as they develop no permanent net magnetic moment.

Paired Electrons

Paired electrons are an indispensable factor when deducing the magnetic properties of an atom or an ion. Each electron carries a magnetic moment due to its spin, which can be thought of as a tiny magnet with a north and south pole.

In an orbital, two electrons can pair up with their spins in opposite directions. When the spins are opposite, the magnetic fields they generate cancel each other out, leading to no net magnetic moment for that paired set of electrons. This cancellation is what characterizes diamagnetic materials: they have all electrons paired and hence do not have an unpaired electron's magnetic field to align with an external magnetic field.

In the exercise provided, the ions with all paired electrons demonstrated no attraction to a magnetic field and were therefore identified as diamagnetic, underscoring the importance of understanding electron pairings when exploring magnetic properties.