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| | '''Molar refractivity''', <math>A</math>, is a measure of the total [[polarizability]] of a [[mole (unit)|mole]] of a substance and is dependent on the [[temperature]], the [[index of refraction]], and the [[pressure]]. |
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| | The molar refractivity is defined as |
| | :<math> A = \frac{4 \pi}{3} N_A \alpha, </math> |
| | where <math>N_A \approx 6.022 \times 10^{23}</math> is the [[Avogadro constant]] and <math>\alpha</math> is the mean [[polarizability]] of a molecule. |
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| | Substituting the molar refractivity into the [[Lorentz-Lorenz]] formula gives |
| | :<math> A = \frac{R T}{p} \frac{n^2 - 1}{n^2 + 2} </math> |
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| | For a gas, <math>n^2 \approx 1</math>, so the molar refractivity can be approximated by |
| | :<math>A = \frac{R T}{p} \frac{n^2 - 1}{3}.</math> |
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| | In [[SI]] units, <math>R</math> has units of J mol<sup>−1</sup> K<sup>−1</sup>, <math>T</math> has units K, <math>n</math> has no units, and <math>p</math> has units of Pa, so the units of <math>A</math> are m<sup>3</sup> mol<sup>−1</sup>. |
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| | In terms of [[density]], ρ [[molecular weight]], M it can be shown that: |
| | :<math>A = \frac{M}{\rho} \frac{n^2 - 1}{n^2 + 2} \approx \frac{M}{\rho} \frac{n^2 - 1}{3}.</math> |
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| | ==References== |
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| | * [[Max Born|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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| | [[Category:Physical chemistry]] |
| | [[Category:Physical optics]] |
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
where 
is the Avogadro constant and 
is the mean polarizability of a molecule.
Substituting the molar refractivity into the Lorentz-Lorenz formula gives
For a gas, 
, so the molar refractivity can be approximated by
In SI units, 
has units of J mol−1 K−1, 
has units K, 
has no units, and 
has units of Pa, so the units of are m3 mol−1.
In terms of density, ρ molecular weight, M it can be shown that:
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