Explain the compressibility factor $(Z)$.

(N/A) The compressibility factor $(Z)$ is defined as the ratio of the product of pressure $(p)$ and molar volume $(V_m)$ to the product of the gas constant $(R)$ and temperature $(T)$. It measures the deviation of a real gas from ideal gas behavior.
$Z = \frac{pV_m}{RT} = \frac{pV}{nRT}$
$(i)$ For an ideal gas,$Z = 1$ at all temperatures and pressures,as it follows the equation $pV = nRT$.
$(ii)$ For real gases,$Z \neq 1$.
- If $Z > 1$,the gas shows positive deviation,meaning it is less compressible than an ideal gas (e.g.,$H_2$ and $He$ at all pressures).
- If $Z < 1$,the gas shows negative deviation,meaning it is more compressible than an ideal gas (e.g.,$CH_4$ and $CO_2$ at moderate pressures).
At very low pressures,all real gases approach ideal behavior,and $Z$ approaches $1$.