§ C-35 Salt Hydrolysis in Aqueous Solution: Kₕ = K_w / Kₐ, Degree h & Medium pH (Grade 9–11 · Salt Hydrolysis)
Chapter XXXV. Proton Exchange of Weak-Acid Anions (CH₃COO⁻, CO₃²⁻) & Weak-Base Cations (NH₄⁺, Al³⁺). «Even a neutral salt crystal, once dissolved in water, enters into a subtle protolytic dialogue with the solvent.», J. N. Brønsted, 1923
Theory Summary & Scientific Mechanism
Salt hydrolysis is the proton-transfer reaction between dissolved salt ions and water molecules that shifts solution pH away from neutrality. Only ions conjugate to weak acids or weak bases undergo hydrolysis; the stronger parent electrolyte dictates whether the solution is acidic or basic.
1) Weak-acid + strong-base salt (CH₃COONa, Na₂CO₃): anion hydrolysis A⁻ + H₂O ⇄ HA + OH⁻ yields a basic solution (pH > 7). 2) Strong-acid + weak-base salt (NH₄Cl): cation hydrolysis BH⁺ + H₂O ⇄ B + H₃O⁺ yields an acidic solution (pH < 7). 3) Strong-acid + strong-base salts (NaCl) do not hydrolyze (pH = 7.0).
The hydrolysis constant is Kₕ = K_w / K_weak, and the degree of hydrolysis h = √(Kₕ / C) increases upon dilution (C ↓) and heating (since K_w increases strongly with temperature).
Everyday Analogy
In a salt solution, the stronger parent wins! Sodium acetate comes from strong base NaOH + weak acid, so its solution is basic (pH > 7). Ammonium chloride comes from strong acid HCl + weak base, so its solution is acidic (pH < 7)!
Interactive Question & Derivation
Why does an aqueous solution of sodium acetate CH₃COONa turn phenolphthalein pink (pH > 7, alkaline), whereas ammonium chloride NH₄Cl gives an acidic reaction (pH < 7)?
- A: Hydrolysis is driven by the ion of the weak electrolyte: CH₃COO⁻ + H₂O ⇄ CH₃COOH + OH⁻ releases OH⁻ (pH > 7), whereas NH₄⁺ + H₂O ⇄ NH₃·H₂O + H₃O⁺ releases H₃O⁺ (pH < 7)
- B: All salts in water always have a strictly neutral pH = 7.00 regardless of the parent acid or base strength
- C: Heating a salt solution completely stops hydrolysis because K_w drops to zero at 80 ^°C
Study Hint: The weak-electrolyte ion hydrolyzes water: CH₃COO⁻ generates OH⁻ (pH > 7), whereas NH₄⁺ generates H₃O⁺ (pH < 7).
Proof & Explanation: Salt hydrolysis is the protolytic reaction of salt ions with water to form a weak electrolyte. 1) Salt of a weak acid & strong base (CH₃COONa): anion hydrolysis A⁻ + H₂O ⇄ HA + OH⁻, Kₕ = K_w / Kₐ, pH = 7 + (1)/(2)(pKₐ + lg C) > 7. 2) Salt of a strong acid & weak base (NH₄Cl): cation hydrolysis BH⁺ + H₂O ⇄ B + H₃O⁺, Kₕ = K_w / K_b, pH = 7 - (1)/(2)(pK_b - lg C) < 7. Dilution (C ↓) and heating (K_w ↑) both increase the degree of hydrolysis h = √(Kₕ / C).
Key Equations & 3D Simulation Parameters
Kₕ = (K_w)/(K_weak), h = √((Kₕ)/(C)), pH = 7 + (1)/(2)(pKₐ + lg C) & (Weak Acid + Strong Base) ; 7 - (1)/(2)(pK_b - lg C) & (Strong Acid + Weak Base)
- Salt (1=NaCl, 2=CH₃COONa, 3=NH₄Cl, 4=Na₂CO₃): 1 … 4 (default: 4)
- Initial salt concentration C₀: 0.01 … 0.5 mol/L (default: 0.1 mol/L)
- Solution temperature t (K_w rises with T): 15 … 85 °C (default: 25 °C)
- Water dilution factor (V / V₀): 1 … 10 × (default: 1 ×)