# Behaviour of Real Gases: Deviation from Real Behaviour

Science depends on the practical applicability of every experiment! Theoretically, the gas laws, from Boyle’s law to Avogadro’s Law seem right, but what about their practical appliance? Real Gases generally observe the various findings of the Gas Laws under controlled physical conditions, but also show deviations from them, let’ see how!

## Applicability of Ideal Gas Equation and Boyle’s Law

We already know the Ideal Gas Equation pV= nRT. It defines the relationship between Temperature, pressure, and volume of gases. For checking the reliability of this relationship we first plot a graph between pV and p. Now we know that at a constant temperature, as the Boyle’s law states, pV shall be a constant. Therefore the graphs between the two (p and pV) shall be a straight line. But the case is not so! At temperature 273 K the data for several gases is shown in the graph below:

From the graph plotted in the figure we can easily conclude that despite the constant temperature, the real gases do not show behaviour as predicted by the Boyle’s law. These gases show a significant deviation from the predicted ideal behaviour as per the Boyle’s law. The plot in the graph signifies the deviating behaviour of real gases like Dihydrogen, Helium, Carbon monoxide and Methane from the behaviour of ideal gas. In faact we see, from the graph that real gases do not show any signs of similar to Ideal gas’s behaviour.

From our next graph that plots the volume to pressure data of gases, we find an apparent deviation from the theoretical prediction of gases in changed conditions. From the graph, we can figure out that at very high pressures the value of volume we calculated is less than the actual practical volume. Hence from the above two graphs, it is clear that generally real gases, under all conditions do not follow The Ideal Gas Behaviour or equation.

## Problem: Deviation of Gases From Real Behaviour

The question now is that why do gases deviate from the ideal behaviour? The answer lies in the basic behaviour of these gases. We already know that the intermolecular forces between gases are minimal, the reason being the scattered molecules in the gaseous state.

According to the Kinetic Theory, molecules of gases do not have any force of attraction, and the volume of the molecules is insignificantly small when compared to the space occupied by the gases. Hence, at low temperatures how does a gaseous matter change into the liquid state? If there is no force of attraction, then how does the state of matter change?

### Solution: Intermolecular Force

This negligible intermolecular force is the secret behind the deviation of real gases from the ideal gas. Molecules in the gases, interact with each other. Though the interaction is weak at high temperatures, yet with decreasing temperature the interactive forces increases. At high pressure also, these molecules come close to each other, hence leading to a decrease in volume.

With increasing pressure, the interaction between these molecules increases. This interaction between the molecules prevents them from bombarding on the container. The attractive forces between the molecules prevent the molecules from colliding with the walls of the container.

This is where the difference between ideal gases and real gases become transparent. Ideal gases are those gases which follow Gas laws and the molecules of these gases have no interaction with each other, while real gases are those gases which occupy space and the molecules have a force of interaction between each other.

### Vander Walls Equation of State

Now from the above difference, it is clear that in ideal gases the pressure exerted by molecules on the container is greater than that exerted by real gases, so pideal = preal + an2/ V2; an2/ V2 here is a constant and is known as the correction term.

Now, let’s consider the repulsive forces. The forces which come into play when the molecules are in contact with each other are called repulsive forces. Being short-range interactions, these forces make molecules behaviour like the impenetrable spheres.  It is because of this force that the volumes of the molecule rise significantly and at high-pressure volume V becomes V-nb. Here, nb is the volume occupied by the molecules.

(p+ an2/V) (V-nb) = nRT

a and b are constants that depend on the nature of the gas. This equation is also known as the van der Waals equation. ‘n’ here is the number of moles while a and b are constants referred as van der Waals constants. The value of these van der Waals is specific to the characteristic of the gas and is independent of pressure and temperature.

It should be noted here that at low temperature the intermolecular forces become significantly high, thus the molecules attract with each other at greater speed.  Similarly at higher pressure the intermolecular forces increase. So at high pressure and low temperature, the molecules of gases have high intermolecular forces. Real gases exhibit ideal behaviour only when the intermolecular forces are minimal. The lesser the pressure, the greater the chances of a real gas behaving like an ideal gas!

### Compressibility Factor

Let Z = pV/nRT be a number. it will have no units as is clear from the equation. What does this number signify?

For perfect ideal behaviour, Z = 1 at all temperatures and pressures, because if Z=1 then pV= nRT. The temperature at which a real gas follows an Ideal gas law is known as the Boyle temperature or Boyle point. The Boyle point doesn’t depend on physical conditions, rather it is dependent on the nature of the gas.

Generally, at low pressure, all gases show ideal behaviour hence giving Z as = 1. Lower the pressure, greater the volume. If Z ≠ 1, then the gas is not ideal but real. Hence with the help of the compressibility factor, we can find the measure of the deviation of real gases from the ideal behaviour.

## Solved Examples From You

Q : Assertion: CH4, CO2 has a value of Z (compressibility factor) less than one at 0oC.

Reason: Z < 1 is due to the fact that the attractive forces dominate among the molecules.

1. Both the assertion and reason are correct and the reason is the correct explanation of the assertion.
2. The two statements are correct but the reason is not the correct explanation.
3. Assertion is correct and the reason is wrong.
4. Assertion as well as the reason are wrong.

Solution: A) As we discussed above, the compressibility factor tells us about the measure of the deviation of real gases from the ideal behaviour. If you look at the plots of Boyle’s law for these gases as given above, you will find that the assertion is true. This is due to the attractive forces of the gases.

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