1. APPLICATIONS Applications of Raoult’s law
Qualitative description of phase diagrams for mixtures

6. Raoult’s law Model the vapor phase as a mixture of ideal gases:
Model the liquid phase as an ideal solution

7. VLE according to Raoult’s law:

8. Acetonitrile (1)/nitromethane (2)
Antoine equations for saturation pressures:
Calculate P vs. x1 and P vs. y1 at 75 oC

9. Diagram is at constant T
Bubble line
66.72
Dew line
0.75

10. Calculate the P-x-y diagram
Knowing T and x1, calculate P and y1
Bubble pressure calculations

11. Diagram is at constant T
59.74
0.43

12. Knowing T and y1, get P and x1
Dew point calculation

13. In this diagram, the pressure
is constant
78oC
0.51
0.67

14. Calculate a T-x1-y1 diagram
(1)
Given P and y1 solve
for T and x1
(2)
Why is this temperature
a reasonable guess?
get the two saturation temperatures
Then select a temperature from the range between
T1sat and T2sat
At the selected T,
summing (1) and (2) solve for x1

15. Given P and x1, get T and y1

16. Iterate to find T, then calculate y1
(II)
(III)
Estimate P1sat/P2sat using a guess T
Then calculate P2sat from (III)
Then get T from (I)
Compare calculated T with guessed T
Finally, y1 = P1sat x1/P and y2 = 1-y2

17. In this diagram, the pressure
is constant
Dew points
Bubble
points
78oC
76.4
0.51
0.75

18. Knowing P and y, get T and x
Start from point c last slide (70 kPa and y1= 0.6)

19. Iterate to find T, and then calculate x
Estimate P1sat/P2sat using a guess T
Then calculate P1sat from (III)
And then get T from (I)
(II)
(III)
x1= Py1/P1sat

20. 79.6
0.44

21. Ki = yi/xi
Ki = Pisat/P

22. Read
Examples
10.4, 10.5, 10.6

23. Flash Problem mass balance: L + V =1 V, {yi} mass balance component i
T and P
mass balance component i
zi = xi L + yi V for i = 1, 2, …n
zi = xi (1-V) + yi V
1 mol of
L-V mixture
overall
composition {zi}
Using Ki values, Ki = yi/xi
xi= yi /Ki;
yi = zi Ki/[1 + V(Ki -1)]
L, {xi}
read and work examples 10.5 and 10.6

24. Flash calculations

25. F=2-p+N
For a binary
F=4-p
For one phase:
P, T, x (or y)
Subcooled-liquid
above the upper
surface
Superheated-vapor
below the under surface
L is a bubble point
W is a dew point
LV is a tie-line
Line of critical points

27. Each interior loop represents the PT
behavior of a mixture of fixed composition
In a pure component, the bubble and dew
lines coincide
What happens at points A and B?
Critical point of a mixture is the point where
the nose of a loop is tangent to the envelope
curve
Tc and Pc are functions of
composition, and do not necessarily
coincide with the highest T and P
How do we calculate a P-T envelope?

28. At the left of C, reduction
of P leads to vaporization
At F, reduction in P leads to
condensation and then
vaporization (retrograde
condensation)
Important in the operation of
deep natural-gas wells
At constant pressure,
retrograde vaporization
may occur
Fraction of the
overall system
that is liquid

30. Class exercise
From Figure 10.5, take P = 800 psia and generate a table T, x1, y1. We call ethane component 1 and heptane component 2. In the table complete all the T, x1, y1 entries that you can based on Figure For example, at T= 150 F, x1 = 0.771, we don’t know y1 (leave it empty for now). Continue for all the points at P = 800 psia. Once the table is complete, graph T vs. x1, y1. Also fill in the empty cells in the table reading the values from the graph.

31. Minimum and maximum of
the more volatile species
obtainable by distillation
at this pressure
(these are mixture CPs)

33. azeotrope
This is a mixture of very dissimilar
components

34. The P-x curve in (a) lies below
Raoult’s law; in this case there are stronger
intermolecular attractions between unlike
than between like molecular pairs
This behavior may result in a minimum
point as in (b), where x1=y1
Is called an azeotrope
The P-x curve in (c) lies above Raoult’s
law; in this case there are weaker
than between like molecular pairs; it could
end as L-L immiscibility
This behavior may result in a maximum
point as in (d), where x1=y1, it is also
an azeotrope

35. Usually distillation is carried
out at constant P
Minimum-P azeotrope is a
maximum-T (maximum boiling)
Point (case b)
Maximum-P azeotrope is a
minimum-T (minimum boiling)
Point (case d)

37. Limitations of Raoult’s law
When a component critical temperature is < T,
the saturation pressure is not defined.
Example: air + liquid water; what is in the vapor phase?
And in the liquid?
Calculate the mole fraction of air in water at 25oC and 1 atm
Tc air << 25oC

38. Henry’s law
For a species present at infinite dilution in the liquid phase,
The partial pressure of that species in the vapor phase is
directly proportional to the liquid mole fraction
Henry’s constant

39. Calculate the mole fraction of air in water at 25oC and 1 atm.
First calculate y2 (for water, assuming that air does not dissolve in water)
Then calculate x1 (for air, applying Henry’s law)
See also Example 10.2

40. Modified Raoult’s law Fugacity vapor Fugacity liquid
g is the activity coefficient, a function of composition and
temperature
It corrects for non-idealities in the Liquid phase