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 property of materials with one or more unpaired electrons, leading to a magnetic moment and attraction to a magnetic field. Experimentally, paramagnetism can be determined using magnetic susceptibility measurements or a SQUID magnetometer. Among the given ions, ${\mathrm{O}}_2^{+}$ (with one unpaired electron) and ${\mathrm{N}}_2^{2-}$ (with two unpaired electrons) are paramagnetic, while ${\mathrm{Li}}_2^{+}$ and ${\mathrm{O}}_2^{2-}$ are not paramagnetic.

Step-by-step solution

Part (a): Defining Paramagnetism

Paramagnetism is a property of materials that have one or more unpaired electrons in their atomic or molecular orbitals. These unpaired electrons lead to a magnetic moment, which causes the substance to be attracted to an external magnetic field. Paramagnetic substances will have a positive magnetic susceptibility, meaning they will magnetize in the direction of the applied field.

Part (b): Experimental Determination of Paramagnetism

To experimentally determine if a substance is paramagnetic, one can use a magnetic susceptibility measurement. The sample should be placed between the poles of a magnet and observe if it is attracted, repelled, or remains unaffected by the magnetic field. Another common method to test for paramagnetism is by using a SQUID magnetometer, which measures the magnetic susceptibility of the material.

Part (c): Identifying Paramagnetic Ions

To solve this part of the problem, we will examine the given ions: ${\mathrm{O}}_2^{+},{\mathrm{N}}_2^{2-},{\mathrm{Li}}_2^{+},{\mathrm{O}}_2^{2-}$. Our task is to find the number of unpaired electrons for each of the ions and determine if they are paramagnetic. 1. ${\mathrm{O}}_2^{+}$: Molecular oxygen (${\mathrm{O}}_2$) has 2 unpaired electrons in the *π antibonding orbitals. When it is ionized to ${\mathrm{O}}_2^{+}$, it loses one electron. Therefore, there is still 1 unpaired electron left, making it paramagnetic. 2. ${\mathrm{N}}_2^{2-}$: Molecular nitrogen (${\mathrm{N}}_2$) has no unpaired electrons, as all the electrons are paired in the molecular orbitals. Adding 2 electrons to form ${\mathrm{N}}_2^{2-}$ results in both electrons being placed in the *π antibonding orbitals. Thus, there are 2 unpaired electrons, making it paramagnetic. 3. ${\mathrm{Li}}_2^{+}$: In its neutral state, ${\mathrm{Li}}_2$ has no unpaired electrons. When it is ionized to ${\mathrm{Li}}_2^{+}$, it loses one electron. The remaining electron is still paired in the bonding orbital, so there are no unpaired electrons. Therefore, it is not paramagnetic. 4. ${\mathrm{O}}_2^{2-}$: As mentioned earlier, molecular oxygen (${\mathrm{O}}_2$) has 2 unpaired electrons. When we add 2 more electrons to form ${\mathrm{O}}_2^{2-}$, these additional electrons will fill up the *π antibonding orbitals, and all the electrons become paired. Thus, there are no unpaired electrons, and it is not paramagnetic. In summary, ions ${\mathrm{O}}_2^{+}$ and ${\mathrm{N}}_2^{2-}$ are paramagnetic, while ${\mathrm{Li}}_2^{+}$ and ${\mathrm{O}}_2^{2-}$ are not. Furthermore, ${\mathrm{O}}_2^{+}$ has one unpaired electron while ${\mathrm{N}}_2^{2-}$ has two unpaired electrons.

Key concepts

Magnetic Susceptibility

Magnetic susceptibility is a key concept when discussing paramagnetic materials. It refers to how a material responds to an external magnetic field. Paramagnetic substances have a positive magnetic susceptibility, meaning they align with the magnetic field. This is because they contain unpaired electrons that create a magnetic moment, allowing them to be attracted by a magnetic field.

In contrast, diamagnetic materials, with all paired electrons, show negative susceptibility as they are slightly repelled by magnetic fields. The measurement of magnetic susceptibility can be determined using various methods, such as a magnetic balance or a SQUID magnetometer, which provides precise data on how a sample reacts to magnetism.

Electron Configuration

Electron configuration helps us understand whether a material will be paramagnetic or not. It shows the distribution of electrons in atomic or molecular orbitals. Unpaired electrons in these configurations are the primary cause of paramagnetism.

Let's take an example: Consider ${\mathrm{O}}_2^{+}$. Oxygen molecules usually have two unpaired electrons which make them paramagnetic. When ionized to ${\mathrm{O}}_2^{+}$, it loses one electron but retains one unpaired electron, hence remaining paramagnetic. On the other hand, neutral ${\mathrm{Li}}_2$ has paired electrons, and upon losing one electron to form ${\mathrm{Li}}_2^{+}$, it remains with no unpaired electron, making it diamagnetic.

Molecular Orbitals

Molecular orbitals (MOs) are essential for understanding the electron behavior in molecules, especially when determining magnetic properties.

Molecular Orbital Theory explains how atomic orbitals combine to form molecular orbitals that can be occupied by electrons from different atoms in a molecule. These orbitals can be bonding, antibonding, or non-bonding.

For instance, examining the orbital configuration of ${\mathrm{O}}_2^{+}$, electrons occupy antibonding $\pi$ orbitals, resulting in unpaired electrons which are crucial for paramagnetism. Conversely, ${\mathrm{O}}_2^{2-}$, having added electrons, completely fills these orbitals, leading to all paired electrons, thereby showing diamagnetic properties. Understanding how electrons populate molecular orbitals helps predict whether a molecule will exhibit paramagnetism.