Molar refractivity
Encyclopedia
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
where
is the number of molecules per unit volume and 
is the refractive index
. The ratio
is simply the molar volume
. Evaluating the ideal gas law
for 1 mole gives
where
is the universal gas constant, 
is the absolute temperature, and 
is the pressure. Then the molar refractivity is
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:
, is a measure of the total polarizabilityPolarizability
Polarizability is the measure of the change in a molecule's electron distribution in response to an applied electric field, which can also be induced by electric interactions with solvents or ionic reagents. It is a property of matter...
of a mole
Mole (unit)
The mole is a unit of measurement used in chemistry to express amounts of a chemical substance, defined as an amount of a substance that contains as many elementary entities as there are atoms in 12 grams of pure carbon-12 , the isotope of carbon with atomic weight 12. This corresponds to a value...
of a substance and is dependent on the temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
, the index of refraction, and the pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
.
The molar refractivity is defined as
where
is the Avogadro constant and is the mean polarizabilityPolarizability
Polarizability is the measure of the change in a molecule's electron distribution in response to an applied electric field, which can also be induced by electric interactions with solvents or ionic reagents. It is a property of matter...
of a molecule.
Substituting the molar refractivity into the Lorentz-Lorenz
Lorentz-Lorenz
The Lorentz–Lorenz equation, also known as the Clausius–Mossotti relation and Maxwell's formula, relates the refractive index of a substance to its polarizability....
formula gives
where
is the number of molecules per unit volume and is the refractive indexRefractive index
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 relative to that in the considered medium....
. The ratio
is simply the molar volumeMolar volume
The molar volume, symbol Vm, is the volume occupied by one mole of a substance at a given temperature and pressure. It is equal to the molar mass divided by the mass density...
. Evaluating the ideal gas lawIdeal gas law
The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's law...
for 1 mole gives
where
is the universal gas constant, is the absolute temperature, and is the pressure. Then the molar refractivity isFor a gas,
, so the molar refractivity can be approximated byIn SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
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
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
, ρ molecular weight, M it can be shown that: