Explanation of Behaviour of Real Gases by Vanderwaal’s Equation

Vanderwaal’s Equation explains the behaviour of real gases under different conditions of temperature and pressure as follows;

(1).   AT LOW PRESSURES

At extremely low pressure, V is very large. Hence the correction term a/V² is very small as compared to ‘V’. Thus, both the correction terms can be neglected, due to which Vanderwaal’s equation reduces to PV = RT. This explains why at extremely low pressures, the gases obey the Ideal gas equation.

(2).  AT MODERATE PRESSURE

As the pressure is increased, the volume decreases and hence the factor a/V² increases. Thus the factor a/V² can no longer be neglected. However if pressure is not too high, the volume ‘V’ is still sufficiently large so that ‘b’ can be neglected in comparison to V. Thus Vanderwall’s equation reduces to

(P+(a/V²))V = RT

PV + a/V = RT

PV = RT – a/V

Thus ‘PV’ is less than RT by a factor ‘a/V’. This explains why a dip in the plots of PV Vs P of real gases.

(3).   AT HIGH PRESSURES

As the pressure is increased further so that it is fairly high ‘V’ is so small the ‘b’ can no longer be neglected in comparison to V. No doubt that under these conditions the factor a/V² is quite large but since ‘P’ is very large so that a/V² can be neglected in comparison to ‘P’. Thus Vanderwall’s equation reduces to

P(V – b)  =  RT

PV – Pb  =  RT

PV  =  RT + Pb

Thus PV is greater than RT by factor Pb. Now as pressure is increased, the factor ‘Pb’ increases more and more. This explains why after the minima (dip) in the curves, the product PV increased continuously as pressure is increased more and more.

(4).  AT HIGH TEMPERATURE

At any given pressure, if the temperature is sufficiently high, ‘V’ is very large hence a/V² will be very small to neglect and b is also neglected as comparison with volume ‘V’. Thus, Vanderwaal’s equation reduces to PV = RT. Hence at high temperature real gases behave like the Ideal gas.

(5).  EXCEPTIONAL BEHAVIOUR OF HYDROGEN AND HELIUM

In case of hydrogen and helium, their molecules have very small masses. Hence in case of these gases, intermolecular attractions are extremely small even at high pressures. In other words, the factor a/V² is negligible at all pressures. Hence Vanderwaal’s equation is applicable in the following form at all pressures and ordinary temperatures.

P (v – b)   =   RT

PV – Pb   =   RT

PV =  RT  +  Pb

This explains why hydrogen and helium show positive deviation only which increases with increase in the value of P.