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

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⁻]