Ideal gas equation is represented as PV = nRT. Gases present in universe were found to be ideal in the Boyle’s temperature range only and deviated more from ideal behavior at high pressure and low temperature. The deviations are explained in terms of compressibility factor Z. For ideal behavior $Z=\frac{PV}{nRT}=1$  . The main cause to show deviations were due to wrong assumptions made about forces of attractions(which becomes significant at high pressure) and volume occupied by molecules (V) in PV = nRT is supposed to be volume of gas or the volume of container in which gas is placed by assuming that gaseous molecules do not have appreciable volume. Actually volume of the gas is that volume in which each molecule of a gas can move freely. If volume occupied by gaseous molecule is not negligible, then term V should be replaced by the ideal volume which is available for free motion of each molecule of gas in 1 mole gas
 V_actual = volume of container – volume occupied by molecules 
            = V – b
Where, b represents the effective volume of co-volume or excluded volume occupied by molecules present in one mole of gas.
Similarly for ‘n’  mole of a gas  V_actual  = V – nb
The excluded volume can be calculated by considering bimolecular collisions. The excluded volume is the volume occupied by the sphere of 2r for each pair of molecule

 
Thus, excluded volume for one pair of molecules $\frac{4}{3}\pi {\left(2r\right)}^3=\frac{4\times 8\pi r^3}{3}\mathrm{.....................}\left(i\right)$  
$\therefore$ exclude volume for 1 molecule $=\frac{2}{3}\times 8\pi r^3\mathrm{..............}\left(ii\right)$ 
                      $=4\times \left(\frac{4}{3}\pi r^3\right)$
                     = 4 x volume of one molecule = 4v
$\therefore$  excluded volume for $N_A$molecules = 4 $N_{A}v$= b (b = $4N_{A}v$ where $N_A$is Avogadro’s No.)