8. Dilute Liquid Solutions SVNA 10.4,12.1

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8. Dilute Liquid Solutions SVNA 10.4,12.1

• There are many non-ideal systems in which one
  component is significantly more volatile than
  others. In these cases, the liquid phase is very
  rich in the heavy components, and lean in the
  light component.
• The most common system encountered in
  environmental and biochemical engineering is H2O
  (1) / O2 (2).
• The very low O2 content found in the liquid phase
  under practical engineering conditions allows us
  to simplify phase equilibrium calculations
• for H2O
• for O2
• Since the origin of most non-ideal behaviour is
  found in the liquid, we will focus on
  simplifications to liquid phase properties.

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Rigorous Treatment of Liquid Mixture Fugacity

• Shown is a plot of the mixture fugacities of MEK
  (1) and Toluene (2) at 50C as a function of
  liquid composition
• For component 1, MEK
• For component 2, Toluene

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Dilute Liquid Solution Approximations

• This figure illustrates the fugacity of a
  component in a liquid mixture.
• Note that the Lewis-Randall rule applies for the
  predominant component of a liquid solution
• x1?1 ?1 ?1, f1l ? f1l x1
• If the component is present in very small amounts
  (x1 lt 0.02), its mixture fugacity can be
  approximated by a linear relationship, such that
• x1?0 f1l ? k1x1

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Dilute Solution Simplifications Heavy Component

• For the heavy component (1) of a dilute solution,
  we can apply the Lewis-Randall rule
• The equilibrium relationship for the heavy
  component (such as H2O in the water-oxygen
  system) becomes
• or,
• or,
• for the predominant component in solution
  (x1gt0.98)

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Dilute Solution Simplifications Light Component

• For the light component (2) of a dilute liquid
  solution, we create a new construct, the Henrys
  constant, k2
• (12.2)
• This is the slope of the f2l vs x2 curve as x2 ?
  0.
• The Henrys constant is tabulated for a specific
  system at a given temperature.
• The equilibrium relationship for the light
  component (such as O2 in the water-oxygen system)
  becomes
• where the Henrys constant, k2 is that of oxygen
  in water at the temperature of interest.

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Dilute Liquid Solution Approximations Example 1

• Suppose we are designing a bioreactor in which
  pure O2 is bubbled through an aqueous medium to
  replenish the oxygen consumed by the cell
  culture.
• The process is operated at atmospheric pressure
  and a temperature of 25C.
• How do we define a thermodynamic system that
  provides relevant phase equilibrium data?
• What is the concentration of oxygen in the liquid
  phase, given a Henrys Coefficient, kO2 4400
  MPa at 25C?

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Dilute Liquid Solution Approximations Example 2

• As a research engineer in a hydrogenation plant,
  you are asked to compile VLE data on the H2 /
  chlorobenzene system in a way that plant
  engineers can readily apply.
• The objective is to conduct VLE experiments on
  the system, treat the data according to
  thermodynamic theory, and summarize the results
  in a simple manner.
• How will you start?
• What simplifications can be made?
• In what form will you summarize the data?