Kohlrausch’s Law of Independent Migration of Ions
Every ion migrates at its own fixed speed, contributing its own fixed share of conductivity, regardless of which partner ion accompanies it. Dial in real or custom ions below and watch the field respond — then see the two competing transport mechanisms behind the numbers, and why the law rescues chemists from an impossible extrapolation.
1 Migration Simulator
Choose any cation/anion pair — or override with a custom mobility — and adjust temperature. The animation speed and the computed Λmo update live. Hover any ion in the tube for its transport mechanism.
2 The Law, Precisely
At infinite dilution (c → 0), interionic electrostatic interactions vanish and every ion moves as if no other ion existed. Under these conditions each ion contributes a fixed, additive amount to the electrolyte’s limiting molar conductivity:
3 Additivity in Action — Assembling Λmo(CH₃COOH)
Acetic acid is weak and cannot be extrapolated directly (Section 5). Kohlrausch’s Law builds its value instead from three strong-electrolyte values, chosen so the unwanted Na⁺ and Cl⁻ terms cancel exactly:
4 Two Transport Mechanisms — Why H⁺ and OH⁻ Break the Pattern
H⁺ (349.6) and OH⁻ (199.1) are anomalously fast — roughly 3–7× any other singly-charged ion. They aren’t simply “smaller”; they use a fundamentally different transport mechanism.
5 The Extrapolation Problem
For a strong electrolyte, the Debye–Hückel–Onsager relation Λm = Λmo − (A + BΛmo)√c predicts a near-linear fall as concentration rises — so a short linear plot extrapolates cleanly to c = 0. A weak electrolyte’s Λm depends on its degree of dissociation α, which itself rises steeply as c → 0, producing a curve that shoots upward with no linear region to extrapolate.
6 Limiting Ionic Molar Conductivities (25°C, aqueous)
| Cation | λ°+ | Anion | λ°− |
|---|---|---|---|
| H⁺ | 349.6 | OH⁻ | 199.1 |
| K⁺ | 73.5 | Cl⁻ | 76.3 |
| NH₄⁺ | 73.5 | Br⁻ | 78.1 |
| Ag⁺ | 61.9 | NO₃⁻ | 71.4 |
| Na⁺ | 50.1 | CH₃COO⁻ | 40.9 |
| Li⁺ | 38.7 | HCO₃⁻ | 44.5 |
| ½ Ca²⁺ | 119.0 | ½ SO₄²⁻ | 80.0 |
| ½ Mg²⁺ | 106.1 | ½ CO₃²⁻ | 69.3 |
7 Dissociation Deepens on Dilution
For a weak electrolyte, α = Λm/Λmo is literally the fraction of dissolved molecules that exist as free ions rather than associated pairs. Diluting the solution shifts the equilibrium toward dissociation (Le Chatelier), which is exactly why Λm climbs toward Λmo as c → 0.
8 The Payoff — Ostwald’s Dilution Law
Combining α = Λm/Λmo with the equilibrium expression for a weak monoprotic acid HA ⇌ H⁺ + A⁻ gives:
9 Key Takeaways
CogitaVerse · Physical Chemistry Series
Download Complete Notes for Kohlrausch’s Law Below
(4) Calculation of the Degree of Dissociation or Conductance Ratio
An electrolyte’s apparent degree of dissociation, α, at dilution V can be found using the formula, α * λv/λ∞ where λv is the electrolyte’s equivalent conductance at dilution V, and λ∞ is its equivalent conductance at infinite dilution.
Kohlrausch’s Law states that this is equal to the sum λ anion and λ cation.
(5) Calculation of the Ionic product for water
The observed specific conductance of the purest water at 25oC is 5.54 × 10-8 mho cm-1 . The conductance of one litre of water containing 1 gram eqvt of it would be:
When the temperature is the same, the conductance of H+ ions andOH– ions is:
λH+ = 349.8 mho cm-1
λ OH– = 198.5 mho cm-1
According to Kohlrausch’s Law
λH2O = λH+ + λ OH–
349.8 + 198.5 = 548.3 mho cm-1
Since one water molecule gives one H+ ion and one OH– ion
So
H2O = H+ + OH –
Assuming that conductance and ionic concentration are proportionate, we have
[H+] = [OH–] = (is 5.54 × 10-8) / 548.3= 1.01 × 10-7 g ion litre-1
The ionic product of water is then
For most purposes, the value of Kw is taken to be 10-14
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