CHAPTER 4 PHASE DIAGRAMS AND MIXTURES 83
(4.16)
Substituting this expression for the chemical potential into the relation-
ship 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=PA+PB
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 con-
sequently decreased. The change in the Gibbs energy due to mixing, ΔGmix,
can now be calculated:
ΔGmix=Gf−Gi (4.19)
ΔGmix=
ΔGmix=
ΔGmix=
=
RT nP
P
nP
A P
A
B⎛ ln + ln B
⎝⎜⎜
⎞
⎠
⎟⎟
0RT nP
P
nP
P
nP
P
nP
A P
A
ABB
ln ln ln Bln
0 000−+−
⎛
⎝
⎜⎜⎜
⎞
⎠
⎟⎟
nRTP
P
nRTP
P
nRTP
P
A ln A B ln B ABln nRTl
000+−+nnP
P 0
−+ ++nPnRT() ln () lnP
P
nPnRTP
AAμμ 0 A BB B
0(^0) PP
0
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
nPnRTP
P
nPnRTP
AA AA
BB B
μμ() ln () lnB
0
0+++ (^0) PP
0
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
Gn P RT
P
P
f=+() ln nP()⎛
⎝
⎜⎜
⎞
⎠
AAμμ 0 A⎟⎟+ BB
00 + ln⎛
⎝
⎜⎜
⎞
⎠
RT ⎟⎟
P
P
B
0Gn P RT
P
P
i=+() ln nP()⎛
⎝
⎜⎜
⎞
⎠
AAμμ 0 ⎟⎟+ B B
00 ++
⎛
⎝
⎜⎜
⎞
⎠
RTln ⎟⎟P
P 0
μμ()PPRT( ) ln
P
P
=+ 0
0