Answer and Explanation:
To find the pH of the solution, we need to determine the concentration of the hydronium ion (H3O+) in the solution. Since we have a weak acid (HF) and its conjugate base (NaF), we can use the concept of the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
First, let's calculate the concentrations of HF and NaF in the solution:
[H3O+] = [HF] = 0.40 M (concentration of HF)
[OH-] = [F-] = 0.64 M (concentration of NaF)
Next, we need to determine the pKa value for HF. The pKa is the negative logarithm of the acid dissociation constant (Ka):
pKa = -log(Ka)
pKa = -log(6.6x10^-4)
pKa = 3.18
Now, let's substitute the values into the Henderson-Hasselbalch equation:
pH = 3.18 + log([0.64]/[0.40])
pH = 3.18 + log(1.6)
pH = 3.18 + 0.2041
pH ≈ 3.38
Therefore, the pH of the solution is approximately 3.38.