Thermodynamics and Chemistry

CHAPTER 9 MIXTURES

9.6 EVALUATION OFACTIVITYCOEFFICIENTS 263

b

bc

bc fA

xAfA

0 0:2 0:4 0:6 0:8 1:0

0

2

4

6

8

xA

fA

=kPa

(a)

bc

0 0:2 0:4 0:6 0:8 1:0

0

1

2

3

4

xA

A

(b)

Figure 9.9 Liquid mixtures of ethanol (A) and H 2 O at 25 C and 1 bar.

(a) Ethanol fugacity as a function of mixture composition. The dashed line is Raoult’s

law behavior, and the filled circle is the pure-liquid reference state.

(b) Ethanol activity coefficient as a function of mixture composition.

Table 9.4 Activity coefficients as functions of fugac-

ity. For a constituent of a condensed-phase mixture,fi,

fA, andfBrefer to the fugacity in a gas phase equili-

brated with the condensed phase.

Substance Activity coefficient

Substanceiin a gas mixture iD

fi

pi

Substanceiin a liquid or solid

mixture

(^) iD
fi
xifi
Solvent A of a solution (^) AD
fA
xAfA
Solute B, mole fraction basis (^) x;BD
fB
kH,BxB
Solute B, concentration basis (^) c;BD
fB
kc;BcB
Solute B, molality basis (^) m;BD
fB
km;BmB
Figure9.9(b) shows how (^) Avaries with composition. The open circle is atxAD0:4
and (^) ADfA=.xAfA/. Note how (^) Aapproaches 1 asxAapproaches 1 , as it must according
to Eq.9.5.20.
Water and 1-butanol are two liquids that do not mix in all proportions; that is, 1-butanol
has limited solubility in water. Figures9.10(a) and9.10(b) on the next page show the
fugacity of 1-butanol plotted as functions of both mole fraction and molality. The figures
demonstrate how, treating 1-butanol as a solute, we locate the solute reference state by a