Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.1 MIXINGPROCESSES 310

bc

bc

bc

bc

b

b

0

(^0) xA 1
G
(mix)m
’
“
1
2
Figure 11.4 Molar Gibbs energy of mixing as a function of the composition of a
binary liquid mixture with spontaneous phase separation. The inflection points are
indicated by filled circles.
Molar excess Gibbs energies of real liquid mixtures are often found to be unsymmetric
functions. To represent them, a more general function is needed. A commonly used function
for a binary mixture is theRedlich–Kister seriesgiven by
GmEDxAxB



aCb.xAxB/Cc.xAxB/^2 C



(11.1.35)

where the parametersa; b; c;


depend onTandpbut not on composition. This function
satisfies a necessary condition for the dependence ofGmEon composition:GmEmust equal
zero when eitherxAorxBis zero.^6
For many binary liquid systems, the measured dependence ofGmEon composition is
reproduced reasonably well by the two-parameter Redlich–Kister series

GmEDxAxBå aCb.xAxB/ ç (11.1.36)

in which the parametersaandbare adjusted to fit the experimental data. The activity
coefficients in a mixture obeying this equation are found, from Eq.11.1.20, to be given by

RTln (^) ADx^2 Bå aC.34xB/b ç RTln (^) BDxA^2 å aC.4xA3/b ç (11.1.37)

11.1.6 Phase separation of a liquid mixture

A binary liquid mixture in a system maintained at constantT andpcan spontaneously
separate into two liquid layers if any part of the curve of a plot ofÅGm(mix) versusxAis
concave downward. To understand this phenomenon, consider Fig.11.4. This figure is a
plot ofÅGm(mix) versusxA. It has the form needed to evaluate the quantities.AA/
and.BB/by the variant of the method of intercepts described on page 233. On this

(^6) The reason for this condition can be seen by looking at Eq.11.1.19on page 306. For a binary mixture, this
equation becomesGmEDRT .xAln (^) ACxBln (^) B/. WhenxAis zero, (^) Bis 1 and ln (^) Bis zero. WhenxBis
zero, (^) Ais 1 and ln (^) Ais zero. ThusGEmmust be zero in both cases.