Ihe pll of a \(0.005 M\) codeine \(\left(\mathrm{C}_{18} \mathrm{H}_{21} \mathrm{NO}_{2}\right)\) solution is 9.95. Calculate its ionisation constant.

Understanding the pH and pOH relationship is crucial when dealing with solutions' acidity and basicity. pH (potential of Hydrogen) is a measure of the acidity or hydrogen ion concentration in a solution. On the other hand, pOH represents the alkalinity or hydroxide ion concentration. The pH of a solution is calculated using the formula \( pH = -\log [H_3O^+] \). For the pOH, it's similar, but it relates to the hydroxide ions: \( pOH = -\log [OH^-] \).

These two measures are inversely related and add up to a constant value, 14, at 25°C (298 K) in aqueous solutions. Hence the fundamental relationship: \( pH + pOH = 14 \). When the pH value is known, as in the given exercise, calculating the pOH is as simple as subtracting the pH from 14. This allows us to switch between concentration measures of acidic and basic ions, crucial for determining ionisation constants for weak acids and bases.

Hydroxide ion concentration \( [OH^-] \) is a key indicator of a solution's basicity. It determines the pOH via the formula \( pOH = -\log [OH^-] \) and, consequently, the pH through the relationship between pH and pOH.

In the context of the exercise, we use pOH to calculate the hydroxide ion concentration. By using the inverse logarithm (antilog), we convert the pOH value back to the concentration of hydroxide ions: \( [OH^-] = 10^{-\text{pOH}} \). This step is vital as the hydroxide ion concentration is directly used to calculate the base's ionisation constant (Kb), which is necessary to understand the degree to which a base dissociates in the solution.

Ionisation of a weak base, such as codeine in this exercise, doesn't go to completion, which means only some of the base molecules react with water to form hydroxide ions (OH-) and the corresponding conjugate acid. The equilibrium between these species is represented by the base's ionisation constant (Kb).

For a general weak base \(B\text{ and water (}H_2O\text{), the reaction is: }B + H_2O \longleftrightarrow BH^+ + OH^- \). The Kb expression is \(Kb = \frac{[BH^+][OH^-]}{[B]} \). In our scenario, we simplify the expression by assuming that the concentration of the base remains nearly constant. Therefore, the ionisation constant Kb can be approximated as the concentration of hydroxide ions produced in the reaction, which we've calculated using the pH. Knowing Kb is vital for quantifying the base strength and understanding solution chemistry involving weak bases. It's important for predicting the degree of ionisation and for calculations in buffer solutions and titrations.