Physical Chemistry Third Edition

9

Gas Kinetic Theory: The Molecular

Theory of Dilute Gases at Equilibrium

PRINCIPAL FACTS AND IDEAS

1. A model system that represents a dilute gas consists of randomly moving
   noninteracting point-mass particles that obey classical mechanics.


2. The mathematical analysis of the behavior of this model system includes
   averages over mechanical states of the molecules, using probability
   distributions.


3. The probability distribution for molecular velocities is the
   Maxwell–Boltzmann probability distribution:

(probability of a state of velocityv)∝e−mv

(^2) / 2 kBT

4. The probability distribution for molecular speeds is

(probability of a speedv)∝v^2 e−mv

(^2) / 2 kBT

5. The gas kinetic theory of noninteracting molecules predicts the ideal
   gas law.


6. The gas kinetic theory of noninteracting molecules predicts the rate of
   wall collisions and the rate of effusion of a dilute gas.


7. The molecules of real gases and liquids are fairly accurately described by
   a pair potential function that corresponds to intermolecular attractions at
   moderate distances and repulsions at short distances.


8. The second model of a dilute gas is the hard-sphere gas, which allows
   analysis of molecular collisions.


9. The properties of a liquid can be understood qualitatively in terms of
   intermolecular forces.

383