Chemistry Reference
In-Depth Information
ð
ð
ð
2
1
1
p
cos
2
dx
A
ð
1
x
A
Þ
dx
B
ð
1
x
B
Þ
¼
d
w
w
0
1
1
þ
4
ð
ð
dx
A
x
A
ð
2
1
1
p
2
3
dx
B
x
B
¼
8
d
w
p
ð
11
:
76
Þ
0
1
1
so that
ð
a
2
2
F
ðWÞ
a
2
3
2
d
W
¼
8
ð
11
:
77
Þ
p
W
Then:
ð
a
2
2
F
ðWÞ
a
2
3
2
d
W
1
þ
¼
8
1
þ
ð
11
:
78
Þ
p
W
"
!
#
"
!
#
a
2
3
a
2
3
d
da
d
da
ln 8
1
þ
¼
ln8
p
þ
ln 1
þ
p
ð
11
:
79
Þ
1
2
3
a
2
3
a
¼
a
2
3
1
þ
for a
small. Hence, we obtain the final result for the average attraction
energy between the dipoles:
2
A
2
B
h
Vexp
ð
V
=
kT
Þi
m
A
m
B
R
3
2
3
a
¼
3kT
m
2
m
ð
11
:
80
Þ
R
6
This is known as the Keesom or dipole orientation energy (Equa-
tions 11.61 and 11.62). This term depends on R
6
, but is temperature
dependent and decreases in importance with increasing T.
It is of interest to compare the relative importance of all attractive
contributions to the intermolecular energy in the VdW region. For atoms
and centrosymmetrical molecules, induction is zero, so that the only
