# Ideal Gas Equation

Real gases do not obey the ideal gas laws exactly under all conditions of temperature and pressure. Experiments show that at low pressures and moderately high temperatures, gases obey the laws of Boyle, Gay-Lussac and Avogadro approximately, but as the pressure is increased or the temperature is decreased, a marked deviation from ideal behaviour is observed. (Figure) shows, for example, the type of deviation that occurs in Boyle's law for H2 at room temperature.
The curve for a real gas has a tendency to coincide with that of an ideal gas at low pressures when the volume is large. At high pressures, however, deviations are observed.
(5.16)
The deviations can be displayed more clearly, by plotting the ratio of the observed molar volume Vm to the ideal molar (volume Vm), to the ideal molar volume vm ideal (= RT/p). This ratio is called the compressibility factor Z.

For an ideal gas, Z = 1 and is independent of pressure and temperature. For a real gas, Z = f (T, p), a function of both temperature and pressure. Figure shows a graph between Z and p for some gases at 273.15 K, the pressure range in this graph being very large.
It can be noted that
1. Z is always greater than 1 for H2.
2. For N2, Z < 1 in the lower part of the pressure range and is greater than 1 at higher pressures. It decreases with increase of pressure in the lower pressure region, passes through a minimum at some pressure and then increases continuously with pressure in the higher-pressure region.
3. For CO2, there is a large dip in the beginning. In fact, for gases that are easily liquefied, Z dips sharply below the ideal line in the low-pressure region.

It gives an impression that the nature of the deviations depends upon the nature of the gas. In fact, it is not so. The determining factor is the temperature relative to the critical temperature of the particular gas; near the critical temperature, the pV curves are like those for CO2, but when far away, the curves are like those for (H2 fig).

Provided the pressure is of the order of 1 bar or less, and the temperature is not too near the point of liquefaction, the observed deviations from the ideal gas laws are not more than a few per cent. Under these conditions, therefore, the equation pV = RT and related expressions may be used.