Ostwald's Dilution Law
Ostwald's dilution law relates the degree of dissociation of a weak electrolyte to its concentration and dissociation constant Ka.
The Formula
When α << 1: K_a ≈ α²C
α ≈ √(K_a / C)
Ostwald's dilution law (1888), named after chemist Wilhelm Ostwald, describes the equilibrium between a weak electrolyte and its ions. For a weak acid HA dissociating as HA → H&sup+ + A⊃−, the degree of dissociation α depends on both the acid dissociation constant K_a and the concentration C. A key insight: diluting a weak acid increases its degree of dissociation — consistent with Le Chatelier's principle.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| K_a | Acid dissociation constant | mol/L |
| α | Degree of dissociation (fraction of molecules that dissociate) | dimensionless (0 to 1) |
| C | Initial molar concentration of the weak acid | mol/L (M) |
Example 1 — Acetic Acid pH
Find the degree of dissociation and pH of 0.1 M acetic acid (K_a = 1.8 × 10−5).
α ≈ √(K_a / C) = √(1.8 × 10−5 / 0.1) = √(1.8 × 10−4) = 0.01342
Degree of dissociation = 1.342% (about 1.34% of acetic acid molecules dissociate)
[H&sup+;] = α × C = 0.01342 × 0.1 = 1.342 × 10−3 mol/L
pH = −log(1.342 × 10−3) ≈ 2.87
Example 2 — Effect of Dilution
Compare the degree of dissociation of acetic acid at 0.1 M, 0.01 M, and 0.001 M.
At 0.1 M: α = √(1.8×10−5 / 0.1) = 0.0134 (1.34%)
At 0.01 M: α = √(1.8×10−5 / 0.01) = 0.0424 (4.24%)
At 0.001 M: α = √(1.8×10−5 / 0.001) = 0.134 (13.4%) — 10-fold dilution increases dissociation from 1.34% to 13.4%
When to Use It
Use Ostwald's dilution law when:
- Calculating the degree of dissociation of weak acids and bases
- Finding [H&sup+;] and pH of weak acid solutions
- Determining K_a from conductivity measurements (Kohlrausch's law data)
- Predicting how pH changes when a weak acid solution is diluted
- Understanding why pure water has only 10−7 mol/L of H&sup+ ions (water self-ionizes with K_w = 10−14)
The approximation α ≈ √(K_a/C) is valid when α < 0.05 (less than 5% dissociation). For higher degrees of dissociation, use the exact quadratic form: α = [−K_a + √(K_a² + 4K_aC)] / (2C).