Ionic Conductivity — Kohlrausch's Law

Electrolyte

Conditions

Concentration 0.100 mol/L

Temperature 25 °C

Applied voltage 2.0 V

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Molar conductivity Λm

— S·cm²/mol

Dissociation α

100%

Estimated cell current I (1 cm cell, 1 cm² electrodes)

— mA

Λm vs √c — dot marks the current state

How it works

Every strong electrolyte's limiting molar conductivity is the sum of independent ionic contributions — Kohlrausch's Law of Independent Migration:

Λm° = ν₊λ°₊ + ν₋λ°₋

For NaCl: λ°(Na⁺) = 50.1, λ°(Cl⁻) = 76.3 S·cm²/mol → Λm° ≈ 126.4 S·cm²/mol. As concentration rises, ion atmospheres drag on each other and Λm falls off with the square root of concentration (Kohlrausch / Debye-Hückel-Onsager):

Λm(c) = Λm° − K√c

A weak electrolyte like acetic acid only partially ionizes. Its degree of dissociation α is fixed by the acid dissociation constant through the Ostwald dilution law:

Ka = cα² / (1 − α),   Λm = α·Λm°

The lower the concentration, the more complete the dissociation (α → 1 as c → 0) — the opposite trend from a strong electrolyte, whose ions are already 100% dissociated at every concentration.

Strong / Weak — switches between NaCl (fully dissociated, Onsager square-root falloff) and acetic acid (Kₐ = 1.8×10⁻⁵, Ostwald dilution law).
Concentration — logarithmic slider from 0.001 to 1 mol/L; watch ion count, drift speed and Λm respond.
Temperature — raises ionic mobility (~2%/K, lower water viscosity) and hence Λm and drift speed.
Voltage — the field pulling cations to the cathode (left, blue plate) and anions to the anode (right, red plate); it sets drift speed and the estimated current, not Λm itself.

Grey spheres in the weak-electrolyte case are undissociated CH₃COOH molecules — they don't respond to the field, only jitter thermally, visualizing (1 − α).

Cation (→ cathode) Anion (→ anode) Undissociated molecule

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Ionic Conductivity — Kohlrausch's Law of Electrolyte Solutions