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Minimum Boiling Point Azeotrope. Maximum Boiling Point Azeotrope. Single Equilibrium Stage – Ethanol-Water, P = 1 atm. V, y EtOH. Vapor. F, z EtOH. L, x EtOH. Liquid. F is the total moles of ethanol and water fed to the stage.

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single equilibrium stage ethanol water p 1 atm
Single Equilibrium Stage – Ethanol-Water, P = 1 atm

V, yEtOH

Vapor

F, zEtOH

L, xEtOH

Liquid

F is the total moles of ethanol and water fed to the stage.

V is the total moles in the vapor stream exiting the stage.

L is the total moles in the liquid stream exiting the stage.

zEtOH is the mole fraction of ethanol in the feed.

yEtOH is the mole fraction of ethanol in the vapor stream.

xEtOH is the mole fraction of ethanol in the liquid stream.

Lecture 4

feed mole fraction relationships
Feed Mole-Fraction Relationships
  • Note that a feed mole-fraction, zF,can be a subcooled liquid, a saturated liquid, a two-phase mixture, a saturated vapor, or a superheated vapor.
  • The feed phase is dependent upon the temperature, pressure, and the composition (mole fraction).

Lecture 4

z f and x y relationships
zF and x,y Relationships
  • Assuming that the equilibrium stage is at the same temperature and pressure of the feed:
  • If zF is a subcooled liquid, then zF is simply xF and there is no y.
  • If zF is a superheated vapor, zF is yF and there is no x.
  • If zF is a saturated liquid, zF is essentially xF with a single vapor bubble formed of new mole fraction y.
  • If zF is a saturated vapor, zF is essentially yF with a single liquid drop formed of new mole fraction x.
  • If zF is in the two-phase region, the system will separate into a liquid and vapor of new mole fractions x and y, respectively. zF is not equal to either x or y, but x and y be determined from the T vs. x,y data or plot.

Lecture 4

an initial way to investigate this equilibrium behavior
An Initial Way to Investigate this Equilibrium Behavior…
  • Another way to look at this behavior is to first look at a closed system at a particular pressure and initial temperature, and heat or cool the system at constant pressure and z mole fraction.
  • We can do this using the T vs. x,y plot…

Lecture 4

mass balance lever rule
Mass Balance – Lever Rule
  • Assume a two-phase mixture of known mole fraction is allowed to separate at constant temperature and pressure.
  • After a suitable period of time, the system will reach equilibrium.
  • The two-phase mixture at point A separates into the liquid at point B and vapor at point C along the isotherm, Tsys, as illustrated by:

Lecture 4

mass balance lever rule9
Mass Balance – Lever Rule

V, yC

Vapor

F, zA

L, xB

Liquid

Lecture 4

slide14

Temperature-Composition Diagram

for Ethanol-Water, P = 1 atm

100

95

Two Phase

Superheated Vapor Phase

90

C)

o

T(

85

80

Subcooled Liquid Phase

75

zEtOH

0.0

0.2

0.4

0.6

0.8

1.0

x

or y

EtOH

EtOH

Lecture 4

slide15

Temperature-Composition Diagram

for Ethanol-Water, P = 1 atm

100

V

95

Two Phase

Superheated Vapor Phase

≈V

90

L

V

C)

o

V

T(

L

85

≈L

80

L

Subcooled Liquid Phase

75

zEtOH

0.0

0.2

0.4

0.6

0.8

1.0

x

or y

EtOH

EtOH

Lecture 4

note for a two phase mixture
Note for a Two-Phase Mixture…
  • At vapor-liquid equilibrium, the temperatures of the vapor and liquid are equal.
  • When a two-phase mixture separates at vapor-liquid equilibrium conditions, the vapor phase will be at saturated vapor conditions and the liquid phase will be at saturated liquid conditions.
  • We will use this assumption when we do our multi-stage solutions – the vapor and liquid streams exiting a stage will be assumed to be at saturated conditions.
  • Thus, the liquid fed from one stage to another stage can be assumed to be a saturated liquid and the vapor feed to another stage can be assumed to be a saturated vapor.

Lecture 4

enthalpy vs composition ponchon savarit plot
Enthalpy vs. Composition – Ponchon-Savarit Plot
  • Presents the temperature equilibrium relationship for enthalpy vs. x and y.
  • Pressure is constant (note the units).
  • One normally plots the more volatile component.
  • Enthalpy will be required in future problems utilizing energy balances.
  • Note the units of concentration!

Lecture 4

tips for reading charts
Tips For Reading Charts
  • Use a clear ruler.
  • Photocopy and enlarge the diagrams.
  • Draw lines on the diagram to find intersection points.
  • Measure the scale in mm and convert to chart units.
  • E.g., What is the enthalpy of a (two phase) feed stream at 1 kg/cm2 pressure, 82°C, 0.6 wt% ethanol?
  • Measure 21 mm/100 kcal/kg. Intersection at 8.5 mm above 200 kcal/kg. H = 200 kcal/kg+(8.5mm/21mm)×100 kcal/kg=240.5 kcal/kg

Lecture 4