By Contributor | Updated Aug 30, 2022
Ammonia (NH₃) is a volatile gas that dissolves readily in water and acts as a weak base. The equilibrium in aqueous solution is represented by the reaction:
NH₃ + H₂O ⇌ NH₄⁺ + OH⁻
The acidity or basicity of the resulting solution is expressed as the pH, the negative base‑10 logarithm of the hydrogen ion concentration ([H⁺]). For bases, the base dissociation constant (Kb) is defined as:
Kb = [NH₄⁺][OH⁻]/[NH₃]
where the brackets indicate molar concentrations. Kb is temperature‑dependent and is usually tabulated at 25 °C. For ammonia, Kb = 1.8 × 10⁻⁵.
Multiply the Kb value by the total ammonia concentration (Cₜ = [NH₃] + [NH₄⁺]) and by 4. The factor of 4 comes from a quadratic approximation used when the base is weak and the ionization is small. For example, if Cₜ = 0.10 M:
Product term = 4 × Kb × Cₜ = 4 × 1.8 × 10⁻⁵ × 0.10 = 7.2 × 10⁻⁶.
Take the square root of the product term to approximate the concentration of hydroxide ions ([OH⁻]):
[OH⁻] ≈ √(7.2 × 10⁻⁶) = 2.683 × 10⁻³ M (rounded to the nearest thousandth).
Subtract the Kb value from the preliminary [OH⁻] and divide by 2 to obtain a more accurate [OH⁻] (this corrects for the small contribution of Kb to the ion product):
[OH⁻] = (2.683 × 10⁻³ – 1.8 × 10⁻⁵) / 2 = 1.333 × 10⁻³ M.
Use the ion‑product constant of water (Kw = 1.0 × 10⁻¹⁴ M²) to find [H⁺]:
[H⁺] = Kw / [OH⁻] = 1.0 × 10⁻¹⁴ / 1.333 × 10⁻³ = 7.502 × 10⁻¹¹ M.
Finally, compute the pH as the negative base‑10 logarithm of [H⁺]:
pH = –log₁₀(7.502 × 10⁻¹¹) = 10.12.
Thus, a 0.10 M ammonia solution at 25 °C has a pH of approximately 10.12.
