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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![**Question:**
Determine the pH of a 0.461 M C₆H₅CO₂H solution if the Kₐ of C₆H₅CO₂H is 6.5 × 10⁻⁵.
**Options:**
- ○ 4.52
- ○ 11.74
- ○ 9.48
- ○ 2.26
- ○ 5.48
*Explanation:*
To solve for the pH of the solution, use the formula for calculating pH from the equilibrium constant (Kₐ) and the concentration of the acid (C₆H₅CO₂H).
1. Write the ionization equilibrium expression for the acid:
\[
\text{C₆H₅CO₂H} \rightleftharpoons \text{C₆H₅CO₂⁻} + \text{H⁺}
\]
2. Set up the expression for the acid dissociation constant (\(Kₐ\)):
\[
Kₐ = \frac{[\text{C₆H₅CO₂⁻}][\text{H⁺}]}{[\text{C₆H₅CO₂H}]}
\]
3. Assume \(x\) is the amount dissociated at equilibrium, then:
\[
Kₐ = \frac{x \cdot x}{0.461 - x} \approx \frac{x^2}{0.461}
\]
4. Solve for \(x\) using the given \(Kₐ\):
\[
x^2 = 6.5 \times 10^{-5} \cdot 0.461
\]
\[
x = \sqrt{(6.5 \times 10^{-5}) \cdot 0.461}
\]
5. Calculate the pH:
\[
\text{pH} = -\log[\text{H⁺}] = -\log(x)
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c6de790-3967-4822-b83d-f877aa472903%2F662caac8-edee-4a74-a8a7-707af4f7e523%2Fttxncsc_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
Determine the pH of a 0.461 M C₆H₅CO₂H solution if the Kₐ of C₆H₅CO₂H is 6.5 × 10⁻⁵.
**Options:**
- ○ 4.52
- ○ 11.74
- ○ 9.48
- ○ 2.26
- ○ 5.48
*Explanation:*
To solve for the pH of the solution, use the formula for calculating pH from the equilibrium constant (Kₐ) and the concentration of the acid (C₆H₅CO₂H).
1. Write the ionization equilibrium expression for the acid:
\[
\text{C₆H₅CO₂H} \rightleftharpoons \text{C₆H₅CO₂⁻} + \text{H⁺}
\]
2. Set up the expression for the acid dissociation constant (\(Kₐ\)):
\[
Kₐ = \frac{[\text{C₆H₅CO₂⁻}][\text{H⁺}]}{[\text{C₆H₅CO₂H}]}
\]
3. Assume \(x\) is the amount dissociated at equilibrium, then:
\[
Kₐ = \frac{x \cdot x}{0.461 - x} \approx \frac{x^2}{0.461}
\]
4. Solve for \(x\) using the given \(Kₐ\):
\[
x^2 = 6.5 \times 10^{-5} \cdot 0.461
\]
\[
x = \sqrt{(6.5 \times 10^{-5}) \cdot 0.461}
\]
5. Calculate the pH:
\[
\text{pH} = -\log[\text{H⁺}] = -\log(x)
\]
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