The pH of a 0.209 M aqueous solution of chlorous acid is found to be 4.101. Calculate K, for chlorous acid using this information.

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### Calculating the Acid Dissociation Constant (Ka) of Chlorous Acid

**Problem Statement:**

The pH of a 0.209 M aqueous solution of chlorous acid is found to be 4.101. Calculate \( K_a \) for chlorous acid using this information.

**Detailed Explanation:**

To determine the acid dissociation constant (\( K_a \)) for chlorous acid, follow these steps:

1. **Understand the pH and Concentration Relationship:**
   - The pH of a solution is a measure of its hydrogen ion concentration \([H^+]\).
   - The equation relating pH to hydrogen ion concentration is: 
     \[ \text{pH} = -\log[H^+] \]

2. **Calculate \([H^+]\) from pH:**
   - Given: \( \text{pH} = 4.101 \)
   - Using the pH formula, solve for \([H^+]\):
     \[ [H^+] = 10^{-\text{pH}} = 10^{-4.101} \approx 7.94 \times 10^{-5} \text{ M} \]

3. **Set Up the Equilibrium Expression:**
   - Chlorous acid (\( \text{HClO}_2 \)) dissociates in water as follows:
     \[ \text{HClO}_2 \leftrightarrow \text{H}^+ + \text{ClO}_2^- \]
   - Let the initial concentration of \(\text{HClO}_2\) be \( 0.209 \text{ M} \) and the change in concentration of \([H^+]\) and \([\text{ClO}_2^-]\) be \( x \).

4. **Determine the Equilibrium Concentrations:**
   - At equilibrium:
     \[ [\text{H}^+] = x = 7.94 \times 10^{-5} \text{ M} \]
     \[ [\text{ClO}_2^-] = x = 7.94 \times 10^{-5} \text{ M} \]
     \[ [\text{HClO}_2] = 0.209 - x \approx 0.209 \text{ M} \] (since
Transcribed Image Text:### Calculating the Acid Dissociation Constant (Ka) of Chlorous Acid **Problem Statement:** The pH of a 0.209 M aqueous solution of chlorous acid is found to be 4.101. Calculate \( K_a \) for chlorous acid using this information. **Detailed Explanation:** To determine the acid dissociation constant (\( K_a \)) for chlorous acid, follow these steps: 1. **Understand the pH and Concentration Relationship:** - The pH of a solution is a measure of its hydrogen ion concentration \([H^+]\). - The equation relating pH to hydrogen ion concentration is: \[ \text{pH} = -\log[H^+] \] 2. **Calculate \([H^+]\) from pH:** - Given: \( \text{pH} = 4.101 \) - Using the pH formula, solve for \([H^+]\): \[ [H^+] = 10^{-\text{pH}} = 10^{-4.101} \approx 7.94 \times 10^{-5} \text{ M} \] 3. **Set Up the Equilibrium Expression:** - Chlorous acid (\( \text{HClO}_2 \)) dissociates in water as follows: \[ \text{HClO}_2 \leftrightarrow \text{H}^+ + \text{ClO}_2^- \] - Let the initial concentration of \(\text{HClO}_2\) be \( 0.209 \text{ M} \) and the change in concentration of \([H^+]\) and \([\text{ClO}_2^-]\) be \( x \). 4. **Determine the Equilibrium Concentrations:** - At equilibrium: \[ [\text{H}^+] = x = 7.94 \times 10^{-5} \text{ M} \] \[ [\text{ClO}_2^-] = x = 7.94 \times 10^{-5} \text{ M} \] \[ [\text{HClO}_2] = 0.209 - x \approx 0.209 \text{ M} \] (since
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