Deviation From Ideal Gas Behaviour

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Ideal gas behaviour is a theory which expects the gases to behave in a certain way and assumes that the gases have negligible or no space at all and they have no intermolecular force of attraction. Deviation of gases from their ideal gas behaviour occurs when the molecules of a gas are cooled down to a point where they no longer possess sufficient kinetic energy to overcome attractive intermolecular forces.

Ideal and Real Gases

Ideal gases are those gases which obey the ideal equation of PV = nRT under all amounts of pressure and temperature. But there is no such gas which behaves the same in every pressure and temperature. Hence, this concept is theoretical. Real gases are those who obey the gas law if the pressure is low or the temperature is high. All gases are real gases.

Difference Between Ideal Gas and Real Gas

Ideal Gas

Real Gas

Ideal gases obey gas laws under all circumstances.

Real gases obey gas laws if the pressure is low and the temperature is high.

The molecules occupy a negligible amount of volume.

The volume occupied is not negligible in comparison to the total volume of gas. 

There is a negligible force of attraction.

There is some force of attraction.

Pressure, Volume and Temperature Relationship in Gases - Why do the Real Gases Deviate?

The graphs below represent different gases and show how they behave under high and low pressure.

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Figure (a) shows how gases behave differently from their ideal behaviour, particularly in high pressure. At low pressure, as shown in figure(b), the real gases behave more like that of the expected ideal behaviour. For gases such as CO2 and C2H4, they deviate more than other real gases because these gases tend to liquefy at lower pressures.

Now, the graph below shows the behaviour of real gas N2 under different temperatures.

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The figure shows that the real gas Nitrogen behaves more according to the ideal gas behaviour when the temperature is high. Why do gases deviate so much under high pressure and low temperature? At both the conditions, the basic assumptions that the law of the ideal gas holds, that are: the volume of the molecules of the gas are negligible and intermolecular interaction is negligible – these two become invalid.

Under low pressure, the gas molecules are farther apart from each other, and the volume of molecules is the same as the volume of the container. As the pressure increases, the molecular space contracts, and their volume becomes significant as compared to the container. If more pressure is exerted, then the gas liquefies under very high pressure such as CO2.

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All the molecules attract each other by a combination of forces. At high temperature, these have enough energy, and they overcome their attractive force and predominate by the effects of the molecular volume. On the other hand, with the decrease in the temperature, the energy of the molecules also decreases. Eventually, there comes the point where it becomes impossible for the molecules to overcome the force of attraction, and it results in the liquefaction of gas and turns into a liquid state. That is why the ideal gas behaviour is a theoretical concept and does not apply in real situations.

Van der Waals Equation

In 1873, J.D. Van der Waals did some modification with the ideal law of gas equation to explain the behaviour of real gases, in which he took into account:

  • The volume the gas molecules.

  • The forces of attraction between the gas molecules.

He put forward the following equation;

  • \[(P + \frac{a}{v^{2}})(V - b) = RT\]

For n moles of the gas,

  • \[(P + \frac{an^{2}}{v^{2}})(V - nb) = nRT\]

The constants ‘a’ and ‘b’ represent the scale of intermolecular attraction and the excluded volume, respectively. The higher the value of 'a', the greater is the molecular attraction and the easily the gas will compress. The term 'b' represents the excluded volume which is occupied by gas particles. These constants are different for different gases.

FAQ (Frequently Asked Questions)

Q1. When Does a Gas Deviate From the Ideal Behaviour?

Ans. All gases are real gases, and the concept of the ideal gas behaviour is theoretical. Every gas has its properties, and they show different reactions under different amounts of pressure and temperature.

According to the ideal gas behaviour, the gas particles do not occupy space and have no molecular attraction. But this does not apply to the real gases. All the gases show some ideal gas behaviour only if the pressure is low and the temperature is high. Under other situations where the pressure and the temperature are not idle, the gases deviate from their expected behaviour, and some of them even liquify to a liquid state.

Q2. What are the Possible Deviations From the Ideal Behaviour?

Ans. There are different deviations from ideal behaviour under the different magnitude of pressure and temperature.

  • Under high pressure, the deviation is very large, as shown above in the figure. Under high pressure, the magnitude of the volume of the gas decreases as compared to its container and the intermolecular attraction is strong.

  • The deviation also varies from gas to gas. For example, CO2, at very low pressure, deviates the most and does not show any sign of ideal gas behaviour.

  • As the temperature increases, the deviation from that of the ideal gas behaviour decreases and the ideal gas law can be used to predict the behaviour of the gases without any errors.

  • When the temperature is decreased, the deviation is more, and with the maximum deviation, the gas becomes liquid.

Q3. Which Gas Deviates the Most From the Ideal Behaviour?

Ans. As we know that the ideal gas behaviour assumes that the gases have negligible or no size at all. The gas Xenon (Xe) has the largest element size. So, it is assumed that this is the gas that will deviate the most when put under high pressure and low temperature.