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⁻]
