What is conductivity?

Conductivity (noted σ) quantifies the ability of a solution to conduct electrical current (i.e. to allow electrical charges to move freely). This is directly related to the mobility (noted u_i) of the ions present in the solution, which is the concentration-independent part of the conductivity.

For a sphere-shaped ion, mobility follows the subsequent relationship according to Stoke’s theory:

With z_i the charge of the ion, e the elementary charge η the viscosity, R the radius of the solvated ion (hydrodynamic radius), k_B the Boltzmann constant, D the diffusion coefficient and T the temperature. Mobility u_i has for unit m².s^-1.V^-1.

Thus:

with F the Faraday constant in C.mol^-1 (charge of one mole of elementary charges) and C_i the concentration in mol.m^-3.

C_i in mol.m^-3 = 10³C_i en mol.L^-1

For each ion, the ionic molar conductivity λ_i (A_i^Z_i) is defined by:

For polycharged ions, we most often use the ionic molar conductivity per mole of charge (also called equivalent or specific ionic conductivity)) :

When C tends to 0 (infinite dilution), a new quantity is introduced: the ionic limiting molar conductivity (λ°) : λ°_i = limCi → 0 λ_i. Typically in a diluted solution it is considered that :