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

Assuming hydrogen molecules as spheres of radius `1 Å`
So `r= 1 Å=` radius
The volume of hydrogen molecules `=4/3 pi r^(3)`
`= 4/3 (3.14)(10^(-10))^(3)`
`~~ 4 xx 10^(-30) m^(3)`
`"Number of moles of " H_(2) =("Mass")/("Molecular mass")`
`=(0.5)/(2)= 0.25`
Molecules of `H_(2)` present =Number of moles of `H_(2)` present `xx 6.023 xx 10^(23)`
`=0.25 xx 6. 023 xx 10^(23)`
`:.` Volume of molecules present = Molecules number `xx` volume of each molecule
`=0.25 xx 6.023 xx 10^(23) xx 4 xx 10^(-30)`
`=6.023 xx 10^(23) xx 10^(-30)`
`~~ 6xx 10^(-7) m^(3)`
Now. it ideal gas Law is considered to be constant.
`p_(i)V_(i) =p_(f)V_(f)`
`V_(f) = (p_(i))/(p_(f)) V_(i) = ((1)/(100)) (3 xx 10^(-2))^(3)`
`=(27 xx 10^(-6))/(10^(2))`
`=2.7 xx 10^(-7) m^(3) " ".........(ii)`
Hence on compression the volume of the gas is of the order of the molecular volume [form Eq.(i) and Eq.(ii).]. The intermolecular forces will play role and the gas will deviate from ideal gas behaviour.