A \(0.250 \mathrm{M}\) solution of \(\mathrm{NH}_{3}\) has a pH of 11.32 . What percentage of the ammonia is ionized in this solution?

Understanding the pH scale is crucial for studying the properties of solutions in chemistry. The pH is a logarithmic scale that measures the acidity or basicity of an aqueous solution. It is defined as the negative logarithm of the hydrogen ion concentration, represented as \( pH = -\log[H^+] \). However, for basic solutions like ammonia, we often find it more practical to converse in terms of hydroxide ions \( [OH^-] \) and pOH, with the latter being the negative logarithm of the hydroxide ion concentration \( pOH = -\log[OH^-] \).
For any aqueous solution at 25°C, the relationship between pH and pOH is always such that \( pH + pOH = 14 \) due to the constant product of the hydrogen and hydroxide ion concentrations in water. This means one can easily convert between pH and pOH, facilitating the calculation of the hydroxide ion concentration in basic solutions like the ammonia solution mentioned in our problem.
The calculation begins with the known pH and employs the relationship above to find pOH. Then, the pOH is used to determine the hydroxide ion concentration using the formula \( [OH^-] = 10^{-pOH} \). This step is critical as it sets the stage for determining the ionization percentage of ammonia in the following steps.

The hydroxide ion concentration in a solution is a direct measure of its basicity. In a solution of ammonia \( (NH_3) \), hydroxide ions are produced through the process of ionization, where ammonia reacts with water \( (H_2O) \) to form ammonium ions \( (NH_4^+) \) and hydroxide ions \( (OH^-) \).
To calculate the hydroxide ion concentration from pH, you can apply the mathematical relationship derived from basic principles of equilibrium: \( [OH^-] = 10^{-pOH} \), where 'pOH' is derived from \( pOH = 14 - pH \) for any neutral aqueous solution at 25°C. Given the pH value, one can calculate 'pOH' and subsequently use it to find the hydroxide ion concentration, which is essential for determining how much of the ammonia is ionized in the solution.

The concept of chemical equilibrium plays a pivotal role in understanding reactions in solution, particularly those that are reversible, like the ionization of ammonia. At chemical equilibrium, the rates of the forward and reverse reactions are equal, leading to constant concentrations of reactants and products over time.
In the case of ammonia in water, the equilibrium can be written as \( NH_3 (aq) + H_2O (l) \leftrightarrow NH_4^+ (aq) + OH^- (aq) \). The extent to which ammonia ionizes is represented by the equilibrium constant, \( K_b \), for the base ionization. However, not all ammonia molecules will ionize to form ammonium and hydroxide ions. The percentage of ionization is calculated by comparing the concentration of ionized ammonia at equilibrium to the initial concentration of ammonia before ionization.
The concept of equilibrium helps predict the extent of a reaction and the concentrations of the involved species at equilibrium. In our problem, once we know the hydroxide ion concentration at equilibrium, we can infer the degree of ionization of the ammonia.