# Assignment ```ECHE 311/SPRING 2015
Problem Set #8
VLE Calculations
1.
The excess Gibbs energy of the binary liquid mixture at T and P is given by:
GE/RT = (-2.6 x1-1.8 x2) x1x2
For the given T and P,
a) Find expression for ln  1 and ln  2 .
b) Show that when these expressions are combined in accord with Eq.
GE
  xi ln  i the given equation for GE/RT is recovered.
RT
i
c) Show that these expressions satisfy the Gibs/Duhem equation  xi d ln  i  0 .
d) Show that ( d ln  1 / dx1 ) x 1 =( d ln  2 / dx1 ) x  0 =0
1
1
i
Hint: a) Substitute x2=1-x1

b) Apply Eqs. M 1  M  x 2

dM
dM
&amp; Eq. M 2  M  x1
dx1
dx1
for
M=GE/RT
GE
d(
)
GE
RT
ln  1 
 (1  x1 )
RT
dx1
; define
ln  2
GE
d(
)
RT
Find
dx1
Find ln  1 and ln  2
2. Plot values of GERT, ln  1 and ln  2 calculated by the given equation for
GE/RT and by the equations developed in problem (a) vs x1 .
1
3. For a ternary solution at constant T and P, the composition dependence of molar
property M is given by:
M  x1M1  x2 M 2  x3 M 3  x1x2 x 3 C
where M1 , M2 and M3 are the values of M for pure species, 1, 2, and 3 and C is a

parameter independent of composition. Determine the expression for
application of equation

Mi [
 (nM
] P,T ,n j
ni

4. Equations analogous to Eqs

M 2  M  x1
dM
dx1
property with respect to
written for
ln  1 and
M 1  M  x2
and
ln  i is a partial
G E / RT , these analogous equations can be
ln  2 in a binary system.
ln  1  A12 (1 
ln  2  A21 (1 
dM
dx1
apply for excess properties. Since
Write these equations, and apply them to
that Eqs
M 2 by
GE
A12 A21

x1x2 A12 x1  A21x2
A12 x1  2
)
A21x2
A21x2  2
)
A12 x1
and
are indeed obtained.
2
to show
5. The following is a set of VLE data for the system methanol(1)/water(2) at 333oK
______________________________
P/kPa
x1
y1
__________________________
19.953
39.223
42.984
48.852
52.784
56.652
60.614
63.998
67.924
70.229
72.832
84.562
0.0000
0.1686
0.2167
0.3039
0.3681
0.4461
0.5282
0.6044
0.6804
0.7255
0.7776
1.0000
0.0000
0.5714
0.6268
0.6943
0.7345
0.7742
0.8085
0.8383
0.8733
0.8922
0.9141
1.0000
a) Basing calculations on Eq.
i 
yi P
yP
 i sat
xi fi xi Pi
find parameter values for
G E / RT
the Margules equation that provide the best fit of
to the data, and
prepare a Pxy diagram that compares the experimental points with curves
determined from the correlation.
3
```