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Chapter 6: Kinetic Theory of Gases

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Three postulates of the Kinetic Theory
  1. Gases consist of particles (atoms or molecules) in continuous, random motion.
  2. Collisions between gas particles are elastic.
  3. The average energy of translational motion of a gas particle is directly proportional to temperature.
In addition to the postulates above, it is assumed that the volumes of the particles are negligible as compared to container volume and attractive forces between particles are neglected.

Et = average kinetic energy of translation
m = mass of the particle
u = average velocity of the particle

from the third postulate we can formulate

T = temperature in Kelvin, c = constant which has the same value for all gases.
KEavg = 3/2 RT

  1. Average Speed of Gas particles (find u)

    c = constant =
    R = gas constant, NA = Avogadro's #
    substituting for c

    mass times moles (NA) equals Molar Mass (MM), substituting MM and solving for u gives

    using this last equation we can solve for an individual gas particle's speed rms = root mean square, which is the average square root of the speed of the individual particles.
    Use R = 8.3148 J / mol K, in order for the units to come out in m/s

  2. Grahm's Law
    Grahm's Law

    effusion - the flow of gas particles through a small opening or pinhole in a container.
    diffusion - random motion of gas particles.

    if the two gases are at the same temperature then:

    Experimentally usually measure the time for effusion to occur, this time is an inverse of the effusion rate (lower times-faster effusion rates)

    this equation was used for the separation of U238 during WWII by effusion principles.

Real Gases
Deviate at least slightly from Ideal Gas Law because of two factors:

  1. gas molecules attract one another
  2. gas molecules occupy a finite volume

Both of these factors are neglected in the Ideal Gas law. Both increase in importance when molecules are close together (high P, low T)

van der Walls equation

corrects for the attraction between molecules.
nb     corrects for the volume of gas molecules
van der Walls constants are given on page 217
(a and b) for above equation.

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