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
where is the number of molecules per unit volume and is the refractive index. The ratio is simply the molar volume . Evaluating the ideal gas law for 1 mole gives
where is the universal gas constant, is the absolute temperature, and is the pressure. Then the molar refractivity is
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 m3 mol−1.
In terms of density, ρ molecular weight, M it can be shown that: