Question

What is the hydroxide concentration of a 0.10 molar solution of ammonia at equilibrium if its Ka is 5.62 × 10-10?

Answer 1

Answer: 7.5 × 10 ⁻⁶ M

Step-by-step explanation:

1) Equlibrium equation:

NH₃ + H₂O ⇄ NH₄⁺ + OH⁻

2) Mole balance

NH₃ NH₄⁺ + OH⁻

Start 0.1 0 0
React x 0 0
Produced 0 x x
Final 0.1 - x x x


3) Ka equation: Ka = [NH₄⁺] [ OH⁻] / [NH₃] = x² / (0.1 - x) = 5.6 × 10 ⁻¹⁰

4) You can solve that equation easily if you realize tha x is so small that 0.1 - x ≈ 0.1

⇒ x² / 0.1 ≈ 5.6 × 10 ⁻¹⁰


⇒ x = √ ( 5.6 × 10 ⁻¹¹) = 7.50 × 10⁻⁶ M = [OH⁻]