To calculate the pH of a 0.1 M solution of potassium cyanide (KCN), we first need to understand that KCN is a salt formed from the strong base potassium hydroxide (KOH) and the weak acid hydrocyanic acid (HCN).
When KCN dissolves in water, it dissociates into potassium ions (K+) and cyanide ions (CN–). The potassium ions do not affect the pH significantly, but the cyanide ions can react with water in a process called hydrolysis:
CN– + H2O → HCN + OH–
This reaction produces hydroxide ions (OH–), which increases the pH of the solution, making it basic.
To find the concentration of hydroxide ions produced, we can use the base ionization constant (Kb) for CN–. The Kb for the cyanide ion is approximately 6.2 x 10-5.
Using the formula:
Kb = [HCN][OH–] / [CN–]
Assuming that x is the concentration of OH– produced from the hydrolysis, we can express this as:
Kb = (x)(x) / (0.1 – x) ≈ (x2) / 0.1
Since Kb is very small, we can assume that x is small compared to 0.1, allowing us to simplify the equation:
x2 ≈ Kb * 0.1
Now, substituting the value of Kb:
x2 ≈ (6.2 x 10-5) * 0.1 = 6.2 x 10-6
Taking the square root gives us the hydroxide concentration:
x ≈ √(6.2 x 10-6) ≈ 2.49 x 10-3 M
The pOH of the solution can then be calculated as:
pOH = -log[OH–] = -log(2.49 x 10-3) ≈ 2.61
Finally, to find the pH, we can use the relation:
pH + pOH = 14
pH = 14 – pOH ≈ 14 – 2.61 = 11.39
Therefore, the pH of a 0.1 M solution of KCN is approximately 11.39, indicating that the solution is basic.