Physics: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