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

(a) Paramagnetism is a property of substances with at least one unpaired electron in their atomic or molecular orbitals, causing the substance to be temporarily magnetic when exposed to an external magnetic field. (b) The Gouy balance method can be used to experimentally determine paramagnetism, by measuring the change in mass of a substance when placed in a magnetic field. (c) \(\mathrm{O}_{2}^{+}\), \(\mathrm{N}_{2}{ }^{2-}\), and \(\mathrm{Li}_{2}^{+}\) are paramagnetic with 1, 2, and 1 unpaired electrons respectively, while \(\mathrm{O}_{2}^{2-}\) is not paramagnetic as it has no unpaired electrons.

Step-by-step solution

(a) Definition of Paramagnetism:

Paramagnetism is a property of substances that have at least one unpaired electron in their atomic or molecular orbitals. These substances are attracted by an external magnetic field due to the presence of these unpaired electrons. The unpaired electrons create a net magnetic moment, which aligns with the magnetic field, causing the substance to become magnetic temporarily.

(b) Experimental determination of paramagnetism:

A common method to experimentally determine whether a substance is paramagnetic is by using the Gouy balance. This technique involves measuring the change in mass of a substance when placed in a magnetic field. If a substance is paramagnetic, it will be attracted to the magnetic field and thus show an increase in mass when subjected to the field. Conversely, a diamagnetic substance will experience a decrease in mass due to a repulsion from the magnetic field, while for a non-magnetic material, there will be no change in mass. This method allows us to differentiate between paramagnetic, diamagnetic, and non-magnetic substances based on how their mass changes under varying magnetic field strengths.

(c) Determining paramagnetism and unpaired electrons in the given ions:

In order to determine whether the given ions are paramagnetic, we need to consider their molecular orbital diagrams and find the number of unpaired electrons in their respective molecular orbitals. 1. \(\mathrm{O}_{2}^{+}\): For oxygen, the molecular orbital diagram shows that the unpaired electron count in O2 is 2. Since \(\mathrm{O}_{2}^{+}\) is the cation, it will lose one electron, leaving one unpaired electron, making it paramagnetic. 2. \(\mathrm{N}_{2}{ }^{2-}\): In N2, there are no unpaired electrons. However, since we are looking at \(\mathrm{N}_{2}{ }^{2-}\), we must add two electrons to the orbitals, resulting in two unpaired electrons. Thus, this ion is also paramagnetic. 3. \(\mathrm{Li}_{2}^{+}\): Li2 has no unpaired electrons. But \(\mathrm{Li}_{2}^{+}\) loses one electron, leaving the other electron unpaired. Hence, this ion is also paramagnetic. 4. \(\mathrm{O}_{2}^{2-}\): As stated earlier, O2 has two unpaired electrons. When we add two electrons to form the \(\mathrm{O}_{2}^{2-}\) anion, both of the previously unpaired electrons become paired, resulting in no unpaired electrons. Therefore, this ion is not paramagnetic. In summary, \(\mathrm{O}_{2}^{+}\), \(\mathrm{N}_{2}{ }^{2-}\), and \(\mathrm{Li}_{2}^{+}\) are paramagnetic, while \(\mathrm{O}_{2}^{2-}\) is not paramagnetic. The unpaired electron count for the paramagnetic ions are as follows: - \(\mathrm{O}_{2}^{+}\): 1 - \(\mathrm{N}_{2}{ }^{2-}\): 2 - \(\mathrm{Li}_{2}^{+}\): 1

Key concepts

Molecular Orbitals

Molecular orbitals are fundamental concepts in understanding how atoms bond to form molecules. They are formed by the combination of atomic orbitals from individual atoms when atoms come together during chemical bonding. These orbitals can be seen as regions in a molecule where electrons are likely to be found.
Molecular orbitals are crucial for determining the magnetic properties of a molecule. This is because they help identify the number of unpaired electrons present in a molecule or ion. For instance, in the case of \( \mathrm{O}_{2}^{+} \), the molecular orbital diagram shows that there is one unpaired electron after losing an electron from its parent molecule, indicating it is paramagnetic.
In a molecular orbital diagram, bonding orbitals are typically at a lower energy state, whereas anti-bonding orbitals are higher in energy. Electrons fill the lower energy bonding orbitals first before occupying the higher energy anti-bonding orbitals. Paramagnetic substances will have unpaired electrons filling these orbitals.

Magnetic Properties of Substances

The magnetic properties of a substance are defined by its behavior in the presence of a magnetic field. Substances can be classified into three categories based on their magnetic properties: paramagnetic, diamagnetic, and ferromagnetic.
Paramagnetic substances have one or more unpaired electrons. When exposed to a magnetic field, they become magnetized by aligning their magnetic moments with the field.

• Paramagnetic materials are weakly attracted to a magnetic field.
• Their magnetism is temporary—only present when the field is applied.

In contrast, diamagnetic substances have all their electrons paired. They are negligibly affected by magnetic fields and are typically repelled by them. Ferromagnetic materials, like iron, are strongly magnetic due to aligned magnetic domains.
To experimentally determine if a substance is paramagnetic, a Gouy balance can be used. This involves observing the change in mass of a sample in a magnetic field. A noticeable increase in mass indicates paramagnetism as the sample is attracted to the field due to the presence of unpaired electrons.

Unpaired Electrons in Ions

The presence of unpaired electrons in ions is vital to understanding their paramagnetic or diamagnetic nature. Unpaired electrons contribute to a net magnetic moment, rendering an ion paramagnetic.
We determine the presence of unpaired electrons through molecular orbital diagrams for ions. For example:

• \( \mathrm{O}_{2}^{+} \): Loses an electron from \( \mathrm{O}_{2} \), leaving one unpaired electron.
• \( \mathrm{N}_{2}^{2-} \): Gaining two electrons results in two unpaired electrons.
• \( \mathrm{Li}_{2}^{+} \): Loses an electron, resulting in one remaining unpaired electron.

The significance of unpaired electrons lies in their contribution to a material's magnetic properties. Molecules or ions with unpaired electrons align in an external magnetic field, showcasing paramagnetism.
Understanding how electrons pair or remain unpaired in outer orbitals offers insights into the magnetic behaviors of various substances. This knowledge is vital for both theoretical analysis and practical applications in materials science.