A buffer solution at pH 10 has a ratio of ([A−][HA]) of 10. What is the pKa of the acid?
A. 8
B. 9
C. 10
D. 11
E. 12
The Correct Answer and Explanation is:
To find the pKa of the acid in a buffer solution at pH 10 with a given ratio of (\frac{[A^-]}{[HA]} = 10), we can again use the Henderson-Hasselbalch equation, which is expressed as follows:
[
\text{pH} = \text{pKa} + \log\left(\frac{[A^-]}{[HA]}\right)
]
In this case, we are given:
- pH = 10
- (\frac{[A^-]}{[HA]} = 10)
This means that the concentration of the conjugate base ((A^-)) is ten times that of the weak acid ((HA)), which can be expressed mathematically as:
[
[A^-] = 10 \times [HA]
]
Using this ratio, we can substitute it into the equation. First, we can find the logarithm:
[
\log\left(\frac{[A^-]}{[HA]}\right) = \log(10) = 1
]
Now, substituting the values into the Henderson-Hasselbalch equation gives us:
[
10 = \text{pKa} + 1
]
To isolate pKa, we rearrange the equation:
[
\text{pKa} = 10 – 1 = 9
]
Therefore, the pKa of the acid is 9. The correct answer is B. 9.
Explanation
Buffer solutions are essential for maintaining a stable pH in various chemical and biological systems. The Henderson-Hasselbalch equation is fundamental in this context, as it relates the pH of the solution to the ratio of the concentrations of the acid and its conjugate base. The derived pKa provides insight into the strength of the weak acid: a lower pKa indicates a stronger acid, while a higher pKa indicates a weaker acid.
In this scenario, a buffer solution at pH 10, with the acid and conjugate base ratio resulting in a pKa of 9, suggests that the acid in question has a significant ability to resist changes in pH when small amounts of acid or base are added. Understanding these relationships is crucial in fields such as biochemistry, pharmacology, and environmental science, where maintaining specific pH levels is vital for proper functioning.