Thermodynamics and Chemistry

CHAPTER 9 MIXTURES

9.3 GASMIXTURES 243

When we equate these two expressions for^0 i^00 i, divide both sides byRT, subtract the
identity

ln

p^0

p^00

D

Zp 0

p^00

dp

p

(9.3.15)

and take the ideal-gas behavior limitsp^00! 0 andfi^00 !yip^00 D.p^0 i=p^0 /p^00 , we obtain

ln

fi^0

p^0 i

D

Zp 0

0



Vi

RT

1

p



dp (9.3.16)

(gas mixture, constantT)

The fugacity coefficientiof constituentiis defined by

fi defD ipi (9.3.17)

(gas mixture)

Accordingly, the fugacity coefficient at pressurep^0 is given by

lni.p^0 /D

Zp 0

0



Vi

RT

1

p



dp (9.3.18)

(gas mixture, constantT)

Asp^0 approaches zero, the integral in Eqs.9.3.16and9.3.18approaches zero,fi^0 ap-
proachespi^0 , andi.p^0 /approaches unity.

Partial molar quantities

By combining Eqs.9.3.12and9.3.16, we obtain

i.p^0 /Di(g)CRTln

p^0 i

p

C

Zp 0

0



Vi

RT

p



dp (9.3.19)

(gas mixture,

constantT)

which is the analogue for a gas mixture of Eq.7.9.2for a pure gas. Section7.9describes
the procedure needed to obtain formulas for various molar quantities of a pure gas from
Eq.7.9.2. By following a similar procedure with Eq.9.3.19, we obtain the formulas for
differences between partial molar and standard molar quantities of a constituent of a gas
mixture shown in the second column of Table9.1on the next page. These formulas are
obtained with the help of Eqs.9.2.46,9.2.48,9.2.50, and9.2.52.

Equation of state

The equation of state of a real gas mixture can be written as the virial equation

pV=nDRT



1 C

B

.V=n/

C

C

.V=n/^2

C



(9.3.20)

This equation is the same as Eq.2.2.2for a pure gas, except that the molar volumeVmis
replaced by the mean molar volumeV=n, and the virial coefficientsB; C; : : :depend on
composition as well as temperature.