Page 25 - Instant notes

A3
NON-IDEAL GASES

Key Notes
Real gases at moderate and high pressures do not conform to the
ideal gas equation of state, as intermolecular interactions become
important. At intermediate pressures, attractive forces dominate
the molecular interactions, and the volume of the gas becomes
lower than the ideal gas laws would predict. At higher pressures,
repulsive forces dominate the intermolecular interactions. At high
pressure, the volume of all gases is larger than the ideal gas law
predicts, and they are also much less compressible.
The virial equation is a mathematical approach to describing the
deviation of real gases from ideal behavior by expanding the
ideal gas equation using powers of the molar volume, V m :

The virial coefficients B, C, D, etc. are specific to a particular
gas, but have no simple physical significance. A gas at low
pressure has a large molar volume, making the second and
subsequent terms very small, and reduces the equation to that of
the perfect gas equation of state.
This is a modification of the perfect gas equation which allows
for the attractive and repulsive forces between molecules. The
2
equation has the form (V−nb) (p+a(n/V) )=nRT. The van der
Waals parameters, a and b, convey direct information about the
molecular behavior. The term (V−nb) models the repulsive
2
potential between the molecules, and the term (p+a(n/V) )
compensates for the attractive potential. At high temperatures and
low pressures, the correction terms become small compared to V
and T and the equation reduces to the perfect gas equation of
state.
Related topics Perfect gases (A1) Molecular behavior in perfect gases (A2)

Non-ideal gases

Ideal gases are assumed to be comprised of infinitesimally small particles, and to interact
only at the point of collision. At low pressure, the molecules in a real gas are small
relative to the mean free path, and sufficiently far apart that they may be considered only