CHAPTER 4
PHASE DIAGRAMS AND MIXTURES
83
(4.16)
Substituting this expression for the chemical potential into the relationship for the Gibbs energy yields:
(4.17)
After mixing, the molecules A and B will distribute over the entire volume
and the partial pressures will decrease and the Gibbs energy becomes:
(4.18)
P = P A + P B
Notice that since the partial pressures are less than the total pressure,
the ratio of the pressures has decreased and so the Gibbs energy has consequently decreased. The change in the Gibbs energy due to mixing, ΔG mix ,
can now be calculated:
ΔG mix = G f − G i
(4.19)
ΔG mix =
ΔG mix =
ΔG mix =
= RT n
P
P
n
P
P
A
A
B
B
ln
ln
+
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
0
RT n
P
P
n
P
P
n
P
P
n
P
P
A
A
A
B
B
B
ln
ln
ln
ln
0
0
0
0
−
+
−
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟
n RT
P
P
n RT
P
P
n RT
P
P
n RT
A
A
B
B
A
B
ln
ln
ln
l
0
0
0
+
−
+
n n
P
P 0
−
+
+
+
( )
ln
( )
ln
n
P
n RT
P
P
n
P
n RT
P
A A
A
B B
B
μ
μ
0
0
0
P P 0
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
n
P
n RT
P
P
n
P
n RT
P
A A
A
A
B B
B
B
μ
μ
( )
ln
( )
ln
0
0
0
+
+
+
P P 0
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
G
n
P
RT
P
P
n
P
f
( )
ln
( )
=
+
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟ +
A
A
A
B
B
μ
μ
0
0
0
ln
+
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
RT
P
P
B
0
G n
P
RT
P
P
n
P
i
( )
ln
( )
=
+
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟ +
A
A
B
B
μ
μ
0
0
0 + +
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
ln
RT
P
P 0
μ
μ
( )
( )
ln
P
P
RT
P
P
=
+
0
0
9781405124362_4_004.qxd 4/29/08 9:08 Page 83