Réfractivité molaire

La réfractivité molaire est la mesure de la polarisabilité totale de 1 mole de substance en fonction de la température, de l'indice de réfraction et de la pression. Elle est définie par :

A={\frac {4\pi }{3}}N_{A}\alpha ,

où $N_{A}\approx 6.022\times 10^{23}$ est la constante d'Avogadro et $\alpha$ est la polarisabilité moyenne.

En intégrant la réfractivité molaire dans l'équation de Lorentz et Lorenz, cela donne

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

où $N$ est le nombre de molécules par unité de volume et $n$ est l'indice de réfraction. Le rapport $N_{A}/N$ est tout simplement le volume molaire $V_{m}$ .

En vérifiant la Loi des gaz parfaits pour 1 mole, cela donne

V_{m}={\frac {N_{A}}{N}}={\frac {RT}{p}},

où $R$ est la Constante universelle des gaz parfaits, $T$ est la température absolue, et $p$ est la pression. Alors, la réfractivité molaire est

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

Dans le cas d'un gaz, $n^{2}\approx 1$ , donc la réfractivité molaire peut être approchée à

A={\frac {RT}{p}}{\frac {n^{2}-1}{3}}.

Dans le Système International d'unités, les unités de $R$ sont J mol^-1 K^-1, celle de $T$ est K, celle de $p$ est Pa, et $n$ n'a pas d'unités, d'où, les unités de $A$ sont m³ mol^-1.

Bibliographie

Born, Max, et 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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