Page 90 - Separation process principles 2

2.6 Activity-Coefficient Models for the Liquid Phase 55

(68.9 Wa) and Pi = 14.7 psia (101.3 kPa). Also from
Figure 2.16, yy = 21.72 when y2 = 1.0. Thus, ypO/y2 =
21.72, but Pi/ Pf = 1.47. Therefore, a minimum-boiling
azeotrope will occur.
Maximum-boiling azeotropes are less common. They
occur for relatively close-boiling mixtures when negative
deviations from Raoult's law arise such that yi < 1 .O. Crite-
ria for their formation are derived in a manner similar to that
for minimum-boiling azeotropes. At xl = 1, where species 2
is more volatile,

and

For an azeotropic binary system, the two binary interac-
tion parameters A12 and A21 can be determined by solving
(4) of Table 2.9 at the azeotropic composition, as shown in
the following example. Xethanol
Figure 2.19 Liquid-phase activity coefficients for ethanol/
n-hexane system.
EXAMPLE 2.8
From measurements by Sinor and Weber [35] of the azeotropic greater than the value of 21.72 obtained by Orye and Prausnitz [36]
condition for the ethanolln-hexane system at 1 atm (101.3 kPa, from a fit of all experimental data points. However, if Figures 2.16
14.696 psia), calculate A 12 and Azl. and 2.19 are compared, it is seen that widely differing yr values
have little effect on y in the composition region XE = 0.15 to 1.00,
where the two sets of Wilson curves are almost identical. For accu-
SOLUTZON
racy over the entire composition range, commensurate with the
Let E denote ethanol and H denote n-hexane. The azeotrope occurs ability of the Wilson equation, data for at least three well-spaced
at XE = 0.332, x~ = 0.668, and T= 58°C (331.15 K). At 1 atrn, liquid compositions per binary are preferred.
(2-69) can be used to approximate K-values. Thus, at azeotropic
conditions, y, = PI PiS. The vapor pressures at 58°C are Pi = 6.26
The Wilson equation can be extended to liquid-liquid or
psia and Pi = 10.28 psia. Therefore,
vapor-liquid-liquid systems by multiplying the right-hand
side of (2-78) by a third binary-pair constant evaluated from
experimental data [37]. However, for multicomponent sys-
tems of three or more species, the third binary-pair constants
must be the same for all constituent binary pairs. Further-
more, as shown by Hiranuma [40], representation of ternary
Substituting these values together with the above corresponding
systems involving only one partially miscible binary pair
values of xi into the binary form of the Wilson equation in Table 2.9 can be extremely sensitive to the third binary-pair Wilson
gives
constant. For these reasons, application of the Wilson equa-
tion to liquid-liquid systems has not been widespread.
Rather, the success of the Wilson equation for prediction of
activity coefficients for miscible liquid systems greatly stim-
ulated further development of the local-composition concept
of Wilson in an effort to obtain more universal expressions
for liquid-phase activity coefficients.

Solving these two nonlinear equations simultaneously by an itera-
tive procedure, we obtain AEH = 0.041 and AHE = 0.281. From NRTL Model
these constants, the activity-coefficient curves can be predicted if
The nonrandom, two-liquid (NRTL) equation developed by
the temperature variations of AEH and AHE are ignored. The results
are plotted in Figure 2.19. The fit of experimental data is good Renon and Prausnitz [41,42] as listed in Table 2.9, repre-
except, perhaps, for near-infinite-dilution conditions, where sents an accepted extension of Wilson's concept. The NRTL
yp = 49.82 and yp = 9.28. The former value is considerably equation is applicable to multicomponent vapor-liquid,