InterviewSolution
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InterviewSolution
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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`). |
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Answer» 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. |
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