Compare the relative stability of the following species and indicate their magnetic properties (that is, diamagnetic or paramagnetic): \(\mathrm{O}_{2}, \mathrm{O}_{2}^{+}, \mathrm{O}_{2}^{-}\) (superoxide ion), \(\mathrm{O}_{2}^{2-}\) (peroxide ion).

The bond order of a molecule can be determined using the formula : Bond order = (Number of electrons in bonding orbitals - Number of electrons in antibonding orbitals) / 2. From the electron configuration of these species, we can determine the bond order as follows: \( \mathrm{O}_{2} \) has 10 bonding and 6 antibonding, so bond order = (10-6)/2 = 2. \( \mathrm{O}_{2}^{+} \) has 9 bonding and 5 antibonding electrons, so bond order = (9-5)/2 = 2. \( \mathrm{O}_{2}^{-} \) has 11 bonding and 7 antibonding electrons, so bond order = (11-7)/2 = 2. \( \mathrm{O}_{2}^{2-} \) has 12 bonding and 8 antibonding electrons, so bond order = (12-8)/2 = 2. The stability is directly proportional to the bond order, therefore the increasing order of stability is: \( \mathrm{O}_{2}^{2-} \) < \( \mathrm{O}_{2}^{-} \) < \( \mathrm{O}_{2} \) = \( \mathrm{O}_{2}^{+} \).

Magnetic nature can be determined by the presence of unpaired electrons. Species with unpaired electrons are paramagnetic while those with all paired electrons are diamagnetic. Based on electron configuration, \( \mathrm{O}_{2} \) has two unpaired electrons, so it is paramagnetic. \( \mathrm{O}_{2}^{+} \) and \( \mathrm{O}_{2}^{-} \) both have one unpaired electron, so they are paramagnetic. \( \mathrm{O}_{2}^{2-} \) has no unpaired electrons, so it is diamagnetic.