What is the pH of a 0.25 M NH3 solution? Kb 1.8 x 10-5 = pH = [?] pH Enter

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...
icon
Related questions
icon
Concept explainers
Question
### Calculating the pH of a 0.25 M NH₃ Solution

**Problem Statement:**  
What is the pH of a 0.25 M NH₃ solution?  
Given that \( K_b = 1.8 \times 10^{-5} \).

**Solution:**

To calculate the pH of an ammonia (NH₃) solution, follow these steps:

1. **Calculate \( [OH⁻] \):**
   Use the equilibrium expression for ammonia dissociation in water:

   \[ NH₃(aq) + H₂O(l) \rightleftharpoons NH₄⁺(aq) + OH⁻(aq) \]

   The \( K_b \) expression is:

   \[ K_b = \frac{[NH₄⁺][OH⁻]}{[NH₃]} \]

   For this solution:

   \[ 1.8 \times 10^{-5} = \frac{x^2}{0.25 - x} \]

   Where \( x \) represents the concentration of \( OH⁻ \) ions.

2. **Approximate \( x \) for Small \( K_b \):**
   Since \( K_b \) is small, assume \( x \) is much less than 0.25:

   \[ 1.8 \times 10^{-5} \approx \frac{x^2}{0.25} \]

   \[ x^2 = 1.8 \times 10^{-5} \times 0.25 \]

   \[ x^2 = 4.5 \times 10^{-6} \]

   \[ x = \sqrt{4.5 \times 10^{-6}} \]

   \[ x \approx 2.12 \times 10^{-3} \]

   Thus, \( [OH⁻] \approx 2.12 \times 10^{-3} \) M.

3. **Find \( pOH \):**
   
   \[ pOH = -\log[OH⁻] \]

   \[ pOH = -\log(2.12 \times 10^{-3}) \]

   \[ pOH \approx 2.67 \]

4. **Calculate pH:**
   
   Using the relation between pH and pOH:

   \
Transcribed Image Text:### Calculating the pH of a 0.25 M NH₃ Solution **Problem Statement:** What is the pH of a 0.25 M NH₃ solution? Given that \( K_b = 1.8 \times 10^{-5} \). **Solution:** To calculate the pH of an ammonia (NH₃) solution, follow these steps: 1. **Calculate \( [OH⁻] \):** Use the equilibrium expression for ammonia dissociation in water: \[ NH₃(aq) + H₂O(l) \rightleftharpoons NH₄⁺(aq) + OH⁻(aq) \] The \( K_b \) expression is: \[ K_b = \frac{[NH₄⁺][OH⁻]}{[NH₃]} \] For this solution: \[ 1.8 \times 10^{-5} = \frac{x^2}{0.25 - x} \] Where \( x \) represents the concentration of \( OH⁻ \) ions. 2. **Approximate \( x \) for Small \( K_b \):** Since \( K_b \) is small, assume \( x \) is much less than 0.25: \[ 1.8 \times 10^{-5} \approx \frac{x^2}{0.25} \] \[ x^2 = 1.8 \times 10^{-5} \times 0.25 \] \[ x^2 = 4.5 \times 10^{-6} \] \[ x = \sqrt{4.5 \times 10^{-6}} \] \[ x \approx 2.12 \times 10^{-3} \] Thus, \( [OH⁻] \approx 2.12 \times 10^{-3} \) M. 3. **Find \( pOH \):** \[ pOH = -\log[OH⁻] \] \[ pOH = -\log(2.12 \times 10^{-3}) \] \[ pOH \approx 2.67 \] 4. **Calculate pH:** Using the relation between pH and pOH: \
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

Blurred answer
Knowledge Booster
Ionic Equilibrium
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Chemistry
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Chemistry
Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education
Principles of Instrumental Analysis
Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning
Organic Chemistry
Organic Chemistry
Chemistry
ISBN:
9780078021558
Author:
Janice Gorzynski Smith Dr.
Publisher:
McGraw-Hill Education
Chemistry: Principles and Reactions
Chemistry: Principles and Reactions
Chemistry
ISBN:
9781305079373
Author:
William L. Masterton, Cecile N. Hurley
Publisher:
Cengage Learning
Elementary Principles of Chemical Processes, Bind…
Elementary Principles of Chemical Processes, Bind…
Chemistry
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY