Answer:
Determine the pH of the solution half-way to the end-point on the pH titration curve for acetic acid.
Explanation:
The equation for the ionization of acetic acid is
HA + H₂O ⇌ H₃O⁺ + A⁻
For points between the starting and equivalence points, the pH is given by the Henderson-Hasselbalch equation:
[tex]\text{pH} = \text{pK}_{\text{a}} + \log\dfrac{[\text{A}^{-}]}{\text{[HA]}}[/tex]
At the half-way point, half of the HA has been converted to A⁻, so [HA] = [A⁻]. Then,
[tex]\text{pH} = \text{pK}_{\text{a}} + \log\dfrac{1}{1} = \text{pK}_{\text{a}} + 0 \\\\\text{pH} = \text{pK}_{\text{a}}[/tex]
The pKₐ is the pH at the half-way point in the titration.
