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:**
Calculate the pH after 0.010 mol of HCl is added to 250.0 mL of a 0.050 M NH₃/0.15 M NH₄Cl solution.
**Solution:**
The problem involves calculating the pH of a buffer solution containing ammonia (NH₃) and ammonium chloride (NH₄Cl) after the addition of hydrochloric acid (HCl).
1. **Understand the Buffer Solution:**
- The solution contains 0.050 M NH₃ and 0.15 M NH₄Cl.
- NH₃ acts as a weak base, and NH₄⁺ is its conjugate acid.
2. **Reaction with HCl:**
- When 0.010 mol of HCl is added, it reacts with NH₃.
- The reaction:
\[
\text{NH}_3 + \text{HCl} \rightarrow \text{NH}_4^+ + \text{Cl}^-
\]
- This increases the concentration of NH₄⁺.
3. **Use Henderson-Hasselbalch Equation:**
- The equation for buffer solutions:
\[
\text{pH} = \text{p}K_a + \log \left( \frac{[\text{base}]}{[\text{acid}]} \right)
\]
- Determine \([\text{base}] = [\text{NH}_3]\) and \([\text{acid}] = [\text{NH}_4^+]\).
4. **Calculate New Concentrations:**
- Initial moles of NH₃ = 0.050 M × 0.250 L = 0.0125 mol.
- Initial moles of NH₄Cl = 0.15 M × 0.250 L = 0.0375 mol.
- After the reaction with HCl, moles of NH₄⁺ become 0.0475 mol (0.0375 + 0.010) and moles of NH₃ become 0.0025 mol (0.0125 - 0.010).
5. **Calculate pH:**
- Substitute values into the Henderson-Hasselbalch equation to find the pH of the resulting solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85a2fef8-75c6-4f70-afce-e76c8de2cc0b%2F93c0963b-123b-4830-ab60-9990175d16c7%2Fkz4ecs_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Calculate the pH after 0.010 mol of HCl is added to 250.0 mL of a 0.050 M NH₃/0.15 M NH₄Cl solution.
**Solution:**
The problem involves calculating the pH of a buffer solution containing ammonia (NH₃) and ammonium chloride (NH₄Cl) after the addition of hydrochloric acid (HCl).
1. **Understand the Buffer Solution:**
- The solution contains 0.050 M NH₃ and 0.15 M NH₄Cl.
- NH₃ acts as a weak base, and NH₄⁺ is its conjugate acid.
2. **Reaction with HCl:**
- When 0.010 mol of HCl is added, it reacts with NH₃.
- The reaction:
\[
\text{NH}_3 + \text{HCl} \rightarrow \text{NH}_4^+ + \text{Cl}^-
\]
- This increases the concentration of NH₄⁺.
3. **Use Henderson-Hasselbalch Equation:**
- The equation for buffer solutions:
\[
\text{pH} = \text{p}K_a + \log \left( \frac{[\text{base}]}{[\text{acid}]} \right)
\]
- Determine \([\text{base}] = [\text{NH}_3]\) and \([\text{acid}] = [\text{NH}_4^+]\).
4. **Calculate New Concentrations:**
- Initial moles of NH₃ = 0.050 M × 0.250 L = 0.0125 mol.
- Initial moles of NH₄Cl = 0.15 M × 0.250 L = 0.0375 mol.
- After the reaction with HCl, moles of NH₄⁺ become 0.0475 mol (0.0375 + 0.010) and moles of NH₃ become 0.0025 mol (0.0125 - 0.010).
5. **Calculate pH:**
- Substitute values into the Henderson-Hasselbalch equation to find the pH of the resulting solution.
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