Enthalpy vs. Composition

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Enthalpy vs. Composition Ponchon-Savarit
Plot

• We have begun to employ mass balances, both total
  and component.
• We will also need to employ energy balances,
  based on enthalpy, for certain separation
  problems.
• We can use the Enthalpy vs. composition plot to
  obtain this information.

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Enthalpy vs. Composition Ponchon-Savarit Plot
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Enthalpy vs. Composition Ponchon-Savarit
Plot

• 3 phases are shown on the plot solid, liquid,
  and vapor.
• Temperature is represented by isothermal tie
  lines between the saturated liquid (boiling) line
  and the saturated vapor (dew) line.
• Points between the saturated liquid line and the
  saturated vapor line represent a two-phase,
  liquid-vapor system.
• An azeotrope is indicated by the composition at
  which the isotherm becomes vertical. Why?
• Why are the boiling point temperatures of the
  pure components different than those determined
  from the y vs. x and T vs. x,y plots for
  ethanol-water?
• The azeotrope for ethanol-water is indicated as T
  77.65 oC and a concentration of 0.955. Why is
  this different than that determined from the y
  vs. x and T vs. x,y plots for ethanol-water?

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Enthalpy vs. Composition Ponchon-Savarit
Plot

• Note the boiling temperatures of the pure
  components, water and ethanol, and the
  temperature of the azeotrope are different due to
  the pressure at which the data was taken
• P 1 kg/cm2 (0.97 atm) 1 atm
• Water 99.1 oC 100 oC
• Ethanol 77.8 78.30
• Azeotrope 77.65 78.15

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Mole Fraction vs. Weight Fraction

• Note that the enthalpy- composition plot is
  presented in terms of weight fractions we will
  typically use mole fractions so one must convert
  between the two.
• For ethanol-water, this can be readily done using
  the molecular weights, MWEtOH 46.07 and MWw
  18.02.

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Azetrope Composition Mole Fraction
vs. Weight Fraction

• Converting from wt fraction of the azeotrope to
  mole fraction
• Thus, the azeotropic mole fraction is greater at
  P 1 Kg/cm2 than at 1 atm 0.902 vs. 0.8943.
• Although slight, one can begin to see the effect
  of pressure on the azeotropic point.

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Converting Weight Fraction to Mole Fraction In
General

• For a binary mixture
• For a mixture of C components

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Enthalpy vs. Composition Ponchon-Savarit
Plot

• The bubble point temperature and dew point
  temperatures can be determined from the enthalpy
  vs. composition plot.
• The compositions of the 1st bubble formed and the
  last liquid drop can be determined from the
  enthalpy vs. composition plot.
• An auxiliary line is used to assist in these
  determinations

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Enthalpy vs. Composition Bubble Point
Temperature
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Enthalpy vs. Composition 1st Bubble
Composition
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Enthalpy vs. Composition Dew Point
Temperature
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Enthalpy vs. Composition Last Liquid Drop
Composition
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Enthalpy vs. Composition Enthalpy
Determination

• The major purpose of an enthalpy diagram is to
  determine enthalpies.
• We will use enthalpies in energy balances later.
• For example, if one were given a feed mixture of
  35 ethanol (weight ) at T 92oC and P 1
  kg/cm2 and the mixture was allowed to separate
  into vapor and liquid, what would be the
  enthalpies of the feed, vapor, and liquid?

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Enthalpy vs. Composition Enthalpy
Determination
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Equilibrium Data How to Handle?

• Tabular Data
• Generate graphical plots
• Generate analytical expressions (curve fit)
• Graphical
• y vs. x (P constant) McCabe-Theile Pot
• T vs. x,y (P constant) Saturated Liquid, Vapor
  Plot
• Enthalpy vs. composition (P constant, T)
  Ponchon-Savarit Plot
• Analytical expressions
• Thermodynamics Equations of state/Gibbs free
  energy models
• Distribution coefficients, K values
• Relative volatility
• DePreister charts
• Curve fit of data

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Analytical Expressions for Equilibrium

• To date, we have looked at various ways to
  represent equilibrium behavior of binary systems
  graphically.
• There are several disadvantages to using
  graphical techniques
• One cannot readily plot multi-component systems
  graphically (maximum is typically three).
• Separator design often has to be done using
  numerical methods thus, analytical expressions
  for equilibrium behavior are needed.
• We will now look at other representations for
  handling equilibrium data analytically

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Other Equilibrium Relationships
Distribution Coefficient
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Other Equilibrium Relationships DePriester
Charts

• One convenient source of K values for
  hydrocarbons, as a function of temperature and
  pressure (watch units), are the DePriester charts
  (Figs. 2-11 and 2-12, pp. 24-25, Wankat).
• The DePriester plots are presented over two
  different temperature ranges.

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Using DePriester Charts Boiling Temperatures
of Pure Components

• One can determine the boiling point for a given
  component and pressure directly from the
  DePriester Charts one can then determine which
  component in a mixture is the more volatile the
  lower the boiling point, the more volatile a
  component is.
• For a pure component, K 1.0.
• Assume one wishes to determine the boiling point
  temperature of ethylene at a pressure of P 3000
  kPa

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Tbp - 9.5 oC
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Question DePriester Charts

• What are the equilibrium distribution
  coefficients, K, for a mixture containing
• Ethylene
• n-Pentane
• n-Heptane
• at T 120 oC and P 1500 kPa?

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Answer DePriester Charts

• The equilibrium distribution coefficients, K,
  are
• K
• Ethylene 8.5
• n-Pentane 0.64
• n-Heptane 0.17
• at T 120 oC and P 1500 kPa.

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Question Volatility

• What can one say about the volatility of each
  component from the K values?
• K
• Ethylene 8.5
• n-Pentane 0.64
• n-Heptane 0.17

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Answer Volatility

• What can one say about the volatility of each
  component from the K values?
• K T boiling
• Ethylene 8.5 -35.5 oC
• n-Pentane 0.64 153 oC
• n-Heptane 0.17 gt200 oC
• The boiling point temperatures of the pure
  components at P 1500 kPa have also been
  determined from the DePriester charts for K 1.0
  for each component (n-heptanes is off the
  chart).
• From the K values and the boiling point
  temperature of each pure component, one can say
  that the volatility follows the trend that
  ethylenegtn-pentanegtn-heptane.

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Other Equilibrium Relationships DePriester
Equation
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Other Equilibrium Relationships Mole Fraction
Vapor Pressure Relationship
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Other Equilibrium Relationships Distribution
Coefficient Vapor Pressure Relationship
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Other Equilibrium Relationships Relative
Volatility
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Other Equilibrium Relationships Relative
Volatility