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 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 `1Å`).

Explanation

No. In the final state, one is not justified in 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.