Use the Henderson–Hasselbalch equation to calculate the pKa of the acid.
The correct answer and explanation is:
Okay, to use the Henderson-Hasselbalch equation to calculate the pKa, we need values for the pH of a solution containing the acid and its conjugate base, as well as the concentrations of the acid and its conjugate base. Since no specific values were provided in the prompt, I will create a common scenario using typical concentrations to demonstrate the calculation.
Scenario: Assume we have a buffer solution prepared from a weak acid (HA) and its conjugate base (A⁻). We measure the pH of this solution to be 4.50. We also know the concentration of the weak acid [HA] in the solution is 0.10 M, and the concentration of the conjugate base [A⁻] is 0.20 M.
Correct Answer (Calculated pKa):
Using the values from the scenario:
pH = 4.50
[HA] = 0.10 M
[A⁻] = 0.20 M
The Henderson-Hasselbalch equation is:
pH = pKa + log ([A⁻] / [HA])
To find pKa, we rearrange the equation:
pKa = pH – log ([A⁻] / [HA])
Substitute the values:
pKa = 4.50 – log (0.20 M / 0.10 M)
pKa = 4.50 – log (2.0)
pKa ≈ 4.50 – 0.301
pKa ≈ 4.199
Rounding to two decimal places, the calculated pKa is approximately 4.20.
Explanation (Approximately 300 words):
The Henderson-Hasselbalch equation is a fundamental relationship in chemistry used to calculate the pH of a buffer solution or, as requested here, to determine the pKa of a weak acid. The equation is expressed as:
pH = pKa + log ([A⁻] / [HA])
Here, pH represents the measured acidity of the solution, pKa is the negative logarithm of the acid dissociation constant (Ka) which is a characteristic property of the specific acid, [A⁻] is the molar concentration of the conjugate base, and [HA] is the molar concentration of the weak acid.
To calculate the pKa of an acid using this equation, we must rearrange it to isolate pKa:
pKa = pH – log ([A⁻] / [HA])
This rearrangement shows that if we know the pH of a solution containing a significant amount of both the weak acid and its conjugate base (i.e., a buffer solution), and we know their respective molar concentrations, we can directly calculate the pKa.
Consider the scenario above: we had a solution with a measured pH of 4.50, an acid concentration [HA] of 0.10 M, and a conjugate base concentration [A⁻] of 0.20 M. By plugging these values into the rearranged Henderson-Hasselbalch equation:
pKa = 4.50 – log (0.20 / 0.10)
pKa = 4.50 – log (2.0)
Calculating the logarithm of 2.0 gives approximately 0.301. Subtracting this from the pH:
pKa = 4.50 – 0.301 ≈ 4.199
Therefore, based on these measurements, the calculated pKa of the acid is approximately 4.20. The pKa value is a constant specific to the acid at a given temperature and provides a quantitative measure of its strength – a lower pKa indicates a stronger acid. The Henderson-Hasselbalch equation is most accurate when used in the buffer region where the ratio of [A⁻]/[HA] is close to 1, and the concentrations are not extremely dilute or concentrated.