At 298 K, 0.1 mol of ammonium acetate and 0.14 mol of acetic acid are ...
Calculating pH of ammonium acetate solution
Step 1: Write the dissociation reaction of ammonium acetate:
NH4C2H3O2 → NH4+ + C2H3O2-
Step 2: Write the expression for the equilibrium constant:
Ka = [NH4+][C2H3O2-]/[NH4C2H3O2]
Step 3: Calculate the concentration of NH4+ and C2H3O2-
[NH4+] = 0.1 mol/L
[C2H3O2-] = 0.14 mol/L
Step 4: Calculate the concentration of NH4C2H3O2
Since ammonium acetate is a strong electrolyte, the concentration of NH4C2H3O2 is equal to the sum of NH4+ and C2H3O2-
[NH4C2H3O2] = [NH4+] + [C2H3O2-] = 0.1 mol/L + 0.14 mol/L = 0.24 mol/L
Step 5: Substitute the values into the expression for Ka to calculate the value of Ka
Ka = [NH4+][C2H3O2-]/[NH4C2H3O2] = (0.1 mol/L)(0.14 mol/L)/(0.24 mol/L) = 5.83 × 10^-5
Calculating pH of acetic acid solution
Step 1: Write the dissociation reaction of acetic acid:
CH3COOH → H+ + CH3COO-
Step 2: Write the expression for the equilibrium constant:
Ka = [H+][CH3COO-]/[CH3COOH]
Step 3: Calculate the concentration of H+ and CH3COO-
[CH3COO-] = 0.14 mol/L
Since the solution is not neutral, we need to use the Henderson-Hasselbalch equation to calculate the concentration of H+.
pH = pKa + log([A-]/[HA])
where [A-] is the concentration of the conjugate base, and [HA] is the concentration of the acid.
Substituting the values, we get:
pH = 4.75 + log(0.14/0.1) = 4.6
Therefore, the pH of the solution is 4.6, which corresponds to option B.