Thermodynamics and Chemistry

CHAPTER 9 MIXTURES

9.3 GASMIXTURES 242

From Eqs.9.2.50,9.2.52,9.3.7, and9.3.9we obtain the relations

UiDUi (9.3.10)

(ideal gas mixture)

and

Cp;iDCp;i (9.3.11)

(ideal gas mixture)

Thus, in an ideal gas mixture the partial molar internal energy and the partial molar heat
capacity at constant pressure, like the partial molar enthalpy, are functions only ofT.

The definition of an ideal gas mixture given by Eq.9.3.5is consistent with the criteria

for an ideal gas listed at the beginning of Sec.3.5.1, as the following derivation shows.

From Eq.9.3.9and the additivity rule, we find the volume is given byVD

P

P iniViD

iniRT=pDnRT=p, which is the ideal gas equation. From Eq.9.3.10we have

U D

P

iniUi D

P

iniU



i, showing thatUis a function only ofT in a closed

system. These properties apply to any gas mixture obeying Eq.9.3.5, and they are the

properties that define an ideal gas according to Sec.3.5.1.

9.3.4 Real gas mixtures

Fugacity

The fugacityf of a pure gas is defined byD (g)CRTln.f=p/(Eq.7.8.7on
page 183 ). By analogy with this equation, the fugacityfiof substancei in a real gas
mixtureis defined by the relation

iDi(g)CRTln

fi

p

or fi

def

D pexp



ii(g)

RT



(9.3.12)

(gas mixture)

Just as the fugacity of a pure gas is a kind of effective pressure, the fugacity of a constituent
of a gas mixture is a kind of effectivepartialpressure. That is,fiis the partial pressure
substanceiwould have in an ideal gas mixture that is at the same temperature as the real
gas mixture and in which the chemical potential ofiis the same as in the real gas mixture.
To derive a relation allowing us to evaluatefifrom the pressure–volume properties
of the gaseous mixture, we follow the steps described for a pure gas in Sec.7.8.1. The
temperature and composition are constant. From Eq.9.3.12, the difference between the
chemical potentials of substanceiin the mixture at pressuresp^0 andp^00 is

^0 i^00 iDRTln

fi^0

fi^00

(9.3.13)

Integration of diDVidp(from Eq.9.2.49) between these pressures yields

^0 i^00 iD

Zp 0

p^00

Vidp (9.3.14)