(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.

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.

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.

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