149.8
S·cm²/mol
0.8611
86.11
%
20.8
S·cm²/mol
73.5
S·cm²/mol
76.3
S·cm²/mol
149.8
S·cm²/mol
0.8611
86.11
%
20.8
S·cm²/mol
73.5
S·cm²/mol
76.3
S·cm²/mol
Kohlrausch's Law of Independent Migration of Ions is a foundational principle in electrochemistry stating that at infinite dilution, each ion contributes independently to the total molar conductivity of an electrolyte. The Kohlrausch's Law Calculator computes the limiting molar conductivity (Λ°m) from individual ionic conductivities at infinite dilution and stoichiometric coefficients. It also calculates the degree of dissociation (α) when the measured molar conductivity is provided. This law is particularly important for weak electrolytes, where Λ°m cannot be determined by direct extrapolation of conductivity data. By combining ionic conductivities from strong electrolyte measurements, we can calculate Λ°m for any electrolyte, enabling determination of dissociation constants, solubility products, and ionic mobilities. Friedrich Kohlrausch established this law in 1876 through meticulous conductivity measurements, and it remains one of the most practical tools in physical chemistry.
Kohlrausch's Law states that at infinite dilution:
$$\Lambda_m^\circ = \nu_+ \lambda_+^\circ + \nu_- \lambda_-^\circ$$
where ν+ and ν− are the stoichiometric coefficients of the cation and anion, and λ°+ and λ°− are their limiting ionic conductivities.
For example, for CaCl₂ → Ca²⁺ + 2Cl⁻:
$$\Lambda_m^\circ(\text{CaCl}_2) = 1 \times \lambda^\circ(\text{Ca}^{2+}) + 2 \times \lambda^\circ(\text{Cl}^-)$$
The degree of dissociation of a weak electrolyte at any concentration is:
$$\alpha = \frac{\Lambda_m}{\Lambda_m^\circ}$$
Combined with the dissociation equilibrium, this gives Ostwald's dilution law:
$$K_a = \frac{c\alpha^2}{1 - \alpha}$$
The law works because at infinite dilution, each ion moves independently without interionic interactions, so the total conductivity is simply additive.
The limiting molar conductivity (Λ°m) represents the maximum conducting ability of one mole of electrolyte when all interionic interactions are eliminated. Ions like H⁺ (λ° = 349.8) and OH⁻ (λ° = 198.0) have anomalously high conductivities due to the Grotthuss proton-hopping mechanism. The degree of dissociation (α) indicates what fraction of the electrolyte is ionized at the measured concentration. For strong electrolytes, α ≈ 1 at all concentrations (slight deviations reflect ion-atmosphere effects, not incomplete dissociation). For weak electrolytes like acetic acid, α may be as low as 1–5% at moderate concentrations. If α > 1, check that the measured Λm and ionic conductivities are in consistent units.
Inputs
Results
Λ°m(KCl) = 73.5 + 76.3 = 149.8 S·cm²/mol. At 0.1 M, α = 129/149.8 = 0.861 — apparent low α for a strong electrolyte reflects interionic effects, not incomplete dissociation.
Inputs
Results
Λ°m = λ°(H⁺) + λ°(CH₃COO⁻) = 349.8 + 40.9 = 390.7 S·cm²/mol. At 0.01 M, only 4.17% dissociated — typical weak acid behavior.
At infinite dilution, each ion contributes a definite amount to the total molar conductivity, independent of the other ion present. This means λ°(Na⁺) is the same whether it comes from NaCl, NaOH, or Na₂SO₄.
Weak electrolytes are only slightly dissociated at measurable concentrations, so their Λm vs √c plot is non-linear and cannot be extrapolated to find Λ°m. Kohlrausch's law provides an alternative: calculate Λ°m from ionic conductivities obtained from strong electrolyte data.
They are tabulated in reference books. Common values at 25°C (S·cm²/mol): H⁺ = 349.8, OH⁻ = 198.0, K⁺ = 73.5, Na⁺ = 50.1, Cl⁻ = 76.3, NO₃⁻ = 71.4, CH₃COO⁻ = 40.9, SO₄²⁻ = 80.0, Ca²⁺ = 59.5.
α = Λm/Λ°m represents the fraction of electrolyte molecules that have dissociated into ions. For a 0.01 M weak acid with α = 0.04, only 4% of molecules are ionized. This allows calculation of Ka from conductivity data.
For sparingly soluble salts (e.g., AgCl), measure the conductivity of a saturated solution. Use Λ°m from Kohlrausch's law to find concentration: c = κ/(Λ°m × 1000). Then Ksp = c² for a 1:1 salt.
No. The law is strictly valid only at infinite dilution. At finite concentrations, interionic interactions cause deviations described by the Debye-Hückel-Onsager theory. The law provides the reference point (Λ°m) from which these deviations are measured.
For a weak 1:1 electrolyte: Ka = cα²/(1−α). Using α = Λm/Λ°m, this becomes: Ka = cΛ²m / [Λ°m(Λ°m − Λm)]. This connects conductivity measurements directly to thermodynamic dissociation constants.
These ions conduct via the Grotthuss mechanism: instead of physically migrating, protons hop along a chain of hydrogen-bonded water molecules. This chain relay is much faster than conventional ion diffusion through the solvent.
They are the number of each type of ion produced per formula unit. For NaCl: ν+ = 1, ν− = 1. For CaCl₂: ν+ = 1 (Ca²⁺), ν− = 2 (Cl⁻). For Al₂(SO₄)₃: ν+ = 2, ν− = 3.
Yes. Enter the ionic conductivity for each ion type and its stoichiometric coefficient. For example, for MgSO₄: λ°(Mg²⁺) = 53.1, ν+ = 1, λ°(SO₄²⁻) = 80.0, ν− = 1, giving Λ°m = 133.1 S·cm²/mol.
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