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Question

The density of vapours of substance at 1 atm and 600 K is 0.32 kg/m3. Vapours effuse through a small orifice at a rate of 1.414 times faster than O2 at same conditions. The Z of the vapours is:
R=112 l atm/mol K ; 253 J/mol K

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Solution

When the gas effuses, velocity 1M
VxVO2MO2Mx
VxVO2=32x=1.414
32x=2
x=16 g/mol
Molar volume of the gas, Vm=16 gmol×1 kg1000 g×m30.32 kg
=50×103 m3=50L/mol

Compressibility factor , Z=PVmnRT
Z=1 atm×50 L/mol112 L atm/mol K×600 K=1

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