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

We have 0.5 g of hydrogen gas in a cubic chamber of size 3 cm kept at

1.	We have 0.5 g of hydrogen gas in a cubic chamber of size 3 cm kept at NTP. The gas in the chamber is compressed keeping the temperature consist till a final pressure of 100 atm. Is one justified in assuming the ideal gas law, in the final state ? (Hydrogen molecules can be considered as spheres of radius 1Å).
Answer» Solution :No. In the FINAL state, one is not justifiedin assuming the ideal gas law as detailed below: Number of MOLECULES in 0.5 G of hydrogen= `(6.023 XX 10^(23))/(2) xx 0.5 = 1.5 xx 10^(23)` Volume of each molecules = `4/3 pi r^(3) = 4/3 xx 22/7 (10^(-10))^(3) = 4 xx 10^(-30) m^(3)` `:.` TOTAL volume of the molecules contained, `V_(1) = 1.5 xx 10^(23) xx 4 xx 10^(-30)m^(3) = 6 xx 10^(-7)m^(3)` Final volume available , `V_(1) = 1.5 xx 10^(23) xx 4 xx 10^(-30) m^(3) = 6 xx 10^(-7)m^(3)` As `V_(2) = V_(1)`, the intermolecular forces cannot be ignored as done in ideal gas situation.