What is the ratio of [A-]/[HA] at pH 3.75? The pKa of formic acid (methanoic acid. H-COOH) is 3.75.
The Correct Answer and Explanation is :
To calculate the ratio ([A^-]/[HA]) at pH 3.75, where formic acid (HCOOH) has a pKa of 3.75, we can use the Henderson-Hasselbalch equation. This equation relates the pH of a buffer solution to the concentrations of its acidic and conjugate base forms:
[
\text{pH} = \text{pKa} + \log \left( \frac{[A^-]}{[HA]} \right)
]
Where:
- ([A^-]) is the concentration of the conjugate base (formate ion, HCOO⁻),
- ([HA]) is the concentration of the weak acid (formic acid, HCOOH),
- pKa is the dissociation constant of the acid (3.75),
- pH is the pH of the solution (3.75 in this case).
Step-by-Step Calculation:
- Substitute the given values into the Henderson-Hasselbalch equation:
[
\text{pH} = \text{pKa} + \log \left( \frac{[A^-]}{[HA]} \right)
]
[
3.75 = 3.75 + \log \left( \frac{[A^-]}{[HA]} \right)
] - Simplify the equation:
[
0 = \log \left( \frac{[A^-]}{[HA]} \right)
] - Solve for the ratio:
Since (\log \left( \frac{[A^-]}{[HA]} \right) = 0), we know that:
[
\frac{[A^-]}{[HA]} = 10^0 = 1
]
Interpretation:
The ratio ([A^-]/[HA]) is 1 when the pH of the solution equals the pKa of the acid. This indicates that, at pH 3.75, the concentrations of the weak acid (HCOOH) and its conjugate base (HCOO⁻) are equal. In other words, half of the formic acid molecules are dissociated into formate ions, and the other half remain undissociated as formic acid.
This situation is common in buffer solutions, where the pH is near the pKa of the acid, and the acid/base pair is most effective at resisting changes in pH.