(Chemistry) Ka of unknown acid by titrations.

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To determine the Ka of an unknown weak acid, a titration with NaOH was performed, requiring 7.37mL for a complete titration, with a half-titration volume of 3.69mL. The pH of the solution was measured at 4.7, leading to the conclusion that at half-titration, pH equals pKa. Using the formula Ka = 10^-pH, the calculated value for Ka is 2.0 x 10^-5. However, there is uncertainty regarding the concentrations of the acid and its conjugate base, which complicates further calculations. The discussion highlights the need for additional information to accurately determine Ka using the concentrations of [HA] and [A-].
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Homework Statement


Let's say that i have a unknown weak acid.
  • I prepare 10mL of the weak acid diluted in 25mL of water.
  • I titrate the solution with NaOH. 7.37mL of NaOH was needed for a full titration.
  • Therefore, half-titration of this acid was 3.69mL.
  • I measure the pH of the solution with a pH-meter and the pH was 4.7.

I want to find the Ka of the unknown acid.

Homework Equations


Henderson-Hasselbalch pH formula for a buffer solution is:
pH = pKa + log([base] / [acid])

The Attempt at a Solution


Since the weak acid is monoprotic, the half titration of the solution gives an equal concentration of both acid and conjugate base.

pH = pKa + log(1) = pKa

Does it mean that Ka is the concentration of [H+]?
Ka = 10^-pH = 10^-4.7 = 2.0 e-5?

Edit: Is it possible to calculate in a different way using the given data above?
Ka = [H+][A-]/[HA]
I can calculate the concentration of [H+] from the pH but i don't know the initial concentration of [HA]. And what about the concentration of [A-] ion?
 
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