Lesson 2 - Kinetic Molecular Theory of Gases

Written and Composed 

by Ms. Nabeela

Lecturer (Assistant Director)

 at GIK College  Topi

 KINETIC MOLECULAR THEORY OF GASES:

           Introduction: The physical behavior and properties of gases can be theoretically explained using
           kinetic
           theory. The physical behavior of gases described by gas laws and other observations was explored
           in 18th and 19th century. A theory known as Kinetic Molecular Theory was later developed to
           explain the behavior of gases.
           History: A Swiss Mathematician, Daniel Bernoulli in 1738 presented this theory. Later this theory was
           explained and elaborated by a number of scientists. This theory led Clausius (1857) to derive a
           kinetic
           gas equation, and then he proved all the gas laws from it. Considerable work was also done
           BY Maxwell in 1859 and Boltzmann in 1870. Vander Waal also extended this theory.
           Postulates: This theory is based upon the following postulates:
    a.    Gases are considered to be composed of minute discrete particles called Molecules.
    b.    There are large empty spaces between the gas molecules.
    c.    The molecules move randomly in straight line until they collide with one another or with the walls
           of container.
    d.    When molecules collide with one another, the collision is perfectly elastic. (collision in which kinetic
           energy of the particle remain constant)
    e.    The molecules of a gas are thought to be of same size and mass but different from gas to gas.
    f.    Due to the motion and collision of gas molecules with one another, pressure is exerted.
    g.    The average kinetic energy of a molecule is directly proportional to the absolute temperature.
           i.e K.E  α  Temperature
    h.    At a very low pressure, the average distances between molecules are large as compared to the
          molecular diameter.
    i.    There are no attractive or repulsive forces between gas molecules.
    j.    The volume occupied by the gas molecules is negligible as compared to the total volume of the
          container.
    k.    The force of gravity has almost no effect on gas molecules.
           Kinetic Gas Equation: R.J. Clausius derive an equation for the pressure of an ideal gas (a gas
           which obeys all the gas laws at all conditions of temperature and pressure) from the postulates
           of kinetic molecular theory. This equation is called Kinetic Gas Equation. i.e
          PV  =  1/3 mnc2
          P  =  Pressure of the Gas                       V  =  Volume of the Gas
          n  =  Number of mole of the Gas            m  =  Mass of 1mole of the Gas
         and                                                        c2  =  Mean Square Velocity of Gas
         Molecules under the given conditions do not have the same velocity , therefore mean square velocity
         is considered for the gas molecules. For calculating mean square velocity c2, let suppose that n1
         molecules have velocity c1, n2 molecules have velocity c2 etc then:
                                               C2  =  n1c12 + n2c22 + n3c33…/ n1 + n2 + n3…
        Where c2 is the average velocity of all the velocities of all the molecules of a gas. The square root of
        c2 is c which is called Root Mean Square Velocity.

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