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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).

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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 = (Vin/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.

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