Kinetic Molecular Theory (KMT) of Gases

1
Kinetic Molecular Theory (KMT) of Gases

• KMT is a model to explain the behavior of gaseous
  particles and is based on extensive observations
  of the behavior of gases.
• If a gas follows all the postulates of the KMT it
  is said to be an ideal gas.

2
Postulates of the KMT

• Particles are in constant, random, straight line
  motion. Collisions with walls of their container
  generate pressure.
• The actual volume of gas particles is negligible.
  Particles are far apart. The volume of a gas is
  effectively the volume the particles occupy, not
  their particle volume.

3
Postulates of the KMT

• Gas particles do not attract or repel.
• The average kinetic energy of a collection of gas
  particles is directly proportional to the Kelvin
  temperature of the gas.

4
Ideal vs Real Gases

• How do gas volumes respond under a range of
  conditions (such as changing pressures and
  temperatures)?
• If a gas is ideal, the graph of PV/RT vs P for
  one mole of gas will have a slope of 1.
• http//intro.chem.okstate.edu/1314F97/Chapter10/Re
  alGas.html

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Deviations from Ideality

• For an ideal gas
• PV nRT or V nRT/P
• When you actually measure gas volume at high
  pressures and low temperatures, the Vexperimental
  often does not match Vtheoretical

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Deviations from Ideality

• Why doesnt Vexp Vtheor ?
• If Vexp gt Vtheor
• ?Some gas particles do repel each other so volume
  is greater than predicted.
• ?Gas particles do have a volume so volume cannot
  be reduced beyond a certain point.

7
Deviations from Ideality

• Why doesnt Vexp Vtheor ?
• If Vexp lt Vtheor
• ?Some gas particles do attract each other so
  volume is reduced more than expected.

8
Corrections for Deviations from Ideality

• Johannes van der Waals modified the ideal gas law
  to account for deviations.
• P x V nRT
• Pexp a(n/V)2 x (V-nb) nRT
• ?Pexp a(n/V)2 corrects for attractive or
  repulsive forces (a depends on the particle)
• ?V-nb corrects for particle volume (b is a
  measure of particle volume)

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Selected Values for a and b for the van der Waals
Equation
Gas Formula a (L2 atm)/mole2 b L/mole
Helium He 0.03412 0.02370
Hydrogen H2 0.2444 0.02661
Nitrogen N2 1.390 0.03913
Oxygen O2 1.360 0.03183
Carbon dioxide CO2 3.592 0.04267
Acetylene C2H2 4.390 0.05136
Chlorine Cl2 6.493 0.05622
n - Butane C4H10 14.47 0.1226
n - Octane C8H18 37.32 0.2368