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Vander Waals Gas Equation

A number of equations of stage have been suggested to describe the P-V-T relationship in real gases. The oldest and best known equation is that of van der waals

The van der waals gas equation of state

In 1873, J.D. van der Waals proposed his famous equation of state for a non-ideal , he modified the ideal gas equation by suggesting that the gas molecules were not mass points but behave like rigid spheres having a certain diameter and that there exist intermolecular forces of attraction between them

The two correction terms introduced by van der Waals are discussed below

  • Correction due to volume of gas molecules

  • Correction due to intermolecular forces of attractions

Correction due to Volume of Gas Molecules

The ideal gas equation PV="nRT" is derived on the assumption that the gas molecules are mass points, i.e. don’t have finite volume. Van der Waals abandoned this assumption and suggested that a correction term nb should be substracted from the total volume V in order to get the ideal volume which is compressible

In order to understand the meaning of the correction term nb, let consider two gas molecules as unpenetrable and incompressible spheres, each of which has a diameter d.


Correction due to Intermolecular Forces of Attractions

In the derivation of the ideal gas equation, it was assumed that there are no intermolecular forces of attraction. Actually it is not so, in order to take into account the effects of intermolecular forces of attraction, let us consider a molecular lying somewhere in the midst of the vessel. These forces neutralize one another and there is not the molecule. So, it will strike the wall with a lower velocity and will exert a lower pressure than it would have done if there was no force of attraction. Fig 1


 


der waals gas equation

der waals gas equation as follows

p = pressure of the fluid

v = volume of the particles divided by the sum of particles

k = Boltzmann's constant

T = absolute temperature

a' = attraction between the particles

b' = average volume excluded from v by a particle.