Molar refractivity explained

Molar refractivity,^[1]

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 = (4 \pi)/(3) N _{A} \alpha, where N _{A} ≈ 6 . 022 x 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 = (R T)/(p) (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} ≈ 1 , so the molar refractivity can be approximated byA = (R T)/(p) (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 = (M)/(\rho) (n ^{2} -1)/(n ^{2} +2) ≈ (M)/(\rho) (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)

Notes and References

1. W. Foerst et.al. Chemie für Labor und Betrieb, 1967, 3, 32-34.

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