CHAP. 6: THERMODYNAMICS OF HOMOGENEOUS MIXTURES [CONTENTS] 160
Example
Calculate the fugacity coefficient and fugacity of carbon dioxide in an equimolar mixture with
hydrogen at temperature 30◦C and pressure 1 MPa given that the following equation of state
applies to this mixture
Vm=
RT
p
+B 11 x^21 +B 22 x^22 + 2B 12 x 1 x 2
wherex 1 is the mole fraction of carbon dioxide andx 2 is the mole fraction of hydrogen. The
second virial coefficients have the following values:B 11 =− 119 cm^3 mol−^1 , B 22 = 14cm^3 mol−^1
andB 12 =− 1 cm^3 mol−^1.
Solution
We calculate the fugacity coefficient using equation (6.85), and obtain the needed partial molar
volume of carbon dioxide from the equation of state and relation (6.52).
V 1 =
RT
p
+ (2B 12 −B 11 −B 22 )x^22 +B 11.
We integrate (6.85) to obtain
lnφ 1 =
∫p
0
[
Vi
RT
−
1
p
]
dp=
= [(2B 12 −B 11 −B 22 )x^22 +B 11 ]
p
RT
=
= [(− 2 ×1 + 119−14)× 0. 52 −119]×
1
8. 314 × 303. 15
=
= − 0. 026.
Henceφ 1 = 0. 974 , and for the fugacity of carbon dioxide we have
f 1 =φ 1 px 1 = 0. 974 × 1 × 0 .5 = 0. 487 MPa.
