A student needs to prepare a buffer solution with a pH of 5.83. Assuming a pKą of 4.76, how many mL of 0.1 M B- would need to be added to 20.0 mL of 0.1 M HB prepare this buffer? Please include a proper (abbreviated) unit.
A student needs to prepare a buffer solution with a pH of 5.83. Assuming a pKą of 4.76, how many mL of 0.1 M B- would need to be added to 20.0 mL of 0.1 M HB prepare this buffer? Please include a proper (abbreviated) unit.
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
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![### Buffer Solution Preparation Problem
**Problem Statement:**
A student needs to prepare a buffer solution with a pH of 5.83. Assuming a pKₐ of 4.76, how many mL of 0.1 M B⁻ would need to be added to 20.0 mL of 0.1 M HB to prepare this buffer?
**Instructions:**
Please include a proper (abbreviated) unit.
**Hint:** Use the Henderson-Hasselbalch equation:
\[ \text{pH} = \text{p}K_{a} + \log \left( \frac{[\text{B}^{-}]}{[\text{HB}]} \right) \]
or, if concentrations are the same,
\[ \text{pH} = \text{p}K_{a} + \log \left( \frac{\text{Volume of B}^{-}}{\text{Volume of HB}} \right) \]
### Detailed Explanation:
To solve this problem, you need to use the Henderson-Hasselbalch equation as summarized in the hint. The equation relates the pH of a buffer solution to the pKₐ (acid dissociation constant) and the ratio of the concentrations (or volumes when concentrations are the same) of the conjugate base (B⁻) and the weak acid (HB).
To find the volume of B⁻ needed, follow these steps:
1. **Set up the equation using given values:**
\[ 5.83 = 4.76 + \log \left( \frac{\text{Volume of B}^{-}}{20.0 \text{ mL}} \right) \]
2. **Isolate the logarithmic part of the equation:**
\[ 5.83 - 4.76 = \log \left( \frac{\text{Volume of B}^{-}}{20.0 \text{ mL}} \right) \]
\[ 1.07 = \log \left( \frac{\text{Volume of B}^{-}}{20.0 \text{ mL}} \right) \]
3. **Exponentiate both sides to remove the logarithm:**
\[ 10^{1.07} = \frac{\text{Volume of B}^{-}}{20.0 \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c8d8a42-8de4-4466-9c46-ae253053e314%2F2f8b9fad-ac29-4dcf-9cac-9a6eb4b92a35%2Fvq1z8u.png&w=3840&q=75)
Transcribed Image Text:### Buffer Solution Preparation Problem
**Problem Statement:**
A student needs to prepare a buffer solution with a pH of 5.83. Assuming a pKₐ of 4.76, how many mL of 0.1 M B⁻ would need to be added to 20.0 mL of 0.1 M HB to prepare this buffer?
**Instructions:**
Please include a proper (abbreviated) unit.
**Hint:** Use the Henderson-Hasselbalch equation:
\[ \text{pH} = \text{p}K_{a} + \log \left( \frac{[\text{B}^{-}]}{[\text{HB}]} \right) \]
or, if concentrations are the same,
\[ \text{pH} = \text{p}K_{a} + \log \left( \frac{\text{Volume of B}^{-}}{\text{Volume of HB}} \right) \]
### Detailed Explanation:
To solve this problem, you need to use the Henderson-Hasselbalch equation as summarized in the hint. The equation relates the pH of a buffer solution to the pKₐ (acid dissociation constant) and the ratio of the concentrations (or volumes when concentrations are the same) of the conjugate base (B⁻) and the weak acid (HB).
To find the volume of B⁻ needed, follow these steps:
1. **Set up the equation using given values:**
\[ 5.83 = 4.76 + \log \left( \frac{\text{Volume of B}^{-}}{20.0 \text{ mL}} \right) \]
2. **Isolate the logarithmic part of the equation:**
\[ 5.83 - 4.76 = \log \left( \frac{\text{Volume of B}^{-}}{20.0 \text{ mL}} \right) \]
\[ 1.07 = \log \left( \frac{\text{Volume of B}^{-}}{20.0 \text{ mL}} \right) \]
3. **Exponentiate both sides to remove the logarithm:**
\[ 10^{1.07} = \frac{\text{Volume of B}^{-}}{20.0 \
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