- Source: Molar refractivity
Molar refractivity,
A
{\displaystyle 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
,
{\displaystyle A={\frac {4\pi }{3}}N_{A}\alpha ,}
where
N
A
≈
6.022
×
10
23
{\displaystyle N_{A}\approx 6.022\times 10^{23}}
is the Avogadro constant and
α
{\displaystyle \alpha }
is the mean polarizability of a molecule.
Substituting the molar refractivity into the Lorentz-Lorenz formula gives, for gasses
A
=
R
T
p
n
2
−
1
n
2
+
2
{\displaystyle A={\frac {RT}{p}}{\frac {n^{2}-1}{n^{2}+2}}}
where
n
{\displaystyle n}
is the refractive index,
p
{\displaystyle p}
is the pressure of the gas,
R
{\displaystyle R}
is the universal gas constant, and
T
{\displaystyle T}
is the (absolute) temperature. For a gas,
n
2
≈
1
{\displaystyle n^{2}\approx 1}
, so the molar refractivity can be approximated by
A
=
R
T
p
n
2
−
1
3
.
{\displaystyle A={\frac {RT}{p}}{\frac {n^{2}-1}{3}}.}
In SI units,
R
{\displaystyle R}
has units of J mol−1 K−1,
T
{\displaystyle T}
has units K,
n
{\displaystyle n}
has no units, and
p
{\displaystyle p}
has units of Pa, so the units of
A
{\displaystyle 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
.
{\displaystyle 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
Kata Kunci Pencarian:
- Molar refractivity
- Van der Waals radius
- Refractive index
- High-refractive-index polymer
- Polarizability
- Molar mass distribution
- Lipinski's rule of five
- Druglikeness
- Gladstone–Dale relation
- Molecular descriptor
