Answer:
5.7
Explanation:
(C₂H₅)₃NHCl dissociates according to the following equation.
(C₂H₅)₃NHCl ⇒ (C₂H₅)₃NH⁺ + Cl⁻
The molar ratio of (C₂H₅)₃NHCl to (C₂H₅)₃NH⁺ is 1:1. Then, the concentration of (C₂H₅)₃NH⁺ is Ca = 0.166 M.
(C₂H₅)₃NH⁺ is the conjugate acid of (C₂H₅)₃N. Given the Kb of (C₂H₅)₃N, we can calculate Ka for (C₂H₅)₃NH⁺ using the following expression.
Ka × Kb = Kw
Ka = Kw / Kb
Ka = 1.0 × 10⁻¹⁴ / 5.2 × 10⁻⁴
Ka = 1.9 × 10⁻¹¹
(C₂H₅)₃NH⁺ dissociates according to the following equation.
(C₂H₅)₃NH⁺ ⇄ (C₂H₅)₃N + H⁺
We can calculate [H⁺] using the following expression.
[H⁺] = √(Ca × Ka) = √(0.166 × 1.9 × 10⁻¹¹) = 1.8 × 10⁻⁶
The pH is:
pH = -log [H⁺] = -log 1.8 × 10⁻⁶ = 5.7
