Chemical Equilibrium(2)

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Chemical Equilibrium(2)

• Lecture Note 19
• Physical Chemistry II, 2008
• KAIST

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26-8. Equilibrium constants in terms of partition
functions
(chemical equilibrium - chemical potential
partition function)

• For a gas phase reaction

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KP in terms of partition function Q and thus q
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K from Q and q, polyatomic molecule
Better agreement with experimentexpected Improved
spectroscopic constant Relaxation of
rigid-rotator and H.O. Molecular interaction
(nonideal gas)
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• More accurate estimate of equilibrium constants
  require better partition functions including
  corrections to rigid-rotator and
  harmonic-oscillator models and also to non
  ideality
• Many tables and databases of partition function
  and other thermodynamic properties are available
• Contains experimentally determined quantities
  sometimes supplemented with theoretical
  calculations
• Popular places
• Many commercial or public chemical databases(DBs)
• NIST web site
• Journal publications and monographs
• Journal of Physical Chemical reference Data

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D0 calculation from JANAF table
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• Pure gas f0 1
  for an ideal gas at 1 bar
• A component in a mixture
• nonideality

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Fugacity instead of pressure for real gases
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The f rather than P behave more like ideal gas P
! as expected?
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Fugacity coefficient is a measure of nonideality
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(activity for solution is fugacity for gas)

• For a general mixture

Std 1 Raoult Std 2 Henry Std 3 Ideal Gas
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Lewis equation express Gibbs energy change in
terms of activities
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Thermodynamic Equilibrium constant for the
general reaction system
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Example of explicitly considering activity of
pure solid
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(Electrolyte solution deviate from ideality even
at dilution)
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All activity coefficients unity
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Activity coefficients not unity
Solve by iteration
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For solubility, activity coefficients matters
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Enhanced solubility by salt in solution due to
the increased ionic strength
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Summary

• We know how to evaluate thermodynamic quantities
  for ideal gas and solutions (simple mixtures)
  from the EOS and the laws of thermodynamics
• Connection to molecular properties is mainly
  through ideal gas partition functions
  (molecular-partition-function-to-grand-partition-f
  unction is easy for the ideal gas)
• Correction to nonideality relies mostly on
  experimental data using various formal relations
  such as Maxwell relations
• Special attention to standard states to get
  numerically correct values