Chemistry
Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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**Question:**

Calculate the pH of a 0.10 M ammonia (NH₃) solution. The base dissociation constant (K_b) for ammonia is 1.8 x 10⁻⁵.

**Your Answer:**

*Input Box:* [                             ]

**Answer Explanation:**

To solve this problem, follow these steps:

1. Write the equilibrium expression for the dissociation of ammonia (NH₃):
   - NH₃ + H₂O ⇌ NH₄⁺ + OH⁻

2. Set up an expression for the base dissociation constant (K_b):
   - \( K_b = \frac{{[NH_4^+][OH^-]}}{{[NH_3]}} \)

3. Use the initial concentrations and change in concentration (x) to determine the equilibrium concentrations:
   - Initial: [NH₃] = 0.10 M, [NH₄⁺] = 0, [OH⁻] = 0
   - Change: [NH₃] = -x, [NH₄⁺] = +x, [OH⁻] = +x
   - Equilibrium: [NH₃] = 0.10 - x, [NH₄⁺] = x, [OH⁻] = x

4. Substitute the equilibrium concentrations back into the K_b expression:
   - \( 1.8 \times 10^{-5} = \frac{{x^2}}{{0.10 - x}} \)

5. Solve for x, which represents [OH⁻].

6. Calculate the pOH:
   - pOH = -log[OH⁻]

7. Finally, convert pOH to pH:
   - pH = 14 - pOH

This will provide the pH of the 0.10 M ammonia solution.
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Transcribed Image Text:**Question:** Calculate the pH of a 0.10 M ammonia (NH₃) solution. The base dissociation constant (K_b) for ammonia is 1.8 x 10⁻⁵. **Your Answer:** *Input Box:* [ ] **Answer Explanation:** To solve this problem, follow these steps: 1. Write the equilibrium expression for the dissociation of ammonia (NH₃): - NH₃ + H₂O ⇌ NH₄⁺ + OH⁻ 2. Set up an expression for the base dissociation constant (K_b): - \( K_b = \frac{{[NH_4^+][OH^-]}}{{[NH_3]}} \) 3. Use the initial concentrations and change in concentration (x) to determine the equilibrium concentrations: - Initial: [NH₃] = 0.10 M, [NH₄⁺] = 0, [OH⁻] = 0 - Change: [NH₃] = -x, [NH₄⁺] = +x, [OH⁻] = +x - Equilibrium: [NH₃] = 0.10 - x, [NH₄⁺] = x, [OH⁻] = x 4. Substitute the equilibrium concentrations back into the K_b expression: - \( 1.8 \times 10^{-5} = \frac{{x^2}}{{0.10 - x}} \) 5. Solve for x, which represents [OH⁻]. 6. Calculate the pOH: - pOH = -log[OH⁻] 7. Finally, convert pOH to pH: - pH = 14 - pOH This will provide the pH of the 0.10 M ammonia solution.
Expert Solution
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Step 1

Ammonia reacts with water and dissociates into ammonium ion hydroxide ions. 

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