1. Vapor-Liquid Equilibrium (VLE) at Low Pressures
Chapter 8

2. Why study VLE?
Many chemical and environmental processes involve vapor-liquid equilibria
Drying
Distillation
Evaporation

3. Consider the ammonia production process discussed in Chapter 1
N2 + 3 H2 ⇋ 2NH3
Liquid Ammonia
3 moles H2 1 mole N2
Recycled Product Ammonia and unreacted feed
Chiller Condenses most of the ammonia
Separator
Reactor partially converts H2 and N2 to NH3
Bleed Stream
~15% conversion
Controlled by VLE
NH3 vapor+ N2 and H2
+ N2 and H2

4. Most of what we’ve discussed so far in the course is VLE
Raoult’s law is a vapor-liquid equilibrium estimating equation
Henry’s law is vapor-liquid equilibrium estimating equation
The biggest use of VLE analysis is in distillation
Check out the great picture in the text book – page 160
Distillation is separation by boiling point

5. Distillation Columns

6. Simple VLE Measurement Device

7. Othmer Still

8. Some standard conventions used in VLE
The lowest-boiling component (most volatile) is usually called species a.
The next lowest is species b etc.
Tables are arranged similarly

9. Data from Table 8.1
Boiling Temp
Mole Fraction Acetone in Liquid
Mole Fraction Acetone in Vapor
100
74.8
0.05
0.6381
68.53
0.1
0.7301
65.26
0.15
0.7716
63.59
0.2
0.7916
61.87
0.3
0.8124
60.75
0.4
0.8269
59.95
0.5
0.8387
59.12
0.6
0.8532
58.29
0.7
0.8712
57.49
0.8
0.895
56.68
0.9
0.9335
56.3
0.95
0.9627
56.15 1
This data is used in examples 8.1 to 8.3, and is plotted on the next slide

10. Equilibrium Curve
If all we ever dealt with were binary systems, and if tables like the one used to create this figure were available for all combinations of species, we wouldn’t need VLE correlations
Reference Curve
Lowest boiling point component

11. For Multispecies systems, there is no simple graph we can make
The K factor can be used to help solve this problem
Relative volatility is an additional approach

12. Relative Volatility, a
K, acetone
If a is greater than 1.5 to 2 over the whole range of composition, then distillation is almost always the cheapest separation technique
K, water

13. Mathematical Treatment of Low-Pressure VLE
The tables and graphs we’ve just looked at are easy to interpret
It would be nice if we could calculate values, instead of reading them off graphs

14. Our starting point is that the fugacity of the gas phase equals the fugacity of the liquid phase
For ideal gases the activity coefficient is one 1
For gases we usually choose the total pressure as the standard fugacity
For liquids we usually choose the pure component partial pressure as the standard fugacity

15. The activity coefficient of the liquid phase
Partial pressure of the gas
In example 8.2, we use this equation to find the activity coeffients for water and for acetone at a number of concentrations

16. Example 8.2
The pure component vapor pressures are a function of temperature, and can be calculated from the Antoine equation at the appropriate boiling points.

18. Raoult’s Law
If we rearrange this equation, we find…
Which is the same as Raoult’s law, except for the activity coefficient. Raoult’s law applies to ideal solutions, where the activity coefficient is one.
The acetone water system is not ideal, since the calculated activity coefficients are not one!!

19. How much would we be off if we assumed ideal solution behavior for acetone?
At 1 atm and
Xacetone=0.05
Experimental values from Table 8.1
Calculated values using g=1
Equilibrium boiling temperature
74.8
96.4
Mole fraction acetone in the vapor phase
0.6381
0.1656
The calculational details are in Example 8.3

20. The Four most common types of Low Pressure VLE
Ideal Solution Behavior
Positive Deviations from Ideal Solution Behavior
Negative Deviations from Ideal Solution Behavior
Two-Liquid Phase --Heteroazeotropes

21. Ideal Solution Behavior – Type I behavior The activity coefficient of both species is one at all concentrations – Figure 8.7b
Consider a benzene-toluene system
The two species are very similar chemically, and behave as an ideal solution
Benzene has the lower boiling, and therefore the higher vapor pressure
gBenzene=gToluene=1
Activity Coefficient, g
At any P and T
Mole fraction of benzene in the liquid phase, xa

22. Ideal Solution Behavior
Since the activity coefficients of both species is one, they both follow Raoult’s law
Pressure, torr 1
Mole fraction of benzene in the liquid phase, xa

23. Ideal Solution Behavior Figure 8.7a
PTotal
Pressure, torr – at 90 C
PBenzene
PToluene
Mole fraction of benzene in the liquid phase, xa

24. Ideal Solution Behavior Figure 8.7c
Not to Scale
For an ideal solution, the mole fraction of the most volatile component, is always higher in the gas than in the liquid
Equilibrium curve
Mole fraction of benzene in the liquid phase
Reference curve
Mole fraction of benzene in the liquid phase, xa

25. Ideal Solution Behavior Figure 8.7 d
Not to Scale
If we heat a mixture of benzene and toluene, the temperature where it starts to boil is called the bubble point
The combined partial pressures equal 1 atm
Temperature, C
Bubble Point
Mole fraction of benzene in the liquid or vapor phase, xa

26. Ideal Solution Behavior Figure 8.7 d
Not to Scale
If we cool a mixture of benzene and toluene vapor, the temperature where it starts to condense is called the dew point
The combined partial pressures equal 1 atm
Dew Point
Temperature, C
Bubble Point
Mole fraction of benzene in the liquid or vapor phase, xa

27. Dew Point
Temperature, C
Bubble Point
Temperature at the bubble point
Vapor Phase composition at the bubble point
Heat a liquid mixture until it starts to boil
Liquid Phase composition at the dew point
Mole fraction of benzene in the liquid or vapor phase, xa

28. Now let’s look at non-ideal solution behavior
First let’s attack positive deviations from ideal solution behavior (Type II behavior)
The activity coefficients of both (or all) species is greater than one.
The acetone water system is an example of this behavior
So is the isopropanol-water system shown in Figure 8.8

29. Type II behavior of activity coefficients – always greater than 1
Notice that the behavior of each species approaches ideal (g=1) as it’s concentration increases
Not to Scale P=1 atm
gisopropanol
Activity Coefficient, g
gwater
Pure isopropanol
Figure 8.8 b
Pure water
Mole fraction of isopropanol in the liquid phase, xa

30. Type II behavior
Not to Scale
Activity coefficients greater than 1 mean that the partial pressure of the vapor is greater than that predicted with Raoult’s law
1000
800
600
400
200
Actual isopropanol partial pressure
Pressure, torr – at 84 C
Predicted with g=1
Mole fraction of isopropanol in the liquid or vapor phase, xa

31. Type II behavior
Not to Scale
Activity coefficients greater than 1 mean that the partial pressure of the vapor is greater than that predicted with Raoult’s law
1000
800
600
400
200
Pressure, torr – at 84 C
Actual water partial pressure
Predicted with g=1
Mole fraction of isopropanol in the liquid or vapor phase, xa

32. Type II behavior Figure 8.8 a
Not to Scale
In this case (but not every type II case) the total pressure curve (at constant temperature) displays a maximum, which produces a minimum boiling azeotrope.
1000
800
600
400
200
Total pressure
isopropanol partial pressure
Pressure, torr – at 84 C
water partial pressure
Mole fraction of isopropanol in the liquid or vapor phase, xa

33. Type II Solution Behavior Figure 8.8c
Not to Scale
When the total pressure displays a maximum, the equilibrium curve crosses the reference curve
Azeotrope
Equilibrium curve
Mole fraction of isopropanol in the vapor phase
Reference curve
Mole fraction of isopropanol in the liquid phase, xa

34. Azeotropes
Not to Scale
At an azeotrope, the liquid and vapor have the same concentration
Azeotrope
Mole fraction of isopropanol in the liquid phase
Mole fraction of isopropanol in the liquid phase, xa

35. Type II Solution Behavior
Not to Scale
At mole fractions below the azeotrope, almost pure water, and the azeotropic composition can be distilled
At mole fractions above the azeotrope, almost pure isopropanol and the azeotropic composition can be distilled
Azeotrope
Dew Point Curve
Temperature , C
Bubble Point Curve
Mole fraction of isopropanol in the liquid phase, xa

36. Type II Solution Behavior
Type II solutions do not necessarily exhibit an azeotrope
For example, the acetone-water system does not
Two factors contribute to this behavior
Difference in boiling point
Deviation from ideal behavior

37. Type III Behavior g for both species is less than 1
Similar to Type II – just insert maximum for minimum etc
Consider the acetone-chloroform system

38. Type III behavior of activity coefficients – always less than 1
Notice that the behavior of each species approaches ideal (g=1) as it’s concentration increases
Not to Scale P=1 atm
gchloroform
Activity Coefficient, g
gacetone
Figure 8.9 b
Pure chloroform
Pure acetone
Mole fraction of acetone in the liquid phase, xa

39. Type III behavior
Not to Scale
Activity coefficients less than 1 mean that the partial pressure of the vapor is less than that predicted with Raoult’s law
1000
800
600
400
200
Predicted with g=1
Pressure, torr – at 60 C
Actual acetone partial pressure
Mole fraction of acetone in the liquid or vapor phase, xa

40. Type III behavior
Not to Scale
Activity coefficients less than 1 mean that the partial pressure of the vapor is less than that predicted with Raoult’s law
1000
800
600
400
200
Predicted with g=1
Pressure, torr – at60 C
Actual chloroform partial pressure
Mole fraction of acetone in the liquid or vapor phase, xa

41. Type III behavior Figure 8.9 a
Not to Scale
In this case (but not every type III case) the total pressure curve (at constant temperature) displays a minimum, which produces a maximum boiling azeotrope.
1000
800
600
400
200
Total pressure
Actual acetone partial pressure
Pressure, torr – at 60 C
Actual chloroform partial pressure
Mole fraction of acetone in the liquid or vapor phase, xa

42. Type III Solution Behavior Figure 8.9c
Not to Scale
When the total pressure displays a minimum, the equilibrium curve crosses the reference curve
Equilibrium curve
Azeotrope
Reference curve
Mole fraction of acetone iin the vapor phase
Mole fraction of acetone in the liquid phase, xa

43. Azeotropes
Not to Scale
At an azeotrope, the liquid and vapor have the same concentration
Equilibrium curve
Azeotrope
Mole fraction of acetone iin the vapor phase
Mole fraction of acetone in the liquid phase, xa

44. Type II Solution Behavior
Not to Scale
At mole fractions below the azeotrope, almost pure chloroform, and the azeotropic composition can be distilled
At mole fractions above the azeotrope, almost pure chloroform and the azeotropic composition can be distilled
Azeotrope
Dew Point Curve
Temperature , C
Bubble Point Curve
Mole fraction of acetone in the liquid phase, xa

45. What controls whether the activity coefficients are greater or less than one?
When g>1 it indicates that the solution species are repelled by each other, or at least are more attracted to themselves than to the other species
When g<1 it indicates that the solution species are more attracted to each other than to their own kind

46. More about azeotropes
For a given degree of mutual attraction or repulsion, an azeotrope is more likely for species with a small difference in boiling point
For pairs of compounds with the same difference in boiling point, an azeotrope is more likely for the pair whose activity coefficients deviate from one by the largest amounts

47. Binary azeotropes between compounds with wide differences in boiling point are rare
Most azeotropes are of the minimum boiling type (over 90%)

48. Type IV Behavior Two Liquid Phase --Heteroazeotropes
Type II behavior occurs when two species repel each other
For a moderately strong repulsion an azeotrope forms
If the repulsion is strong enough, the two liquids actually separate into two separate phases

49. For example Consider the water and butanol system
Between 65% water and 98% water, two phases occur
At less than 65% water only a single phase exists
At greater than 98% water only a single phase occurs

50. Water-butanol system From 0 to 65% water one phase exists
Between these values, two phases exist – one of 65% water and one of 98% water
2 phases
1 phase
1 phase
Mole fraction water

51. In the single phase region…
The solution exhibits Type II behavior
Mole fraction of water in the liquid phase, xa
Activity Coefficient, g

52. Type IV Behavior Pressure behavior
In the two phase region the total pressure is the sum of the pressure from each phase
However, both phases must be exposed to the gas phase
Total Pressure
Partial Pressure of water
Pressure, torr – at 90 C
Partial Pressure of n-butanol
Mole fraction of water in the liquid phase, xa

53. Type IV Vapor-Liquid Equilibrium
The composition of the gas phase stays constant when two liquid phases are present
Equilibrium Curve
Mole fraction of water in the vapor phase
Reference Line
Mole fraction of water in the liquid phase(s), xa

54. Type IV Bubble Points and Dew Points
Call the n-butanol rich phase L1
Call the water rich phase L2
Vapor Phase
Dew Point Curve
Temperature , C
Vapor + L1
Vapor + L2 L2
Bubble Point Curve L1
L1 + L2
Mole fraction of water in the liquid phase, xa

55. Boiling is necessary for this behavior
The predicted behavior will only occur if both phases are in contact with the gas phase
Realistically this only occurs during boiling
This type of behavior is common in petroleum refining
Liquid Phase I
Liquid Phase II
Gas Phase

56. Steam Distillation
If we take type IV behavior to the extreme, we consider two liquids that are essentially completely immiscible
For example water and mercury
In this case we are always in the two phase region

57. The total pressure is the sum of the pure component vapor pressures
Consider example 8.7
If n-butanol and water were completely insoluable, what would the boiling point be at one atm?
What would the composition of the vapor be?

58. Estimate the partial pressures of each component with the Antoine Equation
Solve for T iteratively
T=89 0C

59. At the boiling point of 89 C
PH20 = 0.67 atm
Pn-butanol= 0.33 atm
Compare these results to Figure 8.12
Remember that butanol and water actually do exhibit considerable solubility

61. Distillation of the Four Types of Behavior
For systems that do not have an azeotrope, distillation columns can produce practically pure products
The highest vapor pressure component is separated into the overhead component
The lower vapor pressure component is separated into the bottoms

62. Gas-Liquid Equilibrium – Henry’s Law
In the previous discussions, both components could exist as a pure liquid at the temperatures of interest
In other words we were interested in vapor-liquid equilibria
How can we extend this discussion to include gas-liquid equilibria, for species that do not condense
Use Henry’s Law

63. Our discussions so far have been about systems at low pressure
At low pressures, the gas phase obeys the ideal gas law
At higher pressures we’ll need to consider the fugacity coefficient in our calculations
At both low and moderate pressures (up to ~1/2 the critical pressure) we won’t need to adjust our liquid phase calculations

64. Low Pressure VLE Calculations
Graphs are great to get a general idea of how systems behave, but they aren’t very accurate
We need to develop a standard approach to calculate vapor-liquid equilibrium properties

65. At low pressures the fugacity coefficients are 1 – but the liquid phase activity coefficients aren’t
Estimate them using the Van Laar equation
There are other estimating equations – this one is just easy to use -- the basis for the Van Laar equation is developed in chapter 9

66. The 6 Most Common VLE Calculations
Find the dew point, for a known temperature
Find the dew point, for a known pressure
Find the bubble point for a known temperature
Find the bubble point for a known pressure
Isothermal flash calculations
Adiabatic flash calculations
These are all examples problems that can be formulated as equilibrium flash calculations

67. Flash Calculations V F T, P L
F can be a liquid, a gas or a two phase mixture
Vapour F
T, P
This is called a flash calculation, because if the pressure is reduced enough, the liquid changes to vapor in a “flash”
Liquid L

68. To solve any of these problems we need to identify our equations and unknowns -- Table 8.6
Material Balances
Summation of mole fractions
Remember from Process Engineering that you can write n independent material balances, if you have n components

69. More equations to be solved
Equilibrium
Vapor Pressure equations
Antoine equation is probably the most accurate of the simple equations
Simplified version assuming ideal gas

70. More equations to be solved
Calculate the activity coefficients
Van Laar equation is simplest analytical approach
Energy balance
Adiabatic flashes

71. We also need the inlet conditions
Feed specification xi
Temperature
Pressure

72. Let’s do some example calculations Dew Point – Example 8.9
Estimate the boiling pressure and the composition of the vapor in equilibrium with a liquid that is:
mol fraction ethanol
remainder water
85.3 oC

73. First – Use Antoine’s equation to find the pure component partial pressures at this temperature
At 85.3 C, Pwater= atm PEtOH=1.3088

74. Second Find Activity Coefficients
Use the Van Laar Equation
Find the values of A and B for water and ethanol in Table A.7
gwater= gEtOH=2.9235

75. Next Calculate the partial pressures
Similarly for Ethanol…
and…

76. Finally Find the vapor phase mole fractions

77. Pressure Specified Calculations are Similar
They are harder, because the Temperature appears in the Antoine Equation
They need to be solved interatively

78. Calculational Steps Guess a Temperature
Calculate the Pure Component Vapor Pressures
Calculate the activity coefficients
Calculate the partial pressures
Calculate the total pressure, and compare to the given pressure

79. Graphical Solution
Add Figure 8.17

80. Bubble Point Calculations
Mirror image of Dew Point Calculations
Temperature specified calculations are easier
Pressure specified calculations require an iterative approach

81. Isothermal Flash Calculations
Both T and P are specified
The division of mass between liquid and vapor is unknown
Consider Example 8.13
An ethanol-water mixture
xaFeed=0.126
is brought to equilibrium at
1 atm
91.8 C
Estimate the vapor fraction and the mole fraction of each species in the vapor phase

82. Let’s Solve it Graphically First
Add figure 8.19

83. Analytical Solution Find the pure component vapor pressures
Assume a value for V/F
Estimate the activity coefficients
Calculate the K factors
Use a material balance to find the mole fractions in the vapor and liquid phase

84. Divide by F
Equation 8.12

85. Adiabatic Flash Calculations
In addition to the equations from the previous example, you need an energy balance
You must “guess” a temperature, then perform the calculations, and finally check to see if the energy balance requirements are met

86. Solutions using K factor approximating tools
Activity coefficients are functions of T,P and x (the liquid composition)
Thus, K is also a function of T,P and the liquid composition
By ignoring the contribution of composition, DePreister created Figure 8.20 – an estimating tool for finding K

87. K factor chart

88. Colligative Properties – Another application of Raoult’s Law
Boiling Point elevation
Freezing Point depression
Osmosis (Chapter 14)
Predictable using Raoult’s Law

89. What happens as the concentration of the solvent approaches 1?
The solvent activity coefficient, g, approaches 1
Thus for dilute solutions of anything the solution obeys Raoult’s law
The identity of the solute doesn’t matter, as long as it’s a dilute solution and it’s not volatile!!

90. Boiling Point Elevation
When the solute has a very high boiling point, the solution vapor pressure only depends on the solvent

91. Boiling Occurs when the vapor pressure equals the pressure of the surroundings
Example 8.15
One mole of sucrose (MW=342.3 g/mole) is dissolved in 1000 g of water
What is the vapor pressure of this solution at 100 0C?
Boiling won’t occur, unless you’re at an altitude above sea level

92. What temperature will cause boiling?
First – determine what pure component vapor pressure is required
From the steam tables we find T= C – or a boiling point elevation of C

93. We can approximate the behavior of this solution at low concentrations of solute
The change in boiling point is directly proportional to the molality of the solution

94. Figure 8.22

95. Freezing Point Depression
Just as adding a non-volatile solute increases the boiling point, it also decreases the freezing point
See Example 8.16