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Real Gases

The ideal gas laws can be derived from the kinetic theory of gases which is based on the following two important assumptions:
  1. The volume occupied by the molecules is negligible in comparison to the total volume of the gas.
  2. The molecules exert no forces of attraction upon one another.
The molecules in gases also have weak forces of attraction (called van der Waals attraction) among themselves; as otherwise, the gases could never be liquefied and solidified.
Correction for forces of attraction:
Description: 28490.png
Correction for molecular size: The container of volume V has n moles of gas molecules, each of which possesses a certain volume of its own. If the total volume blocked by 1 mol of molecules due to their sheer presence is taken as b, then the total volume blocked by them will be nb. We can now look at the container and see that the effective volume for the gas molecules to move is V – nb. This means that in the volume V – nb, the gas molecules have zero volume of their own.
Since PiVi = nRT
Description: 28499.png
where b is called the excluded volume or co-volume. The numerical value of b is four times the actual volume occupied by 1 mol of gas molecules.

Deviation from ideal behavior

If the measurements of pressure, volume, and temperature of a gas do not confirm to the ideal gas law (PV = RT), within the precision of measurements, the gas is said to deviate from ideal behavior and exhibit non-ideal behavior. Such gases are called real gases. At low pressures and moderately high temperatures, real gases obey ideal gas equation. However, as the pressure increases or the temperature decreases, a marked deviation from ideal behavior is observed.
To display deviations more clearly, the ratio of the observed molar volume (Vm) to the ideal molar volume Description: 28509.png is plotted as a function of pressure at constant temperature. This ratio is called the compressibility factor (Z), which is expressed as
Description: 28516.png
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.

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