Chapter 10 Vapor Liquid Equilibrium

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Chapter 10Vapor Liquid Equilibrium

• Phase equilibrium distillation, absorption, and
  extraction.
• Phase equilibrium, what happened ?
• Phase are not in equilibrium, what happened?
• Quantitative treatment of mass transfer, the
  equilibrium T, P, and phase composition must be
  known.

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The Nature of Equilibrium

• Criteria for Equilibrium
• Clausius inequality ds ? 0
• S is maximum at a true equilibrium state.
• S can only increase or decrease in value during
  the system approaching to equilibrium ?

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Equilibrium at Constant Energy and Volume
(Isolated System)

• ?Q 0, ?W 0
• The 2nd law dS gt 0 for actual process (natural
  change)
• S can only increase, S is maximum at a true
  equilibrium state. The system is no longer
  change.
• S must have its maximum possible value.

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Equilibrium at Constant Temperature and Volume

• Constant T, TdS d(TS)
• Constant volume dU ?Q
• The 2nd law dU lt d(TS)
• d(U-TS) lt 0
• The important of these terms U TS, is
  important enough to have its own name and symbol.
  
• Helmholtz energy, A U TS
• dA 0 for equilibrium, and dA lt 0 for actual
  process.
• At equilibrium, A attains its minimum value.

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Equilibrium at Constant Temperature and Pressure

• Most often interest
• Constant pressure dH ?Q
• The 2nd law dH ? d(TS)
• d(H-TS) ? 0
• The important of these terms H TS, is
  important enough to have its own name and symbol.
  
• Gibbs energy, G H TS
• dG 0 for equilibrium, and dG lt 0 for actual
  process.
• At equilibrium, G attains its minimum value.

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• Criteria for Equilibrium
• Clausius inequality ds ? 0
• A and G are constant or
• dS 0
• dA 0
• dG 0

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• How can we assure that the system is in
  equilibrium state ?
• dS 0 is a necessary but not sufficient
  condition for S to achieve a maximum value.
• d2S lt 0 when dS 0 assure that a maximum value
  of the S, or a TRUE equilibrium state..Stability

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• Isolated, adiabatic fixed-boundary system
• Constraint U constant, V constant
• Equilibrium criterion
  S maximum,
  dS 0
• Stability criterion
  d2S lt 0

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• Isothermal closed system with fixed boundaries
• Constraint T constant, V constant
• Equilibrium criterion
  A minimum,
  dA 0
• Stability criterion
  d2A gt 0

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• Isothermal, isobaric closed system
• Constraint T constant, P constant
• Equilibrium criterion
  G minimum,
  dG 0
• Stability criterion
  d2G gt 0

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• Isothermal, isobaric open system moving with the
  fluid velocity
• Constraint T constant, P constant
  
  
• m constant
  
• Equilibrium criterion
  G minimum,
  dG 0
• Stability criterion
  d2G gt 0

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• The Nature of Equilibrium
• Static condition, no changes occur in the
  macroscopic properties of a system with time.
• At the microscopic level, conditions are not
  static.

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Stable equilibrium any deflection causes motion
back towards equilibrium position.
State of Equilibrium

• Winterbone, Advanced Thermodynamics for Engineers,

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State of Equilibrium
Unstable equilibrium any movement causes further
movement from equilibrium position.
Meta-stable equilibrium infinitesimally
variations of position cause return to
equilibrium, larger variations cause movement to
lower position.

• Winterbone, Advanced Thermodynamics for Engineers,

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Stable equilibrium any deflection causes motion
back towards equilibrium position.
Helmholtz Energy A U-TS A indicates the
maximum work that can be obtained from a system.
It can be seen that A lt U, and TS is a measure of
the unavailable energy.Gibbs Energy (Gibbs
potential, Gibbs function H U-TS G indicates
the maximum useful work that can be obtained from
a system. It can be seen that G lt H , and TS is a
measure of the unavailable energy.

• Winterbone, Advanced Thermodynamics for Engineers,

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• The Phase Rule.
• Intensive state of a P V T system containing N
  chemical species and ? phases.
• In each phase T, P and N 1 2 (N - 1)
• For ? phase 2 ? (N - 1)
• For N species and each pair of phases, the
  independent phase equilibrium equations is
  (? - 1) (N)
• F 2 ? (N - 1) - (? - 1) (N )
• F 2 - ? N (J. Willard
  Gibbs, 1875)

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• Vapor Liquid Equilibrium VLE
• 2 chemical species, 2 phases (liquid and vapor)
• N 2, ? 2
• F 2 - ? N 2 2 2 2
• The intensive properties of the system is 2.
• PT diagram
• Pxy diagram
• Txy diagram

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• System of variable composition ideal behavior
• Vapor phase ideal gas mixture
• Liquid phase ideal solution
• Benzene - Toluene

CH3
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• VLE
• The goal is to find by calculation the T, P and
  compositions of phase in equilibrium.
• The two simple behavior of systems are Raoults
  law and Henrys law.

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• Pxy diagram and Txy diagram
• acetonitrile (1) / nitromethane (2) as given by
  Raoults law.

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Bubblepoint
dewpoint
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dewpoint
Bubblepoint
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• Raoults law
• The vapor phase is an ideal gas.
  This law can be applied only for low to
  moderate pressure.
• The liquid phase is an ideal solution.
• This law is approximately validity only when the
  species that comprise the system are chemically
  similar i.e. the molecular species are not too
  different in size and are of the same chemical
  nature.
• The validity of Raoults law is at x close to 1.

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• Raoults law

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• Raoults law

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• Raoults law

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• Raoults law

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• Dewpoint and Bubblepoint calculation with
  Raoults law
• Bulb P Calculate yi and P, given xi and T
• Dew P Calculate xi and P, given yi and T
• Bulb T Calculate yi and T, given xi and P
• Dew T Calculate xi and T, given yi and P

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• Example 1 (10.2)
• Assuming the Raoults law to be valid, prepare a
  P-x-y diagram for a temperature of 90 ?C and a
  t-x-y diagram for a pressure of 90 kPa for bezene
  (1) / ethylbenzene (2).

CH2-CH3
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• Raoults law
• Given 1 benzene, 2 ethylbenzene
• At T 90 ?C, calculate P1sat and P2sat.

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Subcooled liquid
Superheated vapor
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• At given P 90 kPa, we cannot solve t
  explicitly.
• The temperature range is bounded by the
  saturation pressure t1sat and t2sat at P 90
  kPa.
• Guess t between t1sat and t2sat, calculate P1sat
  and P2sat from Antoine equation, then calculate
  x1 and y1 from

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Superheated vapor
Subcooled liquid
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• Fractional distillation

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• Non-ideal solution

The attractive forces between the unlike
molecules are weaker than the attractive forces
between the like molecules.
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• Positive deviation from Raoults law

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• Non-ideal solution

The attractive forces between the unlike
molecules are stronger than the attractive forces
between The like molecules.
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• Negative deviation from Raoults law

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• Modified Raoults Law
• ?i activity coefficient

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• Activity Coefficient
• Activity Coefficient is a function of
  temperature and liquid phase composition e.g.

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• VLE From K Value Correlations
• Ki yi / xi
• K-value is a measure of a lightness of a
  constituent species, i.e., of its tendency to
  favor the vapor phase.
• Ki gt 1 , species i exhibits a higher
  concentration in the vapor phase,
• Ki lt 1 species i exhibits a higher concentration
  in the liquid phase, and is considered a heavy
  constituent.

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• VLE From K Value Correlations
• Relative volatility

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• K Value Correlations

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• How can we know that the system is azeotrope?

Check the value of alpha at x10 and x1 1. If
alpha does not pass through 1.0 for 0lt x1 lt1,
there is no azeotrope.
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• Henrys Law
• In the case that chemical constituents in the
  liquid phase is very small or dilute, Raoults
  cannot be applied. This happens when this specie
  has its critical temperature lower than the
  operating pressure e.g. air dissolves in water.

Where Hi is Henrys constant
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• Henrys Law

Calculate the solubility of N2 gas in water at
25ºC and 4.0 atm pressure. Henry's law constants
for nitrogen gas in water is 6.51 107 Torr.
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• Flash Calculation
• From Pxy diagram. Starting from the liquid
  phase, if we reduce the pressure, what happen?
  The liquid starts to evaporates or flashes. Two
  phase are in equilibrium. (L moles of liquid
  and V moles of vapor)
• L V 1
• zi xiL yiV xi(1-V) yiV