Based on their compositions and structures and on conjugate acid-base relationships, select the stronger base in each of the following pairs: (a) \(\mathrm{NO}_{3}^{-}\) or \(\mathrm{NO}_{2}^{-},\) (b) \(\mathrm{PO}_{4}^{3-}\) or \(\mathrm{AsO}_{4}^{3-},(\mathbf{c})\) \(\mathrm{HCO}_{3}^{-}\) or \(\mathrm{CO}_{3}^{2-}\)

For each of the pairs, identify the conjugate acid, which will have one more hydrogen ion than the corresponding base in the pair. The conjugate acids are: (a) \(\mathrm{HNO}_{3}\) or \(\mathrm{HNO}_{2}\) (b) \(\mathrm{HPO}_{4}^{2-}\) or \(\mathrm{HAsO}_{4}^{2-}\) (c) \(\mathrm{H}_{2}\mathrm{CO}_{3}\) or \(\mathrm{HCO}_{3}^{-}\)

For the first pair, we need to decide whether \(\mathrm{HNO}_{3}\) is more or less stable than \(\mathrm{HNO}_{2}\). \(\mathrm{HNO}_{3}\) has a higher oxidation state than \(\mathrm{HNO}_{2}\), making it less stable and therefore its conjugate base \(\mathrm{NO}_{3}^{-}\) is stronger than \(\mathrm{NO}_{2}^{-}\).

Now, we need to compare the stability of \(\mathrm{HPO}_{4}^{2-}\) and \(\mathrm{HAsO}_{4}^{2-}\). Phosphorus and arsenic are both in Group 15, but arsenic is below phosphorus in the Periodic Table. As we move down a group, the size of the atom increases, and the ability to hold onto a proton decreases. Therefore, \(\mathrm{HPO}_{4}^{2-}\) is more stable than \(\mathrm{HAsO}_{4}^{2-}\). Thus, the conjugate base \(\mathrm{PO}_{4}^{3-}\) is weaker than \(\mathrm{AsO}_{4}^{3-}\).

For the last pair, we need to compare the stability of \(\mathrm{H}_{2}\mathrm{CO}_{3}\) and \(\mathrm{HCO}_{3}^{-}\). In \(\mathrm{H}_{2}\mathrm{CO}_{3}\), there are more hydrogen atoms attached to the central carbon atom than in \(\mathrm{HCO}_{3}^{-}\). As a result, the resonance stabilization effect of \(\mathrm{CO}_{3}^{2-}\) is bigger than the one from \(\mathrm{HCO}_{3}^{-}\). This means that \(\mathrm{H}_{2}\mathrm{CO}_{3}\) is more stable than \(\mathrm{HCO}_{3}^{-}\). Therefore, \(\mathrm{HCO}_{3}^{-}\) is the weaker base compared to \(\mathrm{CO}_{3}^{2-}\). In summary: - \(\mathrm{NO}_{3}^{-}\) is the stronger base in pair (a). - \(\mathrm{AsO}_{4}^{3-}\) is the stronger base in pair (b). - \(\mathrm{CO}_{3}^{2-}\) is the stronger base in pair (c).