Question

We have 0.5 g of hydrogen gas in a cubic chamber of size 3cm kept at NTP. The gas in the chamber is compressed keeping the temperature constant till a final pressure of 100 atm. Is one justified in assuming the ideal gas law, in the final state? (Hydrogen molecules can be consider as spheres of radius 1 Å).

Answer 1

We have 0.25 × 6 × 10²³ molecules, each of volume 10^-30m³.

Molecular volume = 2.56 x 10^-7m³ 

Supposing Ideal gas law is valid.

Final volume = (V_in/100) = ((3)³ x 10^-6)/100 ≈ 2.7 x 10^-7m³

which is about the molecular volume. Hence, intermolecular forces cannot be neglected. Therfore the ideal gas situation does not hold.