CHEM 350 Lecture 6, January 15, 2010
Relation between
B
2
(
T
)
and intermolecular interactions.
We shall consider only the simplest case: that of a gas of filled–shell [or
1
S
–state] atoms, such
as He, Ne, Ar.
If
V
(
R
) is the potential energy (energy of interaction) between two such atoms, then
B
2
(
T
)
is given by
B
2
(
T
) =

2
πN
0
Z
∞
0
(
e

V
(
R
)
/k
B
T

1
)
R
2
dR ,
a result obtained from statistical mechanics.
•
if
V
(
R
)
≡
0, then
B
2
(
T
) = 0 for all temperatures, and the gas is an ideal gas;
•
for simple systems,
V
(
R
) can be obtained quite accurately from quantum chemical cal
culations, but for more complicated systems, its determination is still an active area of
research in chemical physics (or molecular physics);
•
experimentally,
V
(
R
) is determined from measurements of
B
2
(
T
), transport coefficients,
and spectroscopy;
•
typical behaviour of
V
(
R
) at long range (i.e.,
R
very large):
V
(
R
) can be shown from
perturbation theory calculations to behave at large distances as
V
(
R
)
=
⇒

C
6
R
6
,
with
C
6
known as the dispersion coefficient;
•
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 Spring '10
 Leroy
 Chemistry, Atom, Mole, chemical calculations

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