ECHE 311/SPRING 2015
Problem Set #10
The Gamma/Phi Formulation of VLE
1. Assuming Raoult’s law to be valid for the system acetonitrile (1)/nitromethane (2)
(a) Prepare Pxy diagram for a temperature of 100oC.
(b) Prepare a txy diagram for a pressure of 101.33 kPa
sat
Vapor pressure of pure species are given by the following Antoine equations ( Pi
in
kPa and t in oC )
ln P1sat  14.2724 
2,945.47
t  224.00
ln P2sat  14.2043 
2,972.64
t  209.00
.
2. Prepare a Pxy diagram for a temperature of 90oC and txy diagram for a pressure of 90
kPa for the system bezene (1)/ethylenbenzene (2). Vapor pressure of pure species are
given by Antoine equation (use Table 1 which lists parameter values for the Antoine
equation.)
3. Assuming Raoult’s law to apply to the system n-pentane (1)/n-heptane (2)
1
y1 at t=55oC and P= ( P1sat  P2sat ) ? For
2
these conditions plot the fraction of the system that is vapor V vs overall
composition z1 .
(a) What are the values of x1 and
Hint:
P1sat , P2sat

Use Antoine Eqs. to calculate

Since for Raoult’s law P is linear in x, at the specified
0.5
Find y1 for x1 =0.5


and
P.
P, x1
must be
For given pressure, the overall composition z1 ranges from the liquid
composition at the bubble point to the vapor composition at the dew
point. Material balance is
V is obviously linear
in
z1  x1 (1  V )  y1V ; V ( z1 ) 
( z1  x1, x1  0.01.. y )
z1 ;
;
 Plot V ( z1 ) vs z1 .
4. Assuming Raoult’s law to apply to the same system as in P .3 [ n-pentane (1)/n-heptane
(2)]. Plot
Hint:

P , x1 , and y1
At fixed
T
vs V .
and
z1 , calculate x1 , y1 and P
as a function of fraction vapor
(V )
z1 =0.5 ;

Guess:
P1sat (T )  P2sat (T )
x  0 . 5 ; y  0. 5 ; P =
2
Eqs. which relate x1 ,
y1 and P
for given (V ) are:
P  xP1sat (T )  (1  x) P2sat (T )

yP  xP1sat (T )
z1  (1  V ) x  Vy
Plot x1 , y1 and P as a function of
fraction vapor (V )
V=0.0.1..1.0
5. A liquid mixture of cyclohexanone (1)/phenol(2) for which x1 =0.6 is in equilibrium
with its vapor at 144oC, determine the equilibrium pressure P and vapor pressure
composition y1 from the following information:
G E / RT  A(T ) x1 x2
At 144oC
P1sat =75.20 and P2sat  31.66kPa
az
The system forms an azeotrope at 144oC for which x1
Hint:

At the azeotrope x1 = y1 and  1 =
P
Pi sat
 y1az  0.294

 2 P1sat
Therefore

 1 P2sat

Calculate the coefficient A
;
x1 and x2
are defined
ln  1  Ax 2 2 ; ln  2  Ax12 ;
ln(
P2sat
)
2
P1sat
2
2
ln( )  A( x1  x2 ); A  2
1
x2  x12

Evaluate the values for A,  1 and
P y1 .
2
using above equations and calculate