Problem 90 - Chemistry The Central Science In Si Units

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

Step-by-Step Solution

Answer

(a) \( \mathrm{NO}_{2}^{-} \), (b) \( \mathrm{AsO}_{4}^{3-} \), (c) \( \mathrm{CO}_{3}^{2-} \).

Step 1: Identify Conjugate Acids

For each base in the pairs, identify the conjugate acid. (a) For \( \mathrm{NO}_{3}^{-} \), the conjugate acid is \( \mathrm{HNO}_{3} \). For \( \mathrm{NO}_{2}^{-} \), it's \( \mathrm{HNO}_{2} \). (b) For \( \mathrm{PO}_{4}^{3-} \), the conjugate acid is \( \mathrm{HPO}_{4}^{2-} \). For \( \mathrm{AsO}_{4}^{3-} \), it's \( \mathrm{HAsO}_{4}^{2-} \). (c) For \( \mathrm{HCO}_{3}^{-} \), the conjugate acid is \( \mathrm{H}_{2}\mathrm{CO}_{3} \). For \( \mathrm{CO}_{3}^{2-} \), it's \( \mathrm{HCO}_{3}^{-} \).

Step 2: Assess Acid Strength

Compare the strength of the conjugate acids from each pair. Stronger acids have weaker conjugate bases. (a) \( \mathrm{HNO}_{3} \) is a stronger acid than \( \mathrm{HNO}_{2} \), hence \( \mathrm{NO}_{3}^{-} \) is a weaker base. (b) Generally, arsenic acids are weaker than phosphoric acids, so \( \mathrm{HAsO}_{4}^{2-} \) is weaker than \( \mathrm{HPO}_{4}^{2-} \), making \( \mathrm{PO}_{4}^{3-} \) a weaker base. (c) \( \mathrm{H}_{2}\mathrm{CO}_{3} \) is a weak acid compared to \( \mathrm{HCO}_{3}^{-} \), so \( \mathrm{HCO}_{3}^{-} \) is weaker than \( \mathrm{CO}_{3}^{2-} \).

Step 3: Determine Stronger Base

Using the observations that stronger conjugate acids lead to weaker conjugate bases, determine the stronger base in each pair. (a) \( \mathrm{NO}_{2}^{-} \) is stronger than \( \mathrm{NO}_{3}^{-} \).(b) \( \mathrm{AsO}_{4}^{3-} \) is stronger than \( \mathrm{PO}_{4}^{3-} \).(c) \( \mathrm{CO}_{3}^{2-} \) is stronger than \( \mathrm{HCO}_{3}^{-} \).

Key Concepts

Conjugate Acid-Base Pairs

Understanding conjugate acid-base pairs is essential in acid-base chemistry. Conjugate acids and bases differ by a single proton (H⁺). In essence:

• The acid is the species that can donate a proton.
• The base is the species that results from the acid losing a proton.

For example, in the pair \( \mathrm{NO}_{2}^{-} \) and its conjugate acid \( \mathrm{HNO}_{2} \), the base \( \mathrm{NO}_{2}^{-} \) can accept a proton to become \( \mathrm{HNO}_{2} \).
Similarly, \( \mathrm{CO}_{3}^{2-} \) is the conjugate base of \( \mathrm{HCO}_{3}^{-} \), meaning it stems from \( \mathrm{HCO}_{3}^{-} \) losing a proton.
Understanding these pairs helps determine how substances will behave in chemical reactions.
It also sheds light on their tendencies to act as acids or bases, aiding in predicting their behavior in solution.

Base Strength

The strength of a base is pivotal in determining its reactivity and role in chemical reactions. Base strength is inherently related to the strength of its conjugate acid. The basic rule is:

• If a conjugate acid is strong, the base will be relatively weak.
• If a conjugate acid is weak, the base will be relatively strong.

This phenomenon is evident in our examples:
Since \( \mathrm{HNO}_{3} \) is a strong acid, its conjugate base \( \mathrm{NO}_{3}^{-} \) is weak.
Conversely, since \( \mathrm{HNO}_{2} \) is a weaker acid, \( \mathrm{NO}_{2}^{-} \) is a stronger base.
This concept helps predict which substances will more readily participate in acid-base reactions, providing insight into the chemical equilibria and dynamics of different systems.

Chemical Structure and Composition Analysis

Chemical structure and composition are crucial in understanding acid-base relationships. They determine how easily a molecule can donate or accept a proton, influencing its strength as an acid or base.
With similar structures like \( \mathrm{PO}_{4}^{3-} \) and \( \mathrm{AsO}_{4}^{3-} \), the atomic composition, primarily the central atom, can significantly affect their properties.
In these examples:

• Phosphoric acid (\( \mathrm{HPO}_{4}^{2-} \)) is a stronger conjugate acid than arsenic acid (\( \mathrm{HAsO}_{4}^{2-} \)), making \( \mathrm{AsO}_{4}^{3-} \) a stronger base than \( \mathrm{PO}_{4}^{3-} \).

Analyzing the molecular structure, including the type of atoms and their arrangement, is vital in predicting and explaining the behaviors of these chemical species.
Through this evaluation, one gains a better grasp of the intrinsic properties affecting acid and base strength.