Thermodynamics and Chemistry

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

ii(g) RTln

pi^0

p

C

Zp 0

0



Vi

RT

p



dp RTln

pi

p

CB^0 ip

SiSi(g) Rln

p^0 i

p

Zp 0

0

"

@Vi

@T



p

R

p

#

dp Rln

pi

p

p

dB^0 i

dT

HiHi(g)

Zp 0

0

"

ViT



@Vi

@T



p

#

dp p



Bi^0 T

dBi^0

dT



UiUi(g)

Zp 0

0

"

ViT



@Vi

@T



p

#

dpCRTp^0 Vi pT

dBi^0

dT

Cp;iCp;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)