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 \(\mathrm{NO}_{2}^{-},(\mathbf{b}) \mathrm{PO}_{4}^{3-}\) or \(\mathrm{AsO}_{4}^{3-}\) \((\mathbf{c}) \mathrm{HCO}_{3}^{-}\) or \(\mathrm{CO}_{3}^{2-}.\)

For each anion, identify its conjugate acid by adding one proton (H+). The conjugate acids for each anion are as follows: (a) For \(\mathrm{NO}_{3}^{-}\), the conjugate acid is \(\mathrm{HNO}_{3}\) (Nitric acid). For \(\mathrm{NO}_{2}^{-}\), the conjugate acid is \(\mathrm{HNO}_{2}\) (Nitrous acid). (b) For \(\mathrm{PO}_{4}^{3-}\), the conjugate acid is \(\mathrm{HPO}_{4}^{2-}\) (Dihydrogen phosphate ion). For \(\mathrm{AsO}_{4}^{3-}\), the conjugate acid is \(\mathrm{HAsO}_{4}^{2-}\) (Dihydrogen arsenate ion). (c) For \(\mathrm{HCO}_{3}^{-}\), the conjugate acid is \(\mathrm{H}_{2}\mathrm{CO}_{3}\) (Carbonic acid). For \(\mathrm{CO}_{3}^{2-}\), the conjugate acid is \(\mathrm{HCO}_{3}^{-}\) (Bicarbonate ion). ##Step 2: Compare the strength of conjugate acids##

Analyze the strength of the conjugate acids identified in step 1: (a) Nitric acid (\(\mathrm{HNO}_{3}\)) is a strong acid, whereas nitrous acid (\(\mathrm{HNO}_{2}\)) is a weak acid. Therefore, \(\mathrm{NO}_{3}^{-}\) is a weaker base compared to \(\mathrm{NO}_{2}^{-}\). (b) Both \(\mathrm{HPO}_{4}^{2-}\) and \(\mathrm{HAsO}_{4}^{2-}\) are weak acids. However, As(arsenic) is below P(phosphorus) in the periodic table, making \(\mathrm{HAsO}_4^{2-}\) more acidic than \(\mathrm{HPO}_4^{2-}\). As a result, \(\mathrm{AsO}_{4}^{3-}\) is a weaker base compared to \(\mathrm{PO}_{4}^{3-}\). (c) Carbonic acid (\(\mathrm{H}_{2}\mathrm{CO}_{3}\)) is a weak acid, and bicarbonate ion (\(\mathrm{HCO}_{3}^{-}\)) is also a weak acid. However, carbonic acid has two acidic protons, while bicarbonate ion has only one. So, carbonic acid is stronger than bicarbonate ion, making \(\mathrm{CO}_{3}^{2-}\) a stronger base compared to \(\mathrm{HCO}_{3}^{-}\). ##Step 3: Determine the stronger base in each pair##

Based on the comparison of conjugate acid strengths, we can conclude the stronger base in each pair: (a) \(\mathrm{NO}_{2}^{-}\) is a stronger base compared to \(\mathrm{NO}_{3}^{-}\). (b) \(\mathrm{PO}_{4}^{3-}\) is a stronger base compared to \(\mathrm{AsO}_{4}^{3-}\). (c) \(\mathrm{CO}_{3}^{2-}\) is a stronger base compared to \(\mathrm{HCO}_{3}^{-}\).