 Molar refractivity

Molar refractivity, A, 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 α is the mean polarizability of a molecule.
Substituting the molar refractivity into the LorentzLorenz formula gives
where N is the number of molecules per unit volume and n is the refractive index. The ratio N_{A} / N is simply the molar volume V_{m}. Evaluating the ideal gas law for 1 mole gives
where R is the universal gas constant, T is the absolute temperature, and p is the pressure. Then the molar refractivity is
For a gas, , so the molar refractivity can be approximated by
In SI units, R has units of J mol^{1} K^{1}, T has units K, n has no units, and p has units of Pa, so the units of A are m^{3} mol^{1}.
In terms of density, ρ molecular weight, M it can be shown that:
References
 Born, Max, and Wolf, Emil, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (7th ed.), section 2.3.3, Cambridge University Press (1999) ISBN 0521642221
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