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

$A={\frac {RT}{p}}{\frac {n^{2}-1}{n^{2}+2}}$

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

$A={\frac {RT}{p}}{\frac {n^{2}-1}{3}}.$

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:

$A={\frac {M}{\rho }}{\frac {n^{2}-1}{n^{2}+2}}\approx {\frac {M}{\rho }}{\frac {n^{2}-1}{3}}.$

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 0-521-64222-1