The concentrations are [NH₄⁺] = 0.45 mol/L; [Cl⁻] = 0.45 mol/L; [NH₃] = 0.15 mol/L; [OH⁻] = 5.93 × 10⁻⁶ mol/L; [H₃O⁺] = 1.69 × 10⁻⁹ mol/L.
Step 1. Identify the species.
You have two equilibria here — the ionization of ammonia and the ionization of water.
The equations are:
NH₃ + H₂O ⇌ NH₄⁺ + OH⁻
2H₂O = H₃O⁺ + OH⁻
The species involved in the equilibria are NH₃, NH₄⁺, OH⁻, and H₃O⁺.
You also have the Cl⁻ as a spectator ion from the NH₄Cl (5 species in total).
Step 2. Determine the concentrations.
You know immediately that
(1) [NH₃] = 0.15 mol/L
(2) [NH₄⁺] = 0.45 mol/L
(3) [Cl⁻] = o.45 mol/L
Since this is a buffer, we can use the Henderson-Hasselbalch Equation:
The mixture contains a lot of unreacted ammonia molecules and lots of ammonium ions.
Ammonium ions are slightly acidic:
We can make some assumptions which means we don't have to go into working out equilibrium concentrations.
We can write an expression for
The presence of ammonia in the mixture forces the equilibrium to the left.
This means we can assume the ammonium ion concentration is what we started with -
Putting in the numbers:
The chloride ions take no part in any of this so their concentrations remain at