Answer:
pH at equivalence point is 8.47
Explanation:
Benzoic acid react with NaOH, thus:
HC₇H₅O₂ + NaOH → C₇H₅O₂⁻ + H₂O + Na⁺
You reach equivalence point when moles of the acid = moles of NaOH.
Moles of benzoic acid are:
0.025L ₓ (0.0988mol / L) = 0.00247 moles
To have 0.00247 moles of NaOH in solution and reach equivalence point you need to add:
0.00247 moles NaOH ₓ (1L / 0.115mol) = 0.0215L of NaOH solution.
Total volume is 0.0465L.
There are produced 0.00247 moles of C₇H₅O₂⁻ and its molarity will be:
0.00247 mol C₇H₅O₂⁻ / 0.0465L = <em>0.0531M C₇H₅O₂⁻ </em>
C₇H₅O₂⁻ is in equilibrium with water, thus:
C₇H₅O₂⁻(aq) + H₂O ⇄ HC₇H₅O₂(aq) + OH⁻(aq)
<em>Where Kb = Kw / Ka = 1x10⁻¹⁴ / 6.5x10⁻⁵ = 1.54x10⁻¹⁰ is:</em>
<em>Kb = 1.54x10⁻¹⁰ = [HC₇H₅O₂] [OH⁻] / [C₇H₅O₂⁻]</em>
The concentrations in equilibrium of the species are:
[HC₇H₅O₂] = X
[OH⁻] = X
[C₇H₅O₂⁻] = 0.0531M - X
<em>Where X represents how much C₇H₅O₂⁻ react, X is reaction coordinate</em>
Replacing in Kb expression:
1.54x10⁻¹⁰ = [HC₇H₅O₂] [OH⁻] / [C₇H₅O₂⁻]
1.54x10⁻¹⁰ = [X] [X] / [0.0531 - X]
8.169x10⁻¹² - 1.54x10⁻¹⁰X = X²
8.169x10⁻¹² - 1.54x10⁻¹⁰X - X² = 0
Solving for X:
X = -2.858x10⁻⁶M → False solution, there is no negative concentrations
X = 2.858x10⁻⁶M → Right solution
As [OH⁻] = X
[OH⁻] = 2.858x10⁻⁶M
pOH is -log [OH⁻]
pOH = 5.54
pH = 14 - pOH
pH = 8.46
<h3>pH at equivalence point is 8.47</h3>
