Final answer:
To calculate the pH of a 2.19 M solution of KCN, we need to find the Kb for CN- ions using the given Ka for HCN and then calculate the OH- concentration before finding the pH.
Step-by-step explanation:
To calculate the pH of a 2.19 M solution of KCN, we must acknowledge that KCN is a salt of the weak acid HCN and the strong base KOH. Therefore, the KCN solution will behave as a basic solution due to the hydrolysis of the CN- ion. The CN- ion will react with water to produce HCN and OH- ions:
CN-(aq) + H2O(l) ← HCN(aq) + OH-(aq)
The equilibrium constant for this reaction (Kb) is related to the Ka of HCN through the relationship Kw = Ka×Kb. Given that Ka for HCN is 6.2 × 10-10 and Kw (the ion-product constant for water) is 1.0 × 10-14, we can calculate Kb as follows:
Kb = Kw / Ka = (1.0 × 10-14) / (6.2 × 10-10)
Using the formula [ OH-] = √(Kb × [CN-]), we can find the concentration of OH-. Finally, to find the pH, we can use the formula pH = 14 - pOH, where pOH = -log[ OH-].
Following these steps will give us the pH of a 2.19 M solution of KCN.