A 0.10 M solution of sodium acetate (salt of a weak acid with a strong base) has what approximate pH?

A 0.10 M solution of sodium acetate (salt of a weak acid with a strong base) has what approximate pH?

• A. 7.00
• B. 8.87
• C. 9.50
• D. 6.50

Answer: (B)

A salt of a weak acid with a strong base yields a basic solution because the conjugate base of the weak acid hydrolyzes water, producing OH− and raising the pH. In this case, acetate ion (the conjugate base of acetic acid) reacts with water: CH3COO− + H2O ⇌ CH3COOH + OH−. The base hydrolysis constant is Kb = Kw / Ka. With Ka for acetic acid about 1.8 × 10−5 and Kw = 1.0 × 10−14, Kb ≈ 5.6 × 10−10. For a 0.10 M solution, let [OH−] = x. Then x^2/(0.10 − x) ≈ 5.6 × 10−10. Since x is small, x ≈ sqrt(5.6 × 10−11) ≈ 7.5 × 10−6 M. The pOH ≈ −log(7.5 × 10−6) ≈ 5.13, so pH ≈ 14 − 5.13 ≈ 8.87. So the solution is basic, with pH around 8.9, which best matches the given option.

A salt of a weak acid with a strong base yields a basic solution because the conjugate base of the weak acid hydrolyzes water, producing OH− and raising the pH. In this case, acetate ion (the conjugate base of acetic acid) reacts with water: CH3COO− + H2O ⇌ CH3COOH + OH−.

The base hydrolysis constant is Kb = Kw / Ka. With Ka for acetic acid about 1.8 × 10−5 and Kw = 1.0 × 10−14, Kb ≈ 5.6 × 10−10. For a 0.10 M solution, let [OH−] = x. Then x^2/(0.10 − x) ≈ 5.6 × 10−10. Since x is small, x ≈ sqrt(5.6 × 10−11) ≈ 7.5 × 10−6 M. The pOH ≈ −log(7.5 × 10−6) ≈ 5.13, so pH ≈ 14 − 5.13 ≈ 8.87.

So the solution is basic, with pH around 8.9, which best matches the given option.