Ideal Gas and Real Gas

Definitions

An ideal gas is a gas which obeys the equation of state $PV = nRT$ at all pressures and at all temperatures. In an ideal gas intermolecular interactions are completely absent, and its molecules are treated as point particles with no size of their own.

Real gases are composed of atoms or molecules which do interact with one another, and which occupy a finite volume. Hence no real gas is truly ideal as defined above; an ideal gas does not exist in reality. It is a model, used in the same way as a perfect blackbody is used later in this chapter — to deduce properties that real systems approximate.

The ideal state of a real gas

If the atoms or molecules of a real gas are so far apart that there is practically no interatomic or intermolecular interaction, the real gas is said to be in the ideal state. This happens at sufficiently low density of the gas.

• At low pressures the molecules are far apart, so molecular interactions are negligible.

• At high temperatures the molecules are again far apart and move fast, so the time spent within the range of mutual attraction is small.

• In both cases the temperature must be well above the liquefaction temperature of the gas, otherwise the attractive forces that cause condensation cannot be neglected.

Under these conditions the behaviour of a real gas is close to that of an ideal gas, and the laws of Boyle, Charles and Gay-Lussac hold well.

Why deviation is seen at high pressure and low temperature

At high pressure the molecules are packed close together, so the volume actually occupied by the molecules themselves is no longer negligible compared with the volume of the container, and the molecules are constantly within range of each other's attractive forces. At low temperature the molecules move slowly, so the attractive forces have time to act and deflect them, and the gas approaches its liquefaction temperature. Both effects break the assumptions on which $PV = nRT$ rests, so the real gas deviates from ideal gas behaviour.

Effect of molecular size

For an ideal gas the molecules are point particles, so the whole volume $V$ of the container is available to every molecule and collisions between molecules never occur in the idealised treatment. For a real gas the molecules have a finite diameter $d$: the volume available for motion is less than $V$, the molecules collide with one another, and it is this finite size that makes the mean free path finite and inversely proportional to $d^{2}$.

Distinguish between an ideal gas and a real gas

Standard results

• Ideal gas: obeys $PV = nRT$ at all $P$ and $T$; no intermolecular interaction; does not exist in practice.

• A real gas is in the ideal state at low density, i.e. low pressure or high temperature, with $T$ well above its liquefaction temperature.

• Deviation from ideal behaviour is largest at high pressure and low temperature.