We have 0.5 g of hydrogen gas in a cubic chamber of side 3 cm kept at NTP. The  gas in the chamber is compressed keeping the temperature constant until a final  pressure of 100 atm is reached. What is the volume of gas in final state as per ideal  gas assumption? Is one justified in assuming the ideal gas law, in the final state?  (Hydrogen molecules can be considered as spheres of radius 1  $\stackrel{o}{A}$).

The ideal gas law is applicable if the volume of molecules is negligible in  comparision to the volume of the gas.
Volume of hydrogen molecule =  $V=\frac{4}{3}\pi {\left(1\times {10}^{-10}\right)}^3=4\times {10}^{-30}{m}^3$
Number of moles of hydrogen =  $n=\frac{massofgas}{molarmassofgas}=\frac{0.5}{2}=0.25$
Number of  H₂ molecules present =  $N=0.25\times \left(6.023\times {10}^{23}\right)$
Volume of these molecules =  $NV=0.25\times \left(6.023\times {10}^{23}\right)\times \left(4\times {10}^{-30}\right)=6\times {10}^{-7}{m}^3$
Using ideal gas equation,
 $P_1{V}_1=P_2{V}_2$
 $V_2=\frac{P_1{V}_1}{P_2}=\frac{1}{100}{\left(3\times {10}^{-2}\right)}^3=2.7\times {10}^{-7}{m}^3$.
The two volumes are close. Hence, intermolecular forces will play role and gas  behaviour will deviate from ideal gas.