<P> An ideal gas is a theoretical gas composed of many randomly moving point particles whose only interactions are perfectly elastic collisions . The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics . </P> <P> One mole of an ideal gas has a volume of 22.710947 (13) litres at STP (a temperature of 273.15 K and an absolute pressure of exactly 10 Pa) as defined by IUPAC since 1982 . (Until 1982, STP was defined as a temperature of 273.15 K and an absolute pressure of exactly 1 atm . The volume of one mole of an ideal gas at this temperature and pressure is 22.413962 (13) litres . IUPAC recommends that the former use of this definition should be discontinued; however, some textbooks still use these old values .) </P> <P> At normal conditions such as standard temperature and pressure, most real gases behave qualitatively like an ideal gas . Many gases such as nitrogen, oxygen, hydrogen, noble gases, and some heavier gases like carbon dioxide can be treated like ideal gases within reasonable tolerances . Generally, a gas behaves more like an ideal gas at higher temperature and lower pressure, as the potential energy due to intermolecular forces becomes less significant compared with the particles' kinetic energy, and the size of the molecules becomes less significant compared to the empty space between them . </P> <P> The ideal gas model tends to fail at lower temperatures or higher pressures, when intermolecular forces and molecular size become important . It also fails for most heavy gases, such as many refrigerants, and for gases with strong intermolecular forces, notably water vapor . At high pressures, the volume of a real gas is often considerably greater than that of an ideal gas . At low temperatures, the pressure of a real gas is often considerably less than that of an ideal gas . At some point of low temperature and high pressure, real gases undergo a phase transition, such as to a liquid or a solid . The model of an ideal gas, however, does not describe or allow phase transitions . These must be modeled by more complex equations of state . The deviation from the ideal gas behaviour can be described by a dimensionless quantity, the compressibility factor, Z . </P>

When do real gases behave as ideal gases