What do each of the following sets of compounds/ions have in common with each other? a. \(\mathrm{SO}_{3}, \mathrm{NO}_{3}^{-}, \mathrm{CO}_{3}^{2-}\) b. \(\mathrm{O}_{3}, \mathrm{SO}_{2}, \mathrm{NO}_{2}-\)

First, let us identify the oxidation state of the central element in each compound/ion. We have sulfur in \(\mathrm{SO}_{3}\), nitrogen in \(\mathrm{NO}_{3}^{-}\), and carbon in \(\mathrm{CO}_{3}^{2-}\). Since each of these compounds exhibits resonance, the average oxidation state of the central element can be found as follows: - In \(\mathrm{SO}_{3}\): The oxidation state of oxygen is always -2. So, for a neutral compound, the oxidation state of the sulfur must be \(+6\) in order for the overall compound to have a net charge of 0. - In \(\mathrm{NO}_{3}^{-}\): The oxidation state of oxygen is -2 as well. Since the net charge of the ion is -1, the oxidation state of the nitrogen must be \(+5\) to maintain the total charge. - In \(\mathrm{CO}_{3}^{2-}\): Oxygen maintains an oxidation state of -2. To achieve a net charge of -2, the oxidation state of carbon must be \(+4\).

The compounds/ions in set a, \(\mathrm{SO}_{3}, \mathrm{NO}_{3}^{-}, \mathrm{CO}_{3}^{2-}\), have a common feature: all the central elements - sulfur, nitrogen, and carbon - are in their highest possible oxidation states (+6, +5, and +4, respectively).

Now, let's determine the oxidation states of the central elements in each compound/ion. In this set, we have ozone \((\mathrm{O}_{3})\), sulfur dioxide \((\mathrm{SO}_{2})\), and nitrite \((\mathrm{NO}_{2}^{-})\). We will again focus on the average oxidation state of the central element in each compound/ion: - In \(\mathrm{O}_{3}\): Oxygen, being the only element, has an average oxidation state of 0. - In \(\mathrm{SO}_{2}\): Oxygen keeps an oxidation state of -2. For the compound to be neutral, the oxidation state of sulfur must be \(+4\). - In \(\mathrm{NO}_{2}^-\): Oxygen still has an oxidation state of -2. Given the overall ion has a -1 charge, the oxidation state of nitrogen must be \(+3\).

The compounds/ions in set b, \(\mathrm{O}_{3}, \mathrm{SO}_{2}, \mathrm{NO}_{2}^-\), have a common feature: Due to the presence of double bonds or resonance, each of the compounds has a central element with an intermediate oxidation state (0 for oxygen in \(\mathrm{O}_{3}\), +4 for sulfur in \(\mathrm{SO}_{2}\), and +3 for nitrogen in \(\mathrm{NO}_{2}^-\)).