Real gas, Vanderwaal's Equation

REAL GAS

The Ideal gas equation shows big deviation at high pressures and low temperatures from ideal gas equation.

If you compress an Ideal gas to very high pressure when will it become a liquid? ????

Vanderwaal’s equation for real gas.

1. Volume correction.  Actual volume available for gas to freely move is

       V_R = V_j – n b      

      b = Volume correction constant taking into size and gas molecule.

2. Pressure correction:

      P_Real = P_Ideal – attractive forces between molecules.

     P_Real = P_ideal – 

     A = Pressure correction

. a, b are Vander Waals constant; n is the number of moles of gas

 V.W. Constants

‘b’  size of molecule

Thumb rule   b = 4 x Volume and one atom/molecule.

‘a’     Inter molecule forces between atom/molecule gas

Ex: put in increasing order ‘a’ and ‘b’ for H₂, He, NH₃, O₂

b = H₂ < He < NH₃ < O₂

a = He < H₂ < O₂ < NH₃

Compressibility factor   Z

Z = 1         Þ Ideal gas. No. attraction/Repulsion

Z < 1         ÞReal gas. Attractive forces dominate

Z > 1         ÞReal gas. Repulsive forces dominate

 

UNIT OF ‘a’ AND ‘b’

 

Real gas behaves like ideal gas at low pressure and high temperature.

Boyle’s temp =  temperature at which Real gas behave like ideal gas.

Liquefaction of Gas

Critical temperature (T_C) is the temperature above which a gas cannot be liquefied however high pressure may be.

Critical pressure (P_C) is minimum pressure required to liquefy gas at the critical temperature.

Critical volume (V_C) is the volume occupied by one mole of gas at critical temperature and critical pressure.

 

For gas CO₂

 

Real gases can only be liquefied by increasing pressure, if the temperature is below critical temperature

Here Vc and Pc volume and pressure at critical temperature when it touches the curve.