Lecture_4 - CHAPTER 4 LECTURE NOTES Chemical Equilibrium...

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.

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
.