CHAPTER 4 LECTURE NOTES
Chemical Equilibrium Involving Ideal Gases (Replaces Sections 4.1):
Consider a reaction of the type
n
A
A(
g
) +
n
B
B(
g
)
W
n
C
C(
g
) +
n
D
D(
g
),
where A, B, C, and D all behave ideally.
During the reaction, the partial pressure
of each gas changes.
The resulting free energy change for each gas can be
expressed as
,
G
A
=
n
A
RT
ln
æ
è
ç
P
A
,2
P
A
,1
ö
ø
÷
,
,
G
B
=
n
B
RT
ln
æ
è
ç
P
B
,2
P
B
,1
ö
ø
÷
, and so on.
If we assume that the reaction starts with each gas at the standard pressure,
denoted as
P
°, we may write
G
A
=
G
A
±
+
n
A
RT
ln
æ
è
P
A
P
±
ö
ø
,
G
B
=
G
B
±
+
n
B
RT
ln
æ
è
P
B
P
±
ö
ø
, and so on.
It is important to remember that the free energies in the expressions above are
NOT molar quantities, i.e., we need to keep in mind that
G
A
=
n
A
G
m
,
A
,
G
°
A
=
n
A
G
°
m
,
A
, etc.. Now, the free energy change for the reaction may be written as
,
r
G
=
,
r
G
±
+
RT
ln
é
ë
ê
(
P
C
/
P
±
)
n
C
(
P
D
/
P
±
)
n
D
(
P
A
/
P
±
)
n
A
(
P
B
/
P
±
)
n
B
ù
û
ú
,
where
∆
r
G =
(
G
C
+
G
D
) ± (
G
A
+
G
B
)
= (
n
C
G
m
,
C
+
n
D
G
m
,
D
) ± (
n
A
G
m
,
A
+
n
B
G
m
,
B
),
and
∆
r
G
° is similarly defined.
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Now, at equilibrium,
∆
r
G
= 0 and so, we get
,
r
G
±
= −
RT
ln
é
ë
ê
(
P
C
/
P
±
)
n
C
(
P
D
/
P
±
)
n
D
(
P
A
/
P
±
)
n
A
(
P
B
/
P
±
)
n
B
ù
û
ú
eq
.
The partial pressures that enter into this expression are the values measured at
equilibrium and, therefore, is a constant at a given temperature. Note that, because
of the division of each pressure term by the standard pressure, the quantity within
the square brackets is
dimensionless
.
In other words,
,
r
G
±
= −
RT
ln
K
P
±
, or
K
P
±
=
exp
é
ë
−
,
r
G
±
/
(
RT
)
ù
û
.
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 Fall '09
 Physical chemistry, Thermodynamics, Equilibrium, Partial Pressure, pH, Trigraph, RT ln

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