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
=
4
π
3
N
A
α
,
where
N
A
≈
6.022
×
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
=
R
T
p
n
2
−
1
n
2
+
2
For a gas,
n
2
≈
1
, so the molar refractivity can be approximated by
A
=
R
T
p
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
=
M
ρ
n
2
−
1
n
2
+
2
≈
M
ρ
n
2
−
1
3
.
