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**APPLICATIONS Applications of Raoult’s law**

Qualitative description of phase diagrams for mixtures

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**Raoult’s law Model the vapor phase as a mixture of ideal gases:**

Model the liquid phase as an ideal solution

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**VLE according to Raoult’s law:**

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**Acetonitrile (1)/nitromethane (2)**

Antoine equations for saturation pressures: Calculate P vs. x1 and P vs. y1 at 75 oC

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**Diagram is at constant T**

Bubble line 66.72 Dew line 0.75

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**Calculate the P-x-y diagram**

Knowing T and x1, calculate P and y1 Bubble pressure calculations

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**Diagram is at constant T**

59.74 0.43

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**Knowing T and y1, get P and x1**

Dew point calculation

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**In this diagram, the pressure**

is constant 78oC 0.51 0.67

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**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

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Given P and x1, get T and y1

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**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

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**In this diagram, the pressure**

is constant Dew points Bubble points 78oC 76.4 0.51 0.75

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**Knowing P and y, get T and x**

Start from point c last slide (70 kPa and y1= 0.6)

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**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

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79.6 0.44

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Ki = yi/xi Ki = Pisat/P

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Read Examples 10.4, 10.5, 10.6

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**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

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Flash calculations

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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

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**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?

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**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

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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.

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

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azeotrope This is a mixture of very dissimilar components

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**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

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**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)

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**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

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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

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**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

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**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

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