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CHEM350: Lecture 4, Jan 11 2010
Gibbs free energy for nonideal gases (section 7.5 in textbook)
We know from thermodynamics that the total differential for the molar Gibbs free energy
G
(
T
,
P
)
has
the form
d
G
=
−
SdT
+
VdP
from which we obtain the relation
∂
G
∂
P
⎛
⎝
⎜
⎞
⎠
⎟
T
=
V
If we consider a process at constant temtperature
T
, we obtain,
d
G
T
=
VdP
and integrating from initial pressure
P
i
to final pressure
P
f
yields,
d
G
T
P
=
P
i
P
=
P
f
∫
=
V dP
P
=
P
i
P
=
P
f
∫
Using the ideal gas equation of state for
V
, we get
Δ
G
(
)
T
≡
G
(
T
,
P
f
)
−
G
(
T
,
P
i
)
=
RT
ln
P
f
P
i
⎛
⎝
⎜
⎞
⎠
⎟
.
If we let the initial pressure
P
i
be 1 bar, i.e.,
P
i
≡
P
o
, we obtain
G
(
T
,
P
f
)
−
G
(
T
,
P
o
)
=
RT
ln
P
f
P
o
⎛
⎝
⎜
⎞
⎠
⎟
or
G
(
T
,
P
f
)
=
G
o
(
T
)
+
RT
ln
P
f
P
o
⎛
⎝
⎜
⎞
⎠
⎟
How can we proceed for a nonideal gas? We can replace
V
with a more realistic expression such as the
virial equation of state,
P
V
RT
=
1
+
B
'
2
(
T
)
P
+
B
'
3
(
T
)
P
2
+
...
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 Spring '10
 Leroy
 Thermodynamics, Statistical Mechanics, Entropy, RT ln

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