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Kinetic Molecular Theory of Gases

The gas laws so far discussed are the experimental results of various scientists . Maxwell , Boltzmann , Clausius  and others proposed theory which provides an explanation for the observed features of the gaseous state . It is known  as " Kinetic Molecular Theory " of gases . Since the assumptions of the theory are related to atoms and molecules which cannot be seen , it gives a microscopic picture of the gaseous  state .

Postulates of Kinetic Molecular Theory of Gases

The following are the postulates of the kinetic molecular theory of gases :

  • Gases contain large number of tiny  and discrete particles called molecules .
  • The molecules move randomly in all the directions with high velocities . Collisions with each other or with the wlls of the container , change the direction of the movement of these molecules .
  • The gas molecules  are very much apart from each other . The volume of molecules is negligible compared to the volume of the container .
  • Molecules are electrically neutral and do not have attractions or repulsions between them .
  • The molecular collisions are perfectly elastic . It means that there is no change in the total kinetic energy during the collisions  of molecules with each other or with the walls of the container . But there can be transfer of energy among the colliding particles .
  • Molecular motions are unaffected by gravity .
  • Pressure exerted by a gas is due to the collisions of  molecules made on the walls of the vessel . There is no loss of energy in these collisions .
  • Even though molecules have different velocities , their average kinetic anergy is directly proportional to the absolute temperature of the gas .      

                                             Average kinetic energy   `prop` T

Gases which follow the postulates of the kinetic molecular theory are ideal gases . Most of the common gases do not behave as ideal gas . Real gases approach ideal gas behaviour at low pressures and high temperatures .


Kinetic Molecular Theory of Gases (kinetic Gas Equation)

The mathematical expression derived on the basis of assumptions of kinetic molecular theory of gases is known as 'Kinetic gas equation' . From this equation one can prove the various gas laws mathematically .

The gas molecules continuously move in all directions with random speeds . Not only the molecules have different  speeds , but also the speed of each molecule changes rapidly .


RMS Velocity :


Velocity s a vector quantity . It is represented by positive sign in any particular  direction , and negative sign in the opposite direction . As the gas molecules move in all the directions , some times the average velocity of molecules may be given a negative value or zero as per the convention . To avoid this kind of anomaly , the velocities of the molecules are squared which will there always positive . The root of mean of squares of velocities of molecules , thus gives the velocity of the molecules , called Root Mean Square (RMS) velocity. If a gas contains 'n' molecules and the individual  velocities of molecules are C1 , C2 , C3 , C4 .............. Cn , then the RMS velocity (C) is given by the equation

       C   =   `sqrt((C1^2+C2^2+C3^2+.....Cn^2)/(n))`