Deviation of gas from ideal behaviour

All gases, irrespective of their chemical composition, obey certain laws that govern the relationship between the volume, temperature and pressure of the gases. A given mass of a gas, under definite conditions of temperature and pressure, occupies a definite volume. When any of the three variables is altered, then the other variables get altered. Thus these Gas laws establish relationships between the three variables of volume, pressure and temperature of a gas.

Causes for deviations

In order to know the causes for deviations from ideality, Van der Waal pointed out the faulty assumption that were made in formulating the kinetic molecular model of gases.

  • The assumption that the volume occupied by the molecular mass is negligible as compared to the total volume of the gas is invalid. Although this volume is 0.1% volume of the total volume of the gas, the volume of the molecules of gas remain same as compared to the decrease in the total volume of the gas. The decrease in volume occurs with the decrease in temperature and increase in pressure, but the volume of the molecules cannot be neglected.
  • The forces of attraction between the gas molecules were considered to be negligible. This assumption is only valid at low pressures and high temperatures because in these conditions the molecules lie far apart. But at high pressures and low temperatures the volume of the gas is small and so the attractive forces though very small, exist between them.
Hence, Van der Waal who incorporated the idea of finite molecular volume and intermolecular forces modified the Ideal Gas Equation as follows:
  • Volume correction was made stating that the free volume of the gas is actually less than the observed volume. A suitable volume term 'b' is subtracted from the observed volume known as the excluded volume or correct volume. The correction term, 'b' is a constant depending upon the nature of the gas. For 'n' moles of gas, the correction term is 'nb' and so the corrected volume is given by,
Vcorrected = (V-nb) for 'n' moles.

Correction due to intermolecular forces is considered in terms of the pressure. A molecule at the wall of the container experiences an inward pull due to attractive intermolecular force of the neighbours. The molecules strike the wall with a lesser force and so the observed pressure is less than the ideal pressure. The pressure correction term

pressure correction due to intermolecular forces

Substituting these values for pressure and volume, the ideal gas equation can now be written as:

Van der Waal s equation of state

This equation is Van der Waal's equation of state. Here, the constant 'a' measures the forces of attraction between the molecules of the gas and 'b' relates to the incompressible volume of the molecules, measuring the size of the gas molecules.

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