# Molar refractivity

**Molar refractivity**,
, is a measure of the total polarizability of a mole of a substance and is dependent on the temperature, the index of refraction, and the pressure.

The molar refractivity is defined as

where is the Avogadro constant and is the mean polarizability of a molecule.

Substituting the molar refractivity into the Lorentz-Lorenz formula gives, for gasses

where is the refractive index, is the pressure of the gas, is the universal gas constant, and is the (absolute) temperature. For a gas, , so the molar refractivity can be approximated by

In SI units,
has units of J mol^{−1} K^{−1},
has units K,
has no units, and
has units of Pa, so the units of
are m^{3} mol^{−1}.

In terms of density ρ, molecular weight M, it can be shown that: