Citric acid has three pKa values: 3.2,4.8,6.4. What are ratios of the coniuaate base to acid components of this buffer solution at a pH of 6.4 ? A. Conjugate base to acid ratio is 1:1 B. Conjugate base to acid ratio is 1.66:1 C. Conjugate base to acid ratio is 1:10 D. Conjugate base to acid ratio is 10:1
The Correct Answer and Explanation is :
At a pH of 6.4, we are dealing with the second dissociation step of citric acid. Citric acid has three pKa values: 3.2, 4.8, and 6.4. Each of these corresponds to the dissociation of different hydrogen ions from the citric acid molecule.
To calculate the ratio of the conjugate base to acid components at a specific pH, we can use the Henderson-Hasselbalch equation:
[
\text{pH} = \text{pKa} + \log \left( \frac{\text{[A]}}{\text{[HA]}} \right)
]
Where:
- pKa is the dissociation constant for the acid,
- [A] is the concentration of the conjugate base,
- [HA] is the concentration of the acid.
At pH 6.4, we are concerned with the second dissociation of citric acid, which occurs around pKa 6.4. For this step, the acid form (HA) is H2C6H5O7 (the protonated form of citric acid), and the conjugate base form (A) is HC6H5O7²⁻ (the deprotonated form).
Given that the pH is equal to the pKa (pH = pKa = 6.4), the concentrations of the acid and conjugate base will be equal. Thus, the ratio of the conjugate base to acid is 1:1.
Using the Henderson-Hasselbalch equation for this scenario:
[
\text{pH} = \text{pKa} + \log \left( \frac{\text{[A]}}{\text{[HA]}} \right)
]
Substitute pH = 6.4 and pKa = 6.4:
[
6.4 = 6.4 + \log \left( \frac{\text{[A]}}{\text{[HA]}} \right)
]
[
0 = \log \left( \frac{\text{[A]}}{\text{[HA]}} \right)
]
[
\frac{\text{[A]}}{\text{[HA]}} = 1
]
Therefore, the correct answer is:
A. Conjugate base to acid ratio is 1:1.
Explanation:
- The pH of 6.4 corresponds to the second dissociation step of citric acid.
- At pH = pKa (6.4), the acid and conjugate base are present in equal concentrations.
- This results in a ratio of 1:1 for conjugate base to acid.