Physical Chemistry
Lecture 1
Equations of State for Gases
Matter is described by properties.
Microscopic
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Speed
Force
Size
Shape
Energy
Macroscopic
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Temperature
Pressure
Viscosity
Heat capacity
Macroscopic properties
Extensive
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Depends on amount
of material
Mass
Volume
Total energy
Total heat capacity
Intensive
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Not dependent on
amount of material
Temperature
Pressure
Molar mass
Electrical
conductivity
Specific heat
Density
Equation of state
System
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Part of the world being
observed
State
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Condition of a system
Described by values of
properties
Equation of state
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Determines the relation
between properties at
accessible states
Plot of accessible states
Equations of state for gases
Gases are extremely compressible, which is
reflected in an equation of state
First approximation – ideal-gas law
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Combination of Boyle’s Law and Gay-Lussac’s Law
Relates intensive variables
Vm = RT/P
R = 8.31451 joule/K-mol, a universal constant
Works reasonably well under “normal” conditions
Ideal-gas law
Describes most gases at low pressures
and high temperatures
Assumptions
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Noninteracting molecules
Molecules are point particles, no volume
Elastic collisions with system walls (i.e. no
energy exchange with the surroundings at
equilibrium)
Empirical gas laws
Try to “correct” the ideal-gas law to relax
assumptions
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Excluded volume of molecules
Intermolecular interactions
Empirical equations based on “fitting” of
experimental PVT data, i.e. not derived from
theory
Some have modest theoretical bases for
modifications to the ideal-gas law
The result is only as good as the assumptions
underlying it
Van der Waals gas law
Empirical
Accounts for “excluded
volume”
Accounts for “attractive
forces”
First “real-gas law”
(P+a/Vm2)(Vm-b)=RT
Third-order equation
Care must be exercised
in calculation
Multiply-valued function
of P at some T
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Which is the “right” Vm
Empirical gas laws
Van der Waals equation, third order in molar volume
Redlich-Kwong equation, third order in molar volume
1/2)(V (V +b))-1
 P = RT/(Vm-b) – (a/T
m m
Berthelot equation, third order in molar volume
2
 P = RT/(Vm-b) – (a/TVm )
Dieterici equation
 P = (RT/Vm) exp(-a/RTVm)
Beattie-Bridgman equation
Peng-Robinson equation
Each tries to emulate experimental data
All fail to reproduce behavior under some conditions
Gas laws
Gas laws can be quite accurate in predicting
the behavior of gases, even though every one
is an approximation of the actual behavior
One must not use gas-law calculations
indiscriminately; a chemist or engineer must
have the experience to know when to use a
particular equation of state and when not
Gas laws DO NOT apply to solids and liquids