Real Gases

The ideal gas equation of state is not sufficient to describe the P,V, and T behaviour of most real gases.

Most real gases depart from ideal behaviour at deviation from • low temperature

• high pressure

Low Temperatures

The variation of the potential energy of two molecules on their separation.

High positive potential energy (little separation)• Repulsive interactions

Intermediate separations• attractive interactions dominate

Large separations (on the right) • the potential energy is zero and there is

no interaction between the molecules.

High Pressures

Real gas molecules do attract one another

(Pid = Pobs + constant) Real gas molecules are not point

masses

(Vid = Vobs - const.)

Vid = Vobs - nb

• b is a constant for different gases

Pid = Pobs + a (n / V)2

• a is also different for different gases

Ideal gas Law Pid Vid = nRT

2

2

mmobs

obs

V

abV

RTP

nRTnbVVn

aP

The compressibility factor

PVZ

nRT

The deviation from ideal behaviour can be measured in terms of compressibility factor, Z.

For ideal gas Z = 1 at all temperatures and pressures as pV = nRT. For ideal gas Z = 1 at all temperatures and pressures as pV = nRT.

The graph of Z vs p will be a straight line parallel to pressure axis.

For gases which deviate from ideality, value of Z deviates from unity.

PVZ

nRT

Gases show ideal behaviour when the volume occupied is large so that the volume of the molecules can be neglected in comparison to it.

The behaviour of the gas becomes more ideal when pressure is very low.

For a perfect gas, the slope is zero

The temperature at which a real gas obeys ideal gas law over an appreciable range of pressure is called Boyle temperature or Boyle point.

Boyle temperature - for a van der Waals gas, the Boyle temperature (TB) is written

Rba

TB

Critical temperature (Tc) - the temperature above which a gas cannot be liquefied.

Critical pressure (Pc) – the minimum pressure that needs to be applied at Tc to bring about liquefaction.

Critical volume (Vc) – volume of one mole of the gas at critical temperature.

At the critical point

375.0Z ;27

8a

27

aP ;3

c

2c

c

ccc

c

RTVP

RbT

bbV