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Question
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 1 Å).
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Solution
Assuming hydrogen molecules as spheres of radius 1 Å.
So, r = 1 Å = radius
The volume of hydrogen molecules = `4/3 pir^3`
= `4/3 (3.14)(10^-10)^3`
= `4 xx 10^-30 m^3`
Number of moles of H2 = `"Mass"/"Molecular mass"`
= `0.5/2`
= 0.25
Molecules of H2 present = Number of moles of H2 present × 6.023 × 1023
= 0.25 × 6.023 × 1023
∴ Volume of molecules present = Molecules number × Volume of each molecule
= 0.25 × 6.023 × 1023 × 4 × 10–30
= 6.023 × 1023 × 10–30
= 6 × 10–7 m3 ......(i)
Now, if the ideal gas law is considered to be constant,
`p_iV_i = p_fV_f`
`V_f = (p_i/p_f)`
`V_i = (1/100)(3 xx 10^-2)^3`
= `(27 xx 10^-6)/10^2`
= 2.7 × 10–7 m3 ......(ii)
Hence, on compression, the volume of the gas is of the order of the molecular volume [form equation (i) and equation (ii)]. The intermolecular forces will play a role and the gas will deviate from ideal gas behaviour.
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