Presentation is loading. Please wait.

Presentation is loading. Please wait.

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

Similar presentations


Presentation on theme: "APPLICATIONS Applications of Raoult’s law Qualitative description of phase diagrams for mixtures."— Presentation transcript:

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

2

3

4

5

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. x 1 and P vs. y 1 at 75 o C

9 Bubble line Dew line Diagram is at constant T

10 Calculate the P-x-y diagram Bubble pressure calculations Knowing T and x 1, calculate P and y 1

11 Diagram is at constant T

12 Knowing T and y 1, get P and x 1 Dew point calculation

13 In this diagram, the pressure is constant 78 o C

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

15 Given P and x 1, get T and y 1

16 Iterate to find T, then calculate y 1 Estimate P 1 sat /P 2 sat using a guess T Then calculate P 2 sat from (III) Then get T from (I) Compare calculated T with guessed T (I) (II) (III) Finally, y 1 = P 1 sat x 1 /P and y 2 = 1-y 2

17 In this diagram, the pressure is constant 78 o C Dew points Bubble points

18 Knowing P and y, get T and x Start from point c last slide (70 kPa and y 1 = 0.6)

19 Iterate to find T, and then calculate x Estimate P 1 sat /P 2 sat using a guess T Then calculate P 1 sat from (III) And then get T from (I) (I) (II) (III) x 1 = Py 1 /P 1 sat

20

21 K i = y i /x i K i = P i sat /P

22 Read Examples 10.4, 10.5, 10.6

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

24 Flash calculations

25 F=2-  +N For a binary F=4-  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

26

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 Fraction of the overall system that is liquid 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

29

30 Class exercise From Figure 10.5, take P = 800 psia and generate a table T, x 1, y 1. 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, x 1 = 0.771, we don’t know y 1 (leave it empty for now). Continue for all the points at P = 800 psia. Once the table is complete, graph T vs. x 1, y 1. 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)

32

33 This is a mixture of very dissimilar components azeotrope

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 x 1 =y 1 Is called an azeotrope The P-x curve in (c) lies above Raoult’s law; in this case there are weaker intermolecular attractions between unlike than between like molecular pairs; it could end as L-L immiscibility This behavior may result in a maximum point as in (d), where x 1 =y 1, 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)

36

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 25 o C and 1 atm T c air << 25 o C

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 25 o C and 1 atm. First calculate y 2 (for water, assuming that air does not dissolve in water) Then calculate x 1 (for air, applying Henry’s law) See also Example 10.2

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


Download ppt "APPLICATIONS Applications of Raoult’s law Qualitative description of phase diagrams for mixtures."

Similar presentations


Ads by Google