Answer:
pH = 8.92
Step-by-step explanation:
To solve this question we must know that the reaction of KOH with HC3H5O2 is:
KOH + HC3H5O2 → H2O + KC3H5O2
At equivalence point, all propanoic acid reacts to produce KC3H5O2.
This KC3H5O2 = C3H5O2⁻ is in equilibrium in water as follows:
C3H5O2⁻(aq) + H₂O(l) → OH⁻(aq) + HC3H5O2(aq)
Where Kb = Kw / ka = 1x10⁻¹⁴/ 1.34x10⁻⁵ = 7.46x10⁻¹⁰
is defined as:
Kb = 7.46x10⁻¹⁰ = [OH⁻] [HC3H5O2] / [C3H5O2⁻]
As both [OH⁻] [HC3H5O2] ions comes from the same equilibrium,
[OH⁻] = [HC3H5O2] = X
[C3H5O2⁻] is:
Moles KOH = Moles C3H5O2⁻:
0.0325L * (0.15mol / L) = 0.004875 moles
In 32.5 + 20mL = 52.5mL = 0.0525L:
0.004875 moles / 0.0525L = 0.09286M.
Replacing:
7.46x10⁻¹⁰ = [X] [X] / [0.09286M]
6.927x10⁻¹¹ = X²
X = 8.323x10⁻⁶M = [OH-]
As pOH = -log [OH-]
pOH = 5.08
pH = 14 -pOH
pH = 8.92