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.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentNow, 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
±
,o
r
K
P
±
=
exp
é
ë
−
,
r
G
±
/
(
RT
)
ù
û
.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '09
 Physical chemistry, Thermodynamics, Equilibrium, Partial Pressure, pH, Trigraph, RT ln

Click to edit the document details