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

Short answer

The stronger bases in each pair are: (a) \(\mathrm{NO}_{2}^{-}\) (b) \(\mathrm{PO}_{4}^{3-}\) (c) \(\mathrm{CO}_{3}^{2-}\)

Step-by-step solution

Identify the conjugate acids

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##

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##

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

Key concepts

Conjugate Acid-Base Pairs

In acid-base chemistry, understanding conjugate acid-base pairs is crucial for analyzing reactions. A conjugate acid-base pair consists of two species that transform into each other by gaining or losing a proton (\(H^+\)). For example, when a base gains a proton, it turns into its conjugate acid, and when an acid loses a proton, it becomes its conjugate base.
Consider the pair \(\mathrm{NO}_{2}^{-}\) and \(\mathrm{HNO}_{2}\): \(\mathrm{NO}_{2}^{-}\) is a base because it can accept a proton to form \(\mathrm{HNO}_{2}\), its conjugate acid. Conversely, \(\mathrm{HNO}_{2}\) can donate a proton, thus behaving as an acid in this pair.
Understanding these relationships helps us predict reactivity and the nature of solutions:

• A strong acid will have a weak conjugate base because it easily loses protons.
• Conversely, a weak acid will have a stronger conjugate base since it holds on to its protons more firmly.
• These pairs are pivotal in predicting the direction of acid-base reactions and equilibria.

Strong and Weak Acids

Acids are categorized based on their ability to donate protons (\(H^+\)) in solution. This ability determines whether an acid is strong or weak.
Strong acids, like nitric acid (\(\mathrm{HNO}_{3}\)), dissociate completely in water, meaning they fully donate their available protons. This makes their conjugate bases very weak. In the case of \(\mathrm{HNO}_{3}\), \(\mathrm{NO}_{3}^{-}\) barely acts as a base because it's very stable and has little tendency to gain a proton back. On the other hand, weak acids, such as nitrous acid (\(\mathrm{HNO}_{2}\)), only partially dissociate in solution. This incomplete dissociation means that the conjugate base is more reactive or stronger compared to that of a strong acid.
When comparing the strengths of acids, consider:

• Complete dissociation indicates a strong acid. Examples include hydroiodic acid (\(\mathrm{HI}\)) and \(\mathrm{HNO}_{3}\).
  
• Partial dissociation points to a weak acid. Examples include acetic acid (\(\mathrm{CH}_3\mathrm{COOH}\)) and \(\mathrm{HNO}_{2}\).
• Strong acids tend to lead to very weak, often inert, conjugate bases.
• Weak acids have conjugate bases that can readily accept protons and act as bases in solution.

Anions

Anions play a vital role in acid-base chemistry. These are negatively charged ions that often form the base part of a conjugate acid-base pair. Understanding the behavior of different anions can help predict the basicity of the compound.
Anions like \(\mathrm{NO}_{3}^{-}\), \(\mathrm{PO}_{4}^{3-}\), and \(\mathrm{CO}_{3}^{2-}\) typically arise from the dissociation of their corresponding acids. The nature of these anions—as determined by their conjugate acid—indicates their ability to participate in acid-base reactions.
Key points about anions include:

• An anion derived from a strong acid, such as \(\mathrm{NO}_{3}^{-}\), is a weak base because it has minimal tendency to accept a proton.
  
• An anion from a weak acid, such as \(\mathrm{CO}_{3}^{2-}\), can act as a stronger base.
  
• The position of the element in periodic table affects anion behavior; elements lower in the same group often result in weaker bases due to their larger size and lower charge density.
  
• Anion stability is crucial; more stable anions are typically weaker bases.
  

By understanding these properties, one can better predict and explain the acid-base behavior of different compounds in chemical reactions.