Question

# The value of the compressibility factor for an ideal gas is:(a) 2(b) 1(c) 3(d) 4

Hint: The compressibility factor gives us an idea about the degree to which a real gas shows deviation from the ideal gas behaviour. It is the ratio of the observed molar volume of a gas to the calculated molar volume (using ideal gas equation) of the gas at the same pressure and temperature

The compressibility factor for a gas is the ratio of the observed molar volume of a gas to the calculated molar volume (using ideal gas equation) of the gas at the same pressure and temperature. It can also be defined as the ratio of the product and pressure and volume of the gas to the product of the number of moles, the gas constant and the temperature of the gas. The equations are given below:
$Z=\cfrac { PV }{ nRT }$ (Where Z is the compressibility factor)
$\Rightarrow Z=\cfrac { P{ V }_{ real } }{ nRT }$...(1)
Since according to the ideal gas equation: $PV=nRT$
$\Rightarrow { V }_{ real }=\cfrac { nRT }{ P }$
Putting the above equation in equation (1),
$Z=\cfrac { { V }_{ real } }{ { V }_{ ideal } }$
For an ideal gas, ${ V }_{ real }={ V }_{ ideal }$. Hence the compressibility factor for an ideal gas is equal to 1.
For a real gas compressibility factor can be less than 1 or greater than 1:
If the compressibility factor is less than 1 then, the gas will show negative deviation and it will be more compressible than expected. Example: methane gas, carbon dioxide gas.
If the compressibility factor is greater than 1 then the gas shows positive deviation and will be less compressible than expected. Example: Helium gas, Hydrogen gas.
So, the correct answer is “Option B”.

Note: If the compressibility factor is less than 1 then it implies that the attractive forces are predominant among the gas molecules. If the compressibility factor is more than 1 it implies that the repulsive forces are predominant among the gas molecules. Whether the compressibility factor will be greater than or less than 1 at a particular temperature and pressure will depend upon the nature of the gas.