Molar refractivity,, is a measure of the total polarizability of a mole of a substance.

For a perfect dielectric which is made of one type of molecule, the molar refractivity is proportional to the polarizability of a single molecule of the substance. For real materials, intermolecular interactions (the effect of the induced dipole moment of one molecule on the field felt by nearby molecules) give rise to a density dependence.

The molar refractivity is commonly expressed as a sum of components, where the leading order is the value for a perfect dielectric, followed by the density-dependent corrections:

.

The coefficients depend on the wavelength of the applied field (and on the type and composition of the material), but not on thermodynamic state variables such as temperature or pressure.

The leading order (perfect dielectric) molar refractivity is defined as

is the Avogadro constant is the mean polarizability of a molecule.

Lorentz–Lorenz

Substituting the molar refractivity into the Lorentz–Lorenz formula gives, for gasses

is the refractive index is the universal gas constant is the (absolute) temperature; the ideal gas law.)

, so the molar refractivity can be approximated by

is a function of the substance itself and not of its conditions, and therefore does not depend on the three state variables appearing in the right hand side of the expression.

In terms of density ρ and molecular weight) that:

Notes

References

Bibliography

• 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)