Answer:
pH = 9.26
Explanation:
Let's make the reaction of this weak base:
C₅H₅N + H₂O ⇄ C₅H₅NH⁺ + OH⁻ Kb
We do not know the Kb, but we can discover it from pKb
Kb = 10^⁻pKb → 10⁻⁸'⁷⁷ = 1.70×10⁻⁹
So, let's make the expression for Kb
Kb = [OH⁻] . [C₅H₅NH⁺] / [C₅H₅N]
In the equilibrum, we would have 0.20 moles from the begining - x (react)
So we would proudce x moles of OH⁻ and x moles of C₅H₅NH⁺.
In conclussion:
1.70×10⁻⁹ = x . x / (0.20 - x)
To avoid the quadratic formula we can miss the x from the substraction
1.70×10⁻⁹ = x² / 0.20
1.70×10⁻⁹ . 0.20 = x²
We avoid the x from the (0.20-x), because the base is so concentrated, and Kb is very small.
x = √(1.70×10⁻⁹ . 0.20) → 1.84×10⁻⁵
That's the value of [OH⁻], so we can calculate pOH
- log [OH⁻] = pOH → - log 1.84×10⁻⁵ = 4.73
Then pH = 14 - pOH
14 - 4.73 = 9.26
