Introduction to Real Gases

How do "real" gases differ from "ideal" ones?

• They do not obey PV=nRT
• V is nonzero as T0
• They condense to form liquids
• They exhibit "critical behavior"

Critical Behavior in Gases

Real gases liquefy. As P is increased at constant T, at some point liquid will form. The liquification occurs at constant P (horizontal line on the P-V plot.)

Critical Point: (Tc, Vm,c, Pc)

Note that we can pass from gas to liquid without ever seeing 2-phase region:

(1) start in gas region heat gas to T > Tc

(2) Compress isothermally to Vm < Vm,c

(3) Cool to T < Tc

At all times in this process, 1 phase is observed. It is a continuous change from a gas into a liquid.

Below Tc: gas, liquid

Above Tc: "fluid"

Compression Factor: Deviation from Ideality

The compression factor Z is defined as

Z expresses the extent of deviation from ideal gas behavior.
Obviously, Z=1 for an ideal gas. Z may be >1 or <1 for a real gas.

Notes:

1. Z1 as P0 for all gases (this is IG limit)
2. Z>1 molecules occupy more volume than IG (e.g. H₂): repulsive forces
3. Z<1 molecules occupy less volume than IG (e.g. CO₂): attractive forces

Intermolecular Forces in terms of a Potential

Recall that we can define force in terms of an energy potential

Small r: large negative gradient strong force along +r (repulsive)

large r: positive gradient force along r (attractive)

How do we correct the Eq. of State for repulsive and attractive forces?