Conductivity of solutions

Resistance R = ρ l/A, where ρ (resistivity) is in Ω m; 1 Ω m = 100 Ω cm. Conductance G = 1/R, in siemens (S = Ω⁻¹, also called mho).

Conductivity κ = 1/ρ, in S m⁻¹ (1 S cm⁻¹ = 100 S m⁻¹): the conductance of a piece 1 m long with 1 m² cross-section. IUPAC prefers 'resistivity' and 'conductivity' over 'specific resistance' and 'specific conductance'.

Values span a huge range (298.15 K): copper 5.9 × 10³, 0.1 M HCl 3.91, 0.01 M KCl 0.14, 0.1 M acetic acid 0.047 and pure water 3.5 × 10⁻⁵ S m⁻¹, glass 1.0 × 10⁻¹⁶ S m⁻¹. Superconductors have zero resistivity; some ceramics and mixed oxides superconduct at up to 150 K.

Metallic (electronic) conduction is by electrons, depends on the metal's structure and number of valence electrons, falls as temperature rises, and leaves the metal unchanged.

Electrolytic (ionic) conduction is by ions. It depends on the electrolyte, the size and solvation of its ions, the solvent and its viscosity, concentration and temperature (it rises with temperature). Pure water conducts slightly from its ~10⁻⁷ M H⁺ and OH⁻.

Two problems in measuring a solution's resistance: direct current electrolyses it and changes its composition, and a liquid cannot be clamped into a bridge. The fixes are an AC source (audio frequency, 550 to 5000 Hz) and a conductivity cell with platinised platinum electrodes.

The cell constant G* = l/A (unit m⁻¹ or cm⁻¹) is found by filling the cell with KCl of known κ and measuring R: G* = R κ. Then κ of any solution = G*/R.

A Wheatstone bridge with a detector (headphone) balances when no current flows through it; today direct-reading conductivity meters are common.