How many moles of CH3NH;CI need to be added to 200.0 mL of a 0.500 M solution of CH3NH2 (Kb for CH3NH2 is 4.4 × 10-4) to make a buffer with a pH of 10.00?
How many moles of CH3NH;CI need to be added to 200.0 mL of a 0.500 M solution of CH3NH2 (Kb for CH3NH2 is 4.4 × 10-4) to make a buffer with a pH of 10.00?
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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![**Buffer Calculation Problem**
**Question:**
How many moles of CH₃NH₃Cl need to be added to 200.0 mL of a 0.500 M solution of CH₃NH₂ (Kb for CH₃NH₂ is 4.4 × 10⁻⁴) to make a buffer with a pH of 10.00?
**Solution Approach:**
1. **Identify Components:**
- Weak base: CH₃NH₂
- Conjugate acid: CH₃NH₃Cl
- Desired pH = 10.00
- Kb of CH₃NH₂ = 4.4 × 10⁻⁴
2. **Calculate pKa:**
- Use the relation \( pK_a + pK_b = 14 \) to find pKa.
- Calculate pKa from Kb:
\[
pK_a = 14 - (-\log_{10} (4.4 \times 10^{-4}))
\]
3. **Use Henderson-Hasselbalch Equation:**
- \( pH = pK_a + \log \left(\frac{[base]}{[acid]}\right) \)
4. **Solve for [acid]:**
- Rearrange the equation to solve for the concentration of the acid needed.
5. **Calculate Moles of CH₃NH₃Cl:**
- Convert the required concentration to moles using the volume of the solution.
This problem requires understanding of buffer systems and the Henderson-Hasselbalch equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b31c76d-31c3-4f02-9c7e-c3848d4eba7b%2Fcaccecb3-0a84-4222-aa54-b264d2797fa1%2Fdkj94p0e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Buffer Calculation Problem**
**Question:**
How many moles of CH₃NH₃Cl need to be added to 200.0 mL of a 0.500 M solution of CH₃NH₂ (Kb for CH₃NH₂ is 4.4 × 10⁻⁴) to make a buffer with a pH of 10.00?
**Solution Approach:**
1. **Identify Components:**
- Weak base: CH₃NH₂
- Conjugate acid: CH₃NH₃Cl
- Desired pH = 10.00
- Kb of CH₃NH₂ = 4.4 × 10⁻⁴
2. **Calculate pKa:**
- Use the relation \( pK_a + pK_b = 14 \) to find pKa.
- Calculate pKa from Kb:
\[
pK_a = 14 - (-\log_{10} (4.4 \times 10^{-4}))
\]
3. **Use Henderson-Hasselbalch Equation:**
- \( pH = pK_a + \log \left(\frac{[base]}{[acid]}\right) \)
4. **Solve for [acid]:**
- Rearrange the equation to solve for the concentration of the acid needed.
5. **Calculate Moles of CH₃NH₃Cl:**
- Convert the required concentration to moles using the volume of the solution.
This problem requires understanding of buffer systems and the Henderson-Hasselbalch equation.
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