Final answer:
To calculate the equilibrium constant, we use the relationship between pKa and Kb, and the ion product constant for water. Substituting the values, we find pKa as 5.23, and use the Henderson-Hasselbalch approximation to find the equilibrium constant.
Step-by-step explanation:
To calculate the equilibrium constant for the reaction C₅H₅NH⁺(aq) + H₂O(l) ⟶ C₅H₅N(aq) + H₃O⁺(aq), we can use the relationship between pKa and Kb provided in the question. The equation pKa + pKb = pKw holds true, where pKw is the ion product constant for water. Substituting the given values, we can calculate pKa as 5.23. We can then use the Henderson-Hasselbalch approximation to find the equilibrium constant.