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 \(\mathrm{AsO}_{4}^{3-}\), (c) \(\mathrm{HCO}_{3}^{-}\) or \(\mathrm{CO}_{3}^{2-}\).

Short Answer

Expert verified
The stronger bases in each pair are: (a) \(\mathrm{NO}_{2}^{-}\), (b) \(\mathrm{AsO}_{4}^{3-}\), and (c) \(\mathrm{CO}_{3}^{2-}\).

Step by step solution

01

Pair (a): Compare \(\mathrm{NO}_{3}^{-}\) and \(\mathrm{NO}_{2}^{-}\)

To determine the stronger base between \(\mathrm{NO}_{3}^{-}\) and \(\mathrm{NO}_{2}^{-}\), we can look at their conjugate acids: \(\mathrm{HNO}_3\) (nitric acid) and \(\mathrm{HNO}_2\) (nitrous acid). Remember that the stronger the conjugate acid is, the weaker its corresponding base will be. Nitric acid (\(\mathrm{HNO}_3\)) is a strong acid, so its conjugate base, \(\mathrm{NO}_{3}^{-}\), will be a weak base. On the other hand, nitrous acid (\(\mathrm{HNO}_2\)) is a weak acid, so its conjugate base, \(\mathrm{NO}_{2}^{-}\), will be a stronger base. So, the stronger base in this pair is \(\mathrm{NO}_{2}^{-}\).
02

Pair (b): Compare \(\mathrm{PO}_{4}^{3-}\) and \(\mathrm{AsO}_{4}^{3-}\)

To determine the stronger base between \(\mathrm{PO}_{4}^{3-}\) and \(\mathrm{AsO}_{4}^{3-}\), we can again look at their conjugate acids: \(\mathrm{H}_{3}\mathrm{PO}_{4}\) (phosphoric acid) and \(\mathrm{H}_{3}\mathrm{AsO}_{4}\) (arsenic acid). Both phosphoric acid (\(\mathrm{H}_{3}\mathrm{PO}_{4}\)) and arsenic acid (\(\mathrm{H}_{3}\mathrm{AsO}_{4}\)) are weak acids. However, the \(\mathrm{As-O}\) bond in arsenic acid is weaker due to the larger atomic size of arsenic than phosphorus, which makes the conjugate base \(\mathrm{AsO}_{4}^{3-}\) more likely to accept a proton. Thus, the stronger base in this pair is \(\mathrm{AsO}_{4}^{3-}\).
03

Pair (c): Compare \(\mathrm{HCO}_{3}^{-}\) and \(\mathrm{CO}_{3}^{2-}\)

To determine the stronger base between \(\mathrm{HCO}_{3}^{-}\) and \(\mathrm{CO}_{3}^{2-}\), we can look at their conjugate acids: \(\mathrm{H}_{2}\mathrm{CO}_{3}\) (carbonic acid) and \(\mathrm{HCO}_{3}^{-}\) (hydrogen carbonate). When \(\mathrm{HCO}_{3}^{-}\) accepts a proton (H+ ion), it forms the weak acid \(\mathrm{H}_{2}\mathrm{CO}_{3}\). However, when \(\mathrm{CO}_{3}^{2-}\) accepts a proton (H+ ion), it forms \(\mathrm{HCO}_{3}^{-}\), which is a stronger acid than carbonic acid. Therefore, \(\mathrm{CO}_{3}^{2-}\) is a stronger base compared to \(\mathrm{HCO}_{3}^{-}\). Thus, the stronger base in this pair is \(\mathrm{CO}_{3}^{2-}\).

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