7' Correlation of Liquid Phase Data SVNA 12'1

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7. Correlation of Liquid Phase Data SVNA 12.1

• The complexity of molecular interactions in
  non-ideal systems makes prediction of liquid
  phase properties very difficult.
• Experimentation on the system of interest at the
  conditions (P,T,composition) of interest is
  needed.
• Previously, we discussed the use of low-pressure
  VLE data for the calculation of liquid phase
  activity coefficients.
• As practicing engineers, you will rarely have the
  time to conduct your own experiments.
• You must rely on correlations of data developed
  by other researchers.
• These correlations are empirical models (with
  limited fundamental basis) that reduce
  experimental data to a mathematical equation.
• In CHEE 311, we examine BOTH the development of
  empirical models (thermodynamicists) and their
  applications (engineering practice).

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Correlation of Liquid Phase Data

• Recall our development of activity coefficients
  on the basis of the partial excess Gibbs energy
• where the partial molar Gibbs energy of the
  non-ideal model is provided by equation 10.42
• and the ideal solution chemical potential is
• Leaving us with the partial excess Gibbs energy
• (11.21)

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Correlation of Liquid Phase Data

• The partial excess Gibbs energy is defined by
• In terms of the activity coefficient,
• (11.96)
• Therefore, if as practicing engineers we have GE
  as a function of P,T, xn (usually in the form of
  a model equation) we can derive ?i.
• Conversely, if thermodynamicists measure ?i, they
  can calculate GE using the summability
  relationship for partial properties.
• (11.99)
• With this information, they can generate model
  equations that practicing engineers apply
  routinely.

4
Correlation of Liquid Phase Data

• We can now process this our MEK/toluene data one
  step further to give the excess Gibbs energy,
• GE/RT x1ln?1 x2ln?2

5
Correlation of Liquid Phase Data

• Note that GE/(RTx1x2) is reasonably represented
  by a linear function of x1 for this system. This
  is the foundation for correlating experimental
  activity coefficient data

6
Correlation of Liquid Phase Data

• The chloroform/1,4-dioxane system exhibits a
  negative deviation from Raoults Law.
• This low pressure VLE data can be processed in
  the same manner as the MEK/toluene system to
  yield both activity coefficients and the excess
  Gibbs energy of the overall system.

7
Correlation of Liquid Phase Data

• Note that in this example, the activity
  coefficients are less than one, and the excess
  Gibbs energy is negative.
• In spite of the obvious difference from the
  MEK/toluene system behaviour, the plot of
  GE/x1x2RT is well approximated by a line.

8
8.4 Models for the Excess Gibbs Energy

• Models that represent the excess Gibbs energy
  have several purposes
• they reduce experimental data down to a few
  parameters
• they facilitate computerized calculation of
  liquid phase properties by providing equations
  from tabulated data
• In some cases, we can use binary data (A-B, A-C,
  B-C) to calculate the properties of
  multi-component mixtures (A,B,C)
• A series of GE equations is derived from the
  Redlich/Kister expansion
• Equations of this form fit excess Gibbs energy
  data quite well. However, they are empirical and
  cannot be generalized for multi-component (3)
  mixtures or temperature.

9
Symmetric Equation for Binary Mixtures

• The simplest Redlich/Kister expansion results
  from CD0
• To calculate activity coefficients, we express GE
  in terms of moles n1 and n2.
• And through differentiation,
• we find