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

Answer: 7.5 * 10 ⁻⁶ M

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⁻]