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
 * $$ A = \frac{4 \pi}{3} N_A \alpha, $$

where $$N_A \approx 6.022 \times 10^{23}$$ is the Avogadro constant and $$\alpha$$ is the mean polarizability of a molecule.

Substituting the molar refractivity into the Lorentz-Lorenz formula gives, for gasses
 * $$ A = \frac{R T}{p} \frac{n^2 - 1}{n^2 + 2} $$

where $$n$$ is the refractive index, $$p$$ is the pressure of the gas, $$R$$ is the universal gas constant, and $$T$$ is the (absolute) temperature. For a gas, $$n^2 \approx 1$$, so the molar refractivity can be approximated by
 * $$A = \frac{R T}{p} \frac{n^2 - 1}{3}.$$

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 m3 mol−1.

In terms of density ρ, molecular weight M, it can be shown that:
 * $$A = \frac{M}{\rho} \frac{n^2 - 1}{n^2 + 2} \approx \frac{M}{\rho} \frac{n^2 - 1}{3}.$$