Answer:
pH at the equivalence point is 8.6
Explanation:
A titulation between a weak acid and a strong base, gives a basic pH at the equivalence point. In the equivalence point, we need to know the volume of base we added, so:
mmoles acid = mmoles of base
60 mL . 0.1935M = 0.2088 M . volume
(60 mL . 0.1935M) /0.2088 M = 55.6 mL of KOH
The neutralization is:
HBz + KOH ⇄ KBz + H₂O
In the equilibrum:
HBz + OH⁻ ⇄ Bz⁻ + H₂O
mmoles of acid are: 11.61 and mmoles of base are: 11.61
So in the equilibrium we have, 11.61 mmoles of benzoate.
[Bz⁻] = 11.61 mmoles / (volume acid + volume base)
[Bz⁻] = 11.61 mmoles / 60 mL + 55.6 mL = 0.100 M
The conjugate strong base reacts:
Bz⁻ + H₂O ⇄ HBz + OH⁻ Kb
0.1 - x x x
(We don't have pKb, but we can calculate it from pKa)
14 - 4.2 = 9.80 → pKb → 10⁻⁹'⁸ = 1.58×10⁻¹⁰ → Kb
Kb = [HBz] . [OH⁻] / [Bz⁻]
Kb = x² / (0.1 - x)
As Kb is so small, we can avoid the quadratic equation
Kb = x² / 0.1 → Kb . 0.1 = x²
√ 1.58×10⁻¹¹ = [OH⁻] = 3.98 ×10⁻⁶ M
From this value, we calculate pOH and afterwards, pH (14 - pOH)
- log [OH⁻] = pOH → - log 3.98 ×10⁻⁶ = 5.4
pH = 8.6
