12
CHAPTER
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Thermodynamics
Gas Mixtures
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12-1
Dalton’s Law of Additive Pressures
for the Mixture of Two Ideal Gases
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12-2
Amagat’s Law of Additive Volumes
for the Mixture of Two Ideal Gases
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Thermodynamics
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Compressibility Factors: One Way of
Predicting Real-Gas Mixture P-v-T
(Fig. 12-8)
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Another Way of Predicting the P-vT Behavior of a Real-Gas Mixture
Treat a real-gas mixture as a pseudopure substance with critical
properties P´cr and T´cr
(Fig. 12-9)
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Thermodynamics
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12-5
Use of Partial Pressures for
Entropy Evaluation
Partial pressures (not the mixture pressure) are used in the
evaluation of entropy changes of ideal-gas mixtures
(Fig. 12-13)
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Thermodynamics
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12-6
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Chapter Summary
Thermodynamics
• A mixture of two or more gases of fixed chemical
composition is called a nonreacting gas mixture.
The composition of a gas mixture is described by
specifying either the mole fraction or the mass
fraction of each component, defined as
where
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12-7
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Chapter Summary
• The apparent (or average) molar mass and gas
constant of a mixture are expressed as
Thermodynamics
and
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12-8
Chapter Summary
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Thermodynamics
• Dalton's law of additive pressures states that the
pressure of a gas mix-ture is equal to the sum of
the pressures each gas would exert if it existed
alone at the mixture temperature and volume.
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12-9
Chapter Summary
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Thermodynamics
• Amagat's law of additive volumes states that the
volume of a gas mixture is equal to the sum of the
volumes each gas would occupy if it existed alone
at the mixture temperature and pressure.
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12-10
Chapter Summary
• Dalton's and Amagat's laws hold exactly for idealgas mixtures, but only approximately for real-gas
mixtures. They can be expressed as
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Thermodynamics
Dalton's law:
Amagat's law:
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12-11
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Chapter Summary
Thermodynamics
• Here Pi is called the component pressure and Vi is
called the component volume. Also, the ratio Pi/Pm
is called the pressure fraction and the ratio Vi/Vm
is called the volume fraction of component i. For
ideal gases, Pi and Vi can be related to yi by
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Chapter Summary
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Thermodynamics
• The quantity yiPm is called the partial pressure and
the quantity yiVm, is called the partial volume.
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Chapter Summary
Thermodynamics
• The P-v-T behavior of real-gas mixtures can be
predicted by using generalized compressibility
charts. The compressibility factor of the mixture
can be expressed in terms of the compressibility
factors of the individual gases as
where Z is determined either at Tm and Vm,
(Dalton's law) or at Tm and Pm (Amagat's law) for
each individual gas.
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12-14
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Chapter Summary
Thermodynamics
• The P-v-T behavior of a gas mixture can also be
predicted approximately by Kay's rule, which
involves treating a gas mixture as a pure
substance with pseudocritical properties
determined from
and
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12-15
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Chapter Summary
Thermodynamics
• The extensive properties of a gas mixture, in
general, can be determined by summing the
contributions of each component of the mixture.
The evaluation of intensive properties of a gas
mixture, however, involves averaging in terms of
mass or mole fractions:
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Chapter Summary
and
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Thermodynamics
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Chapter Summary
Thermodynamics
• These relations are applicable to both ideal- and
real-gas mixtures. The properties or property
changes of individual components can be
determined by using ideal-gas or real-gas
relations developed in earlier chapters.
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