1. Understand the Chemistry
* Ammonia (NH₃) is a weak base. When it reacts with water, it forms ammonium ions (NH₄⁺) and hydroxide ions (OH⁻).
* Kb is the base dissociation constant, which measures the extent to which a base ionizes in water. A smaller Kb indicates a weaker base.
2. Set Up the Equilibrium
The reaction of ammonia with water is:
NH₃(aq) + H₂O(l) ⇌ NH₄⁺(aq) + OH⁻(aq)
3. Use the pH to find [OH⁻]
* pOH + pH = 14
* pOH = 14 - 11.6 = 2.4
* [OH⁻] = 10⁻²·⁴ M
4. Use the Kb expression and ICE table
* Kb = [NH₄⁺][OH⁻] / [NH₃]
Let 'x' represent the change in concentration of NH₃ and the formation of NH₄⁺ and OH⁻.
| | NH₃ | NH₄⁺ | OH⁻ |
|-------------|---------|---------|---------|
| Initial | C | 0 | 0 |
| Change | -x | +x | +x |
| Equilibrium | C - x | x | x |
Now, substitute the equilibrium concentrations into the Kb expression:
* 1.8 x 10⁻⁵ = (x)(x) / (C - x)
5. Simplify the Equation
Since Kb is small, we can assume x << C, making (C - x) ≈ C. This simplifies the equation:
* 1.8 x 10⁻⁵ = x² / C
6. Solve for C (the initial concentration of ammonia)
* x = [OH⁻] = 10⁻²·⁴ M
* 1.8 x 10⁻⁵ = (10⁻²·⁴)² / C
* C = (10⁻²·⁴)² / (1.8 x 10⁻⁵)
* C ≈ 0.067 M
Therefore, the molarity of the ammonia solution is approximately 0.067 M.
