Calculating the pH of a 0.1 M Solution of Sodium Acetate Assuming Small Degree of Hydrolysis
Sodium acetate (CH₃COONa) is the salt of a weak acid (acetic acid, CH₃COOH) and a strong base (sodium hydroxide, NaOH). When dissolved in water, it undergoes hydrolysis, producing acetate ions (CH₃COO⁻) and sodium ions (Na⁺). The acetate ions can react with water to form acetic acid and hydroxide ions (OH⁻), increasing the pH of the solution.
Understanding Hydrolysis
Hydrolysis is the reaction of a salt with water to produce an acidic or basic solution. In the case of sodium acetate, the acetate ion acts as a weak base and reacts with water according to the following equilibrium:
CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻
The equilibrium constant for this reaction is called the hydrolysis constant (Kh):
Kh = [CH₃COOH][OH⁻] / [CH₃COO⁻]
Approximating the pH using Small Degree of Hydrolysis
We can simplify the calculation of pH if we assume that the degree of hydrolysis is small. This means that only a small fraction of the acetate ions react with water to form hydroxide ions.
Under this assumption, we can use the following approximations:
- [CH₃COO⁻] ≈ initial concentration of sodium acetate = 0.1 M
- [CH₃COOH] ≈ [OH⁻]
We can relate Kh to the acid dissociation constant (Ka) of acetic acid using the following equation:
Kh = Kw / Ka
Where Kw is the ion product of water (1.0 x 10⁻¹⁴ at 25°C).
Calculating the pH
- Find the Ka of acetic acid. The Ka of acetic acid is 1.8 x 10⁻⁵.
- Calculate Kh. Kh = Kw / Ka = 1.0 x 10⁻¹⁴ / 1.8 x 10⁻⁵ = 5.56 x 10⁻¹⁰
- Set up an ICE table.
CH₃COO⁻ CH₃COOH OH⁻ Initial (I) 0.1 M 0 0 Change (C) -x +x +x Equilibrium (E) 0.1-x x x - Substitute the equilibrium concentrations into the Kh expression. 5.56 x 10⁻¹⁰ = (x)(x) / (0.1-x)
- Since the degree of hydrolysis is assumed small, we can approximate 0.1-x ≈ 0.1. 5.56 x 10⁻¹⁰ = x² / 0.1
- Solve for x, which represents [OH⁻]. x = √(5.56 x 10⁻¹¹)= 7.46 x 10⁻⁶ M
- Calculate the pOH. pOH = -log[OH⁻] = -log(7.46 x 10⁻⁶) = 5.13
- Calculate the pH. pH = 14 - pOH = 14 - 5.13 = 8.87
Therefore, the pH of a 0.1 M solution of sodium acetate, assuming a small degree of hydrolysis, is approximately 8.87.
Note: This calculation is an approximation. The actual pH may be slightly different due to the assumption of a small degree of hydrolysis. For a more precise calculation, you can use the quadratic equation to solve for x without the approximation.
