Kohlrausch's law

Kohlrausch noticed regularities among strong electrolytes at 298 K: Λ°m(KX) − Λ°m(NaX) ≈ 23.4 S cm² mol⁻¹ for X = Cl, Br, I, and Λ°m(MBr) − Λ°m(MCl) ≈ 1.8 S cm² mol⁻¹ for M = Na, K.

Law of independent migration of ions: Λ°m of an electrolyte is the sum of the separate contributions of its cation and anion, Λ°m = ν₊λ°₊ + ν₋λ°₋, where ν₊ and ν₋ are the numbers of cations and anions per formula unit.

Limiting ionic conductivities at 298 K (S cm² mol⁻¹): H⁺ 349.6, Na⁺ 50.1, K⁺ 73.5, Ca²⁺ 119.0, Mg²⁺ 106.0, OH⁻ 199.1, Cl⁻ 76.3, Br⁻ 78.1, CH₃COO⁻ 40.9, SO₄²⁻ 160.0.

Λ°m(CaCl₂) = 119.0 + 2(76.3) = 271.6 and Λ°m(MgSO₄) = 106.0 + 160.0 = 266 S cm² mol⁻¹.

A weak electrolyte's Λ°m is built from strong ones: Λ°m(HAc) = Λ°m(HCl) + Λ°m(NaAc) − Λ°m(NaCl) = 425.9 + 91.0 − 126.4 = 390.5 S cm² mol⁻¹.

Degree of dissociation α ≈ Λm/Λ°m, and the dissociation constant Ka = cα²/(1 − α).

Worked: 0.001028 M acetic acid has κ = 4.95 × 10⁻⁵ S cm⁻¹, so Λm = 48.15 S cm² mol⁻¹, α = 48.15/390.5 = 0.1233 and Ka = 1.78 × 10⁻⁵ mol L⁻¹.