Molar refractivity Information & Molar refractivity Links at HealthHaven.com

Molar refractivity 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 $α$ is the mean polarizability.

Substituting the molar refractivity into the Lorentz-Lorenz formula gives

$A = \frac{N_A}{N} \frac{n^2 - 1}{n^2 + 2},$

where $N$ is the number of molecules per unit volume and $n$ is the refractive index. The ratio $N A / N$ is simply the molar volume $V m$ . Evaluating the ideal gas law for 1 mole gives

$V_m = \frac{N_A}{N} = \frac{R T}{p},$

where $R$ is the universal gas constant, $T$ is the absolute temperature, and $p$ is the pressure. Then the molar refractivity is

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

For a gas, $n^2 \approx 1$ , so the molar refractivity can be approximated by

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

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.

[edit] 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