Thermodynamics and Chemistry

CHAPTER 9 MIXTURES

9.6 EVALUATION OFACTIVITYCOEFFICIENTS 264

0:5 1

xB

400

f 200

=B

kPa

b

(a)

5

(^00) 0:01^0
2
4
6
8
0 0:5 1:0
mB=mol kg^1
fB
=kPa
b
(b)
0
0:5
1:0
0 0:01 0:02
xB
x
;B
(c)
0
0:5
1:0
0 0:5 1:0
mB=mol kg^1
m
;B
(d)
Figure 9.10 Dilute aqueous solutions of 1-butanol (B) at50:08C and 1 bar.a
(a)fBin an equilibrated gas phase as a function ofxB, measured up to the solubility
limit atxBD0:015. The dilute region is shown in a magnified view. Dashed line:
Henry’s law behavior on a mole fraction basis. Filled circle: solute reference state
based on mole fraction.
(b)fBas a function ofmB, measured up to the solubility limit atmBD0:85mol kg^1.
Dashed line: Henry’s law behavior on a molality basis. Filled circle: solute reference
state on this basis.
(c) Activity coefficient on a mole fraction basis as a function ofxB.
(d) Activity coefficient on a molality basis as a function ofmB.
aBased on data in Ref. [ 56 ].
linear extrapolation of the fugacity to the standard composition. The fugacityfBis quite
different in the two reference states. At the reference state indicated by a filled circle in
Fig.9.10(a),fBequals the Henry’s law constantkH,B; at the reference state in Fig.9.10(b),
fBequalskm;Bm. Note how the activity coefficients plotted in Figs.9.10(c) and9.10(d)
approach 1 at infinite dilution, in agreement with Eqs.9.5.22and9.5.24, and how they
vary as a linear function ofxBormBin the dilute solution as predicted by the theoretical
argument of Sec.9.5.4.

9.6.2 Activity coefficients from the Gibbs–Duhem equation

If component B of a binary liquid mixture has low volatility, it is not practical to use its fu-
gacity in a gas phase to evaluate its activity coefficient. If, however, component A is volatile