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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![### Determining the pH of a Solution
**Problem Statement:**
What is the pH of a 0.40 M solution of NH₄NO₃ (aq)?
**Given Value:**
- \( K_b \) for \( \text{NH}_3 (\text{aq}) = 1.76 \times 10^{-5} \)
**Explanation:**
To find the pH of a solution of ammonium nitrate (\( \text{NH}_4\text{NO}_3 \)), which is a salt of a weak base \( \text{NH}_3 \) and a strong acid \( \text{HNO}_3 \), you need to consider the hydrolysis of \( \text{NH}_4^+ \).
This involves calculating \( K_a \) using the relation:
\[ K_w = K_a \times K_b \]
where \( K_w = 1.0 \times 10^{-14} \) at 25°C.
**Steps:**
1. Calculate \( K_a \) using:
\[ K_a = \frac{K_w}{K_b} \]
2. Set up the equation for the hydrolysis of \( \text{NH}_4^+ \):
\[ \text{NH}_4^+ (aq) + \text{H}_2\text{O} (l) \rightleftharpoons \text{NH}_3 (aq) + \text{H}_3\text{O}^+ (aq) \]
3. Use the equilibrium expression:
\[ K_a = \frac{[\text{NH}_3][\text{H}_3\text{O}^+]}{[\text{NH}_4^+]} \]
4. Calculate the concentration of \( \text{H}_3\text{O}^+ \) and find the pH:
\[ \text{pH} = -\log([\text{H}_3\text{O}^+]) \]
This procedure helps in understanding the ionization process in a salt solution and determining the pH effectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fedbef1-4110-4bb3-9906-fd5663476380%2F22cbf570-d4b9-49b1-9194-915c76fd4334%2F2zex7ia_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining the pH of a Solution
**Problem Statement:**
What is the pH of a 0.40 M solution of NH₄NO₃ (aq)?
**Given Value:**
- \( K_b \) for \( \text{NH}_3 (\text{aq}) = 1.76 \times 10^{-5} \)
**Explanation:**
To find the pH of a solution of ammonium nitrate (\( \text{NH}_4\text{NO}_3 \)), which is a salt of a weak base \( \text{NH}_3 \) and a strong acid \( \text{HNO}_3 \), you need to consider the hydrolysis of \( \text{NH}_4^+ \).
This involves calculating \( K_a \) using the relation:
\[ K_w = K_a \times K_b \]
where \( K_w = 1.0 \times 10^{-14} \) at 25°C.
**Steps:**
1. Calculate \( K_a \) using:
\[ K_a = \frac{K_w}{K_b} \]
2. Set up the equation for the hydrolysis of \( \text{NH}_4^+ \):
\[ \text{NH}_4^+ (aq) + \text{H}_2\text{O} (l) \rightleftharpoons \text{NH}_3 (aq) + \text{H}_3\text{O}^+ (aq) \]
3. Use the equilibrium expression:
\[ K_a = \frac{[\text{NH}_3][\text{H}_3\text{O}^+]}{[\text{NH}_4^+]} \]
4. Calculate the concentration of \( \text{H}_3\text{O}^+ \) and find the pH:
\[ \text{pH} = -\log([\text{H}_3\text{O}^+]) \]
This procedure helps in understanding the ionization process in a salt solution and determining the pH effectively.
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