Final answer:
To calculate the hydroxide ion concentration of a 0.21 M ammonia solution, the Kb value of ammonia should be used in the equilibrium expression involving NH3 and water, and the [OH-] can be found by solving for x, where Kb = x^2 / [NH3]. Assuming x is much smaller than the initial concentration of NH3 allows for simplification and easy calculation.
Step-by-step explanation:
To determine the concentration of hydroxide ions ([OH-]) in a 0.21 M ammonia solution, we need to use the equilibrium constant for ammonia's reaction with water (Kb). Ammonia (NH3) is a weak base and its Kb value is 1.76 x 10-5. The reaction for ammonia with water can be represented as:
NH3(aq) + H2O(l) ⇌ NH4+(aq) + OH-(aq)
At equilibrium, the concentration of NH4+ and OH- will be the same, let's call this x. Therefore, the equilibrium expression is:
Kb = [NH4+][OH-] / [NH3]
1.76 x 10-5 = x2 / (0.21 - x)
Assuming that x is much smaller than 0.21 M, the equation simplifies to:
1.76 x 10-5 ≈ x2 / 0.21
Solving for x gives us the [OH-] concentration. This simplification is often valid for weak bases, where the degree of ionization is low.