# APPLICATIONS Applications of Raoult’s law

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

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

VLE according to Raoult’s law:

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

Diagram is at constant T
Bubble line 66.72 Dew line 0.75

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

Diagram is at constant T
59.74 0.43

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

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

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

Given P and x1, get T and y1

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

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

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

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

79.6 0.44

Ki = yi/xi Ki = Pisat/P

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

Flash calculations

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

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?

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

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.

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

azeotrope This is a mixture of very dissimilar components

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

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)

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

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

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

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