Suppose you performed a titration of a weak acid and you found that the equivalence point occurred at 19.19 mL of added NaOH. At what volume would you use the pH to determine the pKa of the acid?

Volume at half equivalence point, that is 19.19 mL/2 = 9.595 mL.

Explanation:

From the question we are asked to find the volume that would one can use the pH to determine the pKa of the acid and the answer will be the volume at half equivalence point.

At half equivalence point, the weak acid and the conjugate base will have the same number of moles because the number of moles of sodium Hydroxide, NaOH will neutralize half of the number of moles of the weak acid which in turn will produce more conjugate base. And this concept is what is known as the buffer solution.

HA <> H^+ + A^-

(Note: the reaction above is a reversible reaction. Also, the concentration of HA is equal to the concentration of A^-).

Therefore, we can calculate our pka from the equation below(assuming the pH is given).

pH= pka + log ( [A^-] / log [HA].

===> At half equivalence point pH= pKa.

Recall that, pka = - log ka.

Then, ka = 10^-pka.

Where pH= pKa.

Therefore, ka = 10^-pH.