University of Babylon /College Of Engineering
Electrochemical Engineering Dept.
Second Stage /Thermodynamics
Generalized correlation for mixture of Gases
1) Key`s method : generalized correlation of Pilzer can be used for calculation
of gas mixture
Z  Z O  Z 
To find the compressibility factor Z for a gas mixture use is at pseudo critical
properties
TPC   yiTCi  y ATCA  y BTCB  yC TCC ....
PPC   yi PCi  y A PCA  y B PCB  yC PCC ....
 PC   yiCi  y ACA  y BCB  yC CC ....
Example: Gas mixture at 90 bar and 100 οC has the following composition:
CH420%, C2H4 30%, and N2 50%
Find the molar volume of this mixture by : a) Ideal gas , b) Kay`s method.
RT 8.314 * 373.15

 344.7cm 3 mol 1
P
90
b) From APP B
a) V  
Component
y
PC
TC
CH4
0.2
46
196.6
C2H4
0.3
50.6
282.4
N2
0.5
33.9
126.2
TPC   yiTCi  0.2 * 196  0.3 * 282.4  0.5 * 126.2  187.14
PPC   yi P Ci  0.2 * 46  0.3 * 50.6  0.5 * 33.9  11.32
   yii 0.2 * 0.008  0.3 * 0.085  0.5 * 0.04  0.0471
90
 2.18
11.32
337.15
Tr 
 1.8
187.14
Pr 
And by use figures (3-13) and (3-14)

0.008
0.085
0.040
University of Babylon /College Of Engineering
Electrochemical Engineering Dept.
Second Stage /Thermodynamics
Zo = 0.96, Z‫ =־‬0.17
Z = 0.96 + 0.0471* 0.17 = 0.968
V 
ZRT 0.968 * 8.314 * 373.15

 333.5cm 3 mol 1
P
90
2) Second Virial coefficient equation
Extension of Pitzer correlation to gas mixture depending on the second Virial
coefficient, by use mixing rule
B  i

j
C  i

j
m
m
m
m
yi y j Bij
yi y j yk Cijk
y represent mole fraction
i,j,and k : identify species all run over all species in the mixture
For binary mixture; m=2 → i = 1, 2 and j = 1, 2
With mixing rule for m-component we have Bij = Bji
B12=B21 Cross coefficient and B11≠ B22 pure coefficient
Pitzeer correlation for B , Z  1 
Z 1
Bij 
ij 
BPC Pr
RTC T
RTCij
PCij
B
o
i   j
2
TC ij  TCiTCj
,
BP
RT
BPC
 B o  B
RTC
 B

University of Babylon /College Of Engineering
Electrochemical Engineering Dept.
Second Stage /Thermodynamics
Z C ij 
VCij
Z Ci Z Cj
2
 VCi  VCj
 
2

PC ij 



3
Z Cji RTCij
VCij
Q / Estimate the molar volume of equimolar binary vapor mixture of CO2 and C3H8
at 311 K and 13.78 bar if the second Virial coefficient are B = 112.5 cm3mol-1 for
CO2 and -366.6 cm3mol-1 for C3H8 at 311 K.
Generalized correlation for three components mixture of Gases
For three component system, the Virial coefficient B include an additional coefficients;B33,
B13,B23
B  i
m

m
j
yi y j Bij
m= 3 ; I = 1,2, and 3 , j =1,2, and 3
B  y1 y1 B11  y1 y2 B12  y2 y1 B21  y2 y2 B22  y1 y3 B13  y3 y1 B31  y3 y3 B33
y2 y3 B23  y3 y2 B32
B  y12 B11  2 y1 y2 B12  y22 B22  2 y1 y3 B13  y 32 B33  2 y2 y3 B23