the pKa of the weak acid is approximately 5.82.
To determine the pKa of a weak acid, you need to know the concentration of the acid and its conjugate base at equilibrium.
In this case, since the weak acid is 91% neutralized, it means that 91% of the acid has dissociated to form its conjugate base. Therefore, the concentration of the conjugate base ([A-]) is 91% of the initial concentration of the acid ([HA]).
Now, let's assume the initial concentration of the acid is 1 mole. Since 91% of the acid has dissociated, the concentration of the conjugate base is 0.91 moles.
The equation for the dissociation of the weak acid can be written as follows:
HA ⇌ H+ + A-
Using the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
We know that at pH 5.7, the weak acid is 91% neutralized, so [A-]/[HA] = 0.91.
Therefore:
5.7 = pKa + log(0.91)
Rearranging the equation:
pKa = 5.7 - log(0.91)
Using a calculator, we find:
pKa ≈ 5.82