Molar refractivity

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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

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

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
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