Molar refractivity


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 α is the mean polarizability of a molecule.

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 NA / N is simply the molar volume Vm. 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.

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

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Van der Waals radius — The van der Waals radius, r sub|w, of an atom is the radius of an imaginary hard sphere which can be used to model the atom for many purposes. It is named after Johannes Diderik van der Waals, winner of the 1910 Nobel Prize in Physics, as he was… …   Wikipedia

  • Lorentz–Lorenz equation — The Lorentz–Lorenz equation, also known as the Clausius–Mossotti relation and Maxwell s formula, relates the refractive index of a dilute gas to its temperature, pressure, and molar refractivity. The index of refraction n is given by: n approx… …   Wikipedia

  • Purpurin (data page) — Molecular Formula = C14H14O5:Formula Weight = 262.25796:Composition = C(64.12%) H(5.38%) O(30.50%):Molar Refractivity = 64.57 cm3:Molar Volume = 172.1 cm3:Parachor = 514.5 cm3:Index of Refraction = 1.673 :Surface Tension = 79.7 /cm3:Density =… …   Wikipedia

  • Lipinski's Rule of Five — is a rule of thumb to evaluate druglikeness, or determine if a chemical compound with a certain pharmacological or biological activity has properties that would make it a likely orally active drug in humans. The rule was formulated by Christopher …   Wikipedia

  • Druglikeness — is a qualitative concept used in drug design for how druglike a substance is with respect to factors like bioavailability. It is estimated from the molecular structure before the substance is even synthesized and tested. A druglike molecule has… …   Wikipedia

  • Molecular descriptor — Molecular descriptors play a fundamental role in chemistry, pharmaceutical sciences, environmental protection policy, and health researches, as well as in quality control, being the way molecules, thought of as real bodies, are transformed into… …   Wikipedia

  • Diamond — This article is about the mineral. For the gemstone, see Diamond (gemstone). For other uses, including the shape ◊, see Diamond (disambiguation) …   Wikipedia

  • Refractive index — Refraction of light at the interface between two media. In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum… …   Wikipedia

  • Zinc — This article is about the metallic element. For other uses, see Zinc (disambiguation). copper ← zinc → gallium ↑ Zn ↓ Cd …   Wikipedia

  • Clausius–Mossotti relation — The Clausius–Mossotti relation is named after the Italian physicist Ottaviano Fabrizio Mossotti, whose 1850 book[1] analyzed the relationship between the dielectric constants of two different media, and the German physicist Rudolf Clausius, who… …   Wikipedia