Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![**Problem Statement:**
Determine the hydronium ion concentration of an aqueous solution of 0.591 M hypochlorous acid (K_a = 3.50×10^-8).
\[ \text{[H}_3\text{O}^+\text{]} = \_\_\_\_\_\_\_\_ \text{ M.} \]
**Explanation:**
To calculate the hydronium ion concentration ([H₃O⁺]) of a given solution, it is necessary to use the provided acid dissociation constant (K_a) and the initial concentration of the acid. The calculation typically involves setting up an equilibrium expression and solving for [H₃O⁺].
1. **Write the dissociation equation for hypochlorous acid (HOCl):**
\[ \text{HOCl} \leftrightharpoons \text{H}^+ + \text{OCl}^- \]
2. **Set up the equilibrium expression:**
\[ K_a = \frac{[\text{H}^+][\text{OCl}^-]}{[\text{HOCl}]} \]
Given:
- K_a = 3.50×10^-8
- Initial concentration of HOCl = 0.591 M
3. **Assume the degree of dissociation (x) is equal to the concentration of [H⁺] and [OCl⁻]:**
\[ K_a = \frac{x \cdot x}{0.591 - x} \]
Since K_a is very small, \( x \) will be small and \( 0.591 - x ≈ 0.591 \):
\[ K_a ≈ \frac{x^2}{0.591} \]
4. **Solve for \( x \) (which is [H₃O⁺] or [H⁺]):**
\[ x^2 ≈ 0.591 \cdot 3.50×10^{-8} \]
\[ x^2 ≈ 2.07×10^{-8} \]
\[ x ≈ \sqrt{2.07×10^{-8}} \]
\[ x ≈ 1.44×10^{-4} \]
Therefore:
\[ \text{[H}_3\text{O}^+\text{]} ≈ 1.44×10^{-4} \text{ M} \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03ba95c9-584b-483d-8f8a-8f0f9c4c55b7%2F568d7508-7b0c-4b90-b2dd-293fb7773996%2F01qd0kr_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Determine the hydronium ion concentration of an aqueous solution of 0.591 M hypochlorous acid (K_a = 3.50×10^-8).
\[ \text{[H}_3\text{O}^+\text{]} = \_\_\_\_\_\_\_\_ \text{ M.} \]
**Explanation:**
To calculate the hydronium ion concentration ([H₃O⁺]) of a given solution, it is necessary to use the provided acid dissociation constant (K_a) and the initial concentration of the acid. The calculation typically involves setting up an equilibrium expression and solving for [H₃O⁺].
1. **Write the dissociation equation for hypochlorous acid (HOCl):**
\[ \text{HOCl} \leftrightharpoons \text{H}^+ + \text{OCl}^- \]
2. **Set up the equilibrium expression:**
\[ K_a = \frac{[\text{H}^+][\text{OCl}^-]}{[\text{HOCl}]} \]
Given:
- K_a = 3.50×10^-8
- Initial concentration of HOCl = 0.591 M
3. **Assume the degree of dissociation (x) is equal to the concentration of [H⁺] and [OCl⁻]:**
\[ K_a = \frac{x \cdot x}{0.591 - x} \]
Since K_a is very small, \( x \) will be small and \( 0.591 - x ≈ 0.591 \):
\[ K_a ≈ \frac{x^2}{0.591} \]
4. **Solve for \( x \) (which is [H₃O⁺] or [H⁺]):**
\[ x^2 ≈ 0.591 \cdot 3.50×10^{-8} \]
\[ x^2 ≈ 2.07×10^{-8} \]
\[ x ≈ \sqrt{2.07×10^{-8}} \]
\[ x ≈ 1.44×10^{-4} \]
Therefore:
\[ \text{[H}_3\text{O}^+\text{]} ≈ 1.44×10^{-4} \text{ M} \
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