Final answer:
The pH of a 0.20 M NaCN solution is 11.30. This is calculated using the base ionization constant (Kb) for the cyanide ion in water, which is derived from the provided ionization constant (Ka) for HCN.
Step-by-step explanation:
To calculate the pH of a 0.20 M NaCN solution, we need to consider the chemical reaction of the cyanide ion (CN-) in water and use the provided ionization constant (Ka) for HCN. First, we calculate the base ionization constant (Kb) for cyanide:
Kb = Kw / Ka
Kb = (1.0 × 10-14) / (5.0 × 10-10)
Kb = 2.0 × 10-5
Then, we use the Kb to find the concentration of OH- ions in the solution using the following formula:
[ OH- ] = √(Kb × [CN- ])
[ OH- ] = √(2.0 × 10-5 × 0.20)
[ OH- ] = 2.0 × 10-3
Finally, we find the pOH and the pH:
pOH = -log([ OH- ])
pOH = -log(2.0 × 10-3)
pOH = 2.70
pH = 14 - pOH
pH = 14 - 2.70
pH = 11.30