CHAPTER 9 MIXTURES
9.3 GASMIXTURES 244
Table 9.1 Gas mixture: expressions for differences between partial molar and stan-
dard molar quantities of constituenti
General expression Equation of statea
Difference at pressurep^0 VDnRT=pCnB
i i(g) RTln
pi^0
p
C
Zp 0
0
Vi
RT
p
dp RTln
pi
p
CB^0 ip
Si Si(g) Rln
p^0 i
p
Zp 0
0
"
@Vi
@T
p
R
p
#
dp Rln
pi
p
p
dB^0 i
dT
Hi Hi(g)
Zp 0
0
"
Vi T
@Vi
@T
p
#
dp p
Bi^0 T
dBi^0
dT
Ui Ui(g)
Zp 0
0
"
Vi T
@Vi
@T
p
#
dpCRT p^0 Vi pT
dBi^0
dT
Cp;i Cp;i(g)
Zp 0
0
T
@^2 Vi
@T^2
p
dp pT
d^2 Bi^0
dT^2
aBandB 0
iare defined by Eqs.9.3.24and9.3.26
At low to moderate pressures, the simple equation of state
V=nD
RT
p
CB (9.3.21)
describes a gas mixture to a sufficiently high degree of accuracy (see Eq.2.2.8on page 35 ).
This is equivalent to a compression factor given by
Z defD
pV
nRT
D 1 C
Bp
RT
(9.3.22)
From statistical mechanical theory, the dependence of the second virial coefficientBof
a binary gas mixture on the mole fraction composition is given by
BDyA^2 BAAC2yAyBBABCyB^2 BBB (9.3.23)
(binary gas mixture)
whereBAAandBBBare the second virial coefficients of pure A and B, andBABis a mixed
second virial coefficient.BAA,BBB, andBABare functions ofTonly. For a gas mixture
with any number of constituents, the composition dependence ofBis given by
BD
X
i
X
j
yiyjBij (9.3.24)
(gas mixture,BijDBji)
HereBijis the second virial ofiifiandjare the same, or a mixed second virial coefficient
ifiandjare different.
If a gas mixture obeys the equation of state of Eq.9.3.21, the partial molar volume of
constituentiis given by
ViD
RT
p
CB^0 i (9.3.25)