# if there exists no ideal gas, then how can we apply the gas equations for the real gases???? How do we know the temp limit for the formulae to be applicable????

SAGAR SINGH - IIT DELHI
878 Points
14 years ago

Dear priyanka,

An ideal gas is one, which obeys the general gas equation of PV = nRT and other gas laws at all temperatures and pressures. A real gas, does not obey the general gas equation and other gas laws at all conditions of temperature and pressure.

## Effect of pressure

All gases are known to exist as real gases and show ideal behaviour only to some extent under certain conditions. When PV = nRT for ideal gases, then the ratio

For real gases Z may be less or more than one. If Z<1 then it is called negative deviation which means that the gas more compressible. if z>1 then the gas is less compressible and it is called positive deviation. It is observed that the deviations are low at low pressures. At high pressures the deviations depends on the nature of the gas.

A plot of versus P for some common gases are shown in the figure.

Fig: 2.7 - Plot of compressibility factor as a function of P

For H2 and He, 'Z' is greater than one while for N2, CH4 and CO2 'Z' is lesser than one. This means that these gases are more compressible at low pressures and less compressible at high pressures than expected from ideal behaviour.

## Effect of temperature

The effect of temperature on the behaviour of real gases is studied by plotting the value of 'PV' against temperature. It is observed that the deviations from ideal behaviour is less with the increase in temperature.

Thus, real gases show ideal behaviour at low pressures and high temperatures.

## 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

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

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.

All the best.