Molar conductivity and dilution

Molar conductivity Λm = κ/c. With κ in S m⁻¹ and c in mol m⁻³, Λm is in S m² mol⁻¹; with κ in S cm⁻¹, Λm (S cm² mol⁻¹) = κ × 1000/molarity. 1 S cm² mol⁻¹ = 10⁻⁴ S m² mol⁻¹, and 1 mol L⁻¹ = 1000 mol m⁻³.

Worked: a cell reads 100 Ω with 0.1 M KCl (κ = 1.29 S m⁻¹), so G* = 129 m⁻¹; with 0.02 M KCl it reads 520 Ω, so κ = 0.248 S m⁻¹ and Λm = 0.248/20 = 124 × 10⁻⁴ S m² mol⁻¹.

On dilution κ always falls, for strong and weak electrolytes alike, because fewer ions are left in each unit volume.

Λm rises on dilution. Λm is the conductance of the whole volume holding 1 mol of electrolyte, set between electrodes 1 unit apart; that volume grows faster than κ shrinks.

The limit of Λm as c → 0 is the limiting molar conductivity, Λ°m.

Strong electrolytes: Λm rises slowly and Λm = Λ°m − A c^½, a straight line against √c with intercept Λ°m and slope −A. A depends on the solvent, temperature and electrolyte type (NaCl 1-1, CaCl₂ 2-1, MgSO₄ 2-2), and is the same for all electrolytes of one type.

Worked (KCl): the Λm–√c line gives Λ°m = 150.0 S cm² mol⁻¹ and A = 87.46 S cm² mol⁻¹ (mol L⁻¹)^−½.

Weak electrolytes such as acetic acid: Λm stays low at ordinary concentrations and shoots up steeply near zero, because the degree of dissociation grows on dilution. The curve cannot be extrapolated to find Λ°m.