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  Ao).

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=43π1×10−103=4×10−30m3Number of moles of hydrogen =  n=mass  of gasmolar  mass  of  gas=0.52=0.25Number of  H2 molecules present =  N=0.25×6.023×1023Volume of these molecules =  NV=0.25×6.023×1023×4×10−30=6×10−7m3Using ideal gas equation, P1V1=P2V2 V2=P1V1P2=11003×10−23=2.7×10−7m3.The two volumes are close. Hence, intermolecular forces will play role and gas  behaviour will deviate from ideal gas.