van der Waals Equation for Real Gases






2


P  n 2a  V  nb   nRT
V 


where:
P is the pressure of the gas
V is the total volume of the container
containing the gas
a is a measure of the attraction between the
particles
b is the volume excluded by a mole of
particles
n is the number of moles
R is the gas constant,


The Ideal Gas Law, PV = nRT, assumes that the
molecules that make up the gas have negligible
sizes, that their collision with themselves and the
wall are perfectly elastic, and that the molecules
have no interactions with each other.
a and b are constants particular to a given gas
(provided in reference tables.)
Substance
Air
Carbon Dioxide (CO2)
Nitrogen (N2)
Hydrogen (H2)
Water (H2O)
Ammonia (NH3)
Helium (He)
Freon (CCl2F2)



a
(J. m3/mole2)
0.1358
0.3643
0.1361
0.0247
0.5507
0.4233
0.00341
1.078
b
(m3/mole)
3.64x10-5
4.27x10-5
3.85x10-5
2.65x10-5
3.04x10-5
3.73x10-5
2.34x10-5
9.98x10-5
The parameter b is related to the size of each
molecule. The volume that the molecules have to
move around in is not just the volume of the
container V, but is reduced to ( V - nb ).
The parameter a is related to intermolecular
attractive force between the molecules, and n/V is
the density of molecules. The net effect of the
intermolecular attractive force is to reduce the
pressure for a given volume and temperature.
When the density of the gas is low (i.e., when n/V is
small and nb is small compared to V) the van der
Waals equation reduces to that of the ideal gas law.
Conditions when
real gases are
most ideal
Conditions when
real gases are
least ideal
Low Pressure
High Temperature
Small value of n
Large Volume
High Pressure
Low Temperature
Large value of n
Small volume
Small atomic gases
with weak IMF’s
Large molecular gases
with strong IMF’s