(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 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.

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.

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.