Kohlrausch's Law of Independent Migration
Kohlrausch's law describes how molar conductivity of a strong electrolyte varies with concentration.
Used to determine Ka of weak acids.
The Formula
Λ_m° = Σν+λ+ + Σν−λ−
Friedrich Kohlrausch (1874) discovered that for strong electrolytes, the molar conductivity decreases linearly with the square root of concentration. At infinite dilution (Λ_m°), ions move completely independently of each other. Kohlrausch's law of independent migration states that each ion contributes a fixed amount to the total molar conductivity, regardless of which other ion it is paired with.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| Λ_m | Molar conductivity at concentration C | S·m²/mol |
| Λ_m° | Limiting molar conductivity (at infinite dilution) | S·m²/mol |
| K | Kohlrausch constant (slope of the Λ_m vs √C plot) | depends on electrolyte |
| C | Concentration of the electrolyte | mol/m³ |
| λ+, λ− | Individual ion molar conductivities at infinite dilution | S·m²/mol |
| ν+, ν− | Number of cations and anions per formula unit | dimensionless |
Example 1 — Molar Conductivity of KCl
The molar conductivity of KCl at 25°C: 0.001 M → 14.94 mS·m²/mol; 0.01 M → 14.12; 0.1 M → 12.85. Find Λ_m°.
Plot Λ_m vs √C: points at √C = 0.0316, 0.1, 0.316 give Λ_m = 14.94, 14.12, 12.85
Linear fit: slope K ≈ −6.5, intercept = Λ_m°
Λ_m°(KCl) ≈ 14.99 mS·m²/mol (literature: 14.985). Extrapolation to zero concentration gives limiting conductivity.
Example 2 — Ka from Conductometry
For acetic acid (0.01 M), measured Λ_m = 1.65 mS·m²/mol. Using Λ_m°(CH&sub3;COOH) = Λ_m°(HCl) + Λ_m°(CH&sub3;COONa) − Λ_m°(NaCl) = 39.07 mS·m²/mol.
α = Λ_m / Λ_m° = 1.65 / 39.07 = 0.0422 (degree of dissociation)
K_a = α²C / (1 − α) = (0.0422)² × 0.01 / (1 − 0.0422)
K_a = 1.78 × 10−5 ≈ 1.8 × 10−5 for acetic acid — matches the known value perfectly!
When to Use It
Use Kohlrausch's law when:
- Determining the limiting molar conductivity of a strong electrolyte by extrapolation
- Calculating K_a of a weak acid from conductivity measurements
- Testing water purity — ultra-pure water has very low conductivity; impurities increase it
- Calibrating conductivity meters in industrial water treatment and pharmaceutical labs
- Studying ionic transport in solution for electrochemical cell design