Question

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 \(\mathrm{CO}_{3}^{2-}\)

Short answer

In summary, based on the comparison of the stability of conjugate acids: - The stronger base in pair (a) is \(\mathrm{NO}_{3}^{-}\). - The stronger base in pair (b) is \(\mathrm{AsO}_{4}^{3-}\). - The stronger base in pair (c) is \(\mathrm{CO}_{3}^{2-}\).

Step-by-step solution

Identify the conjugate acids for the bases provided

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 \(\mathrm{HCO}_{3}^{-}\)

Compare the stability of conjugate acids for pair (a)

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 \(\mathrm{NO}_{2}^{-}\).

Compare the stability of conjugate acids for pair (b)

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 \(\mathrm{AsO}_{4}^{3-}\).

Compare the stability of conjugate acids for pair (c)

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).

Key concepts

Conjugate Acid-Base Pairs

Understanding conjugate acid-base pairs is a fundamental concept in acid-base chemistry. These pairs consist of acids and bases that differ by a single proton (H⁺). When an acid donates a proton, it transforms into its conjugate base. Conversely, a base that accepts a proton becomes its conjugate acid.

For example, in the pair involving itrate ( NO_3^- ) and its conjugate acid nitric acid ( HNO_3 ), the removal of a proton from HNO_3 forms NO_3^- . Similarly, in the pair, NO_2^- and HNO_2 , NO_2^- is the conjugate base of HNO_2 .

Identifying these conjugate relationships is crucial because it helps predict the behavior of substances in different chemical reactions. In the context of the original exercise, recognizing which species are acids and which are their conjugate bases allows us to compare their strengths and predict equilibrium positions in acid-base reactions.

Base Strength Comparison

Comparing base strengths is critical for assessing reactivity and stability in acid-base reactions. A stronger base is typically the one whose conjugate acid is weaker or less stable. The stability of conjugate acids can be influenced by factors such as oxidation states, resonance, and periodic trends.

In part (a) of the exercise, NO_3^- is a stronger base than NO_2^- because HNO_3 is less stable due to its higher oxidation state compared to HNO_2 . This higher oxidation state makes it more prone to releasing its proton.

For part (b), PO_4^{3-} and AsO_4^{3-} , the latter is the stronger base because its conjugate acid HAsO_4^{2-} is less stable than HPO_4^{2-} . The size and position of arsenic relative to phosphorus in the periodic table reduces its ability to retain a proton, enhancing AsO_4^{3-} 's base strength.

By comparing base strength, chemists can better predict the outcome of reactions and understand which bases are more likely to dominate an equilibrium.

Chemical Stability

Chemical stability in acids plays a pivotal role in determining the strength of their conjugate bases. The more stable a conjugate acid is, the less likely it is to donate its proton, thereby producing a weaker conjugate base.

In part (c), the exercise compares H_2CO_3 and HCO_3^- . Here, H_2CO_3 is more stable due to its favorable arrangement and the multiple hydrogen bonds that hold the structure more firmly together. Its increased stability results in a weaker conjugate base HCO_3^- compared to CO_3^{2-} , which indicates CO_3^{2-} is the stronger base.

Stability factors can include the ability to form resonance structures and the overall bonding in the molecule. These contribute to how easily or difficultly the acid dissociates, affecting the relative strength of the corresponding conjugate base. By analyzing these factors, students can improve their understanding of acid-base equilibria and develop insight into chemical reactions.