# At a given temperature T , gases Ne, Ar , Xe and Kr are found to deviate from ideal gas behaviour . Their equation of state is given as $p=\frac{RT}{V-b}$  at T  . Here , b is the van der Waals constant . Which gas will exhibit steepest increase in the plot of Z ( compression factor ) Vs p ?Option 1)XeOption 2)KrOption 3)NeOption 4)Ar

S solutionqc

Compressibility Factor -

used to find deviation of a gas from ideal behaviour

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Compressibility Factor -

$\dpi{100} Z=\frac{V_{real}}{V_{ideal}}$

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Compressibility Factor -

For ideal gas Z=1

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Compressibility Factor -

at  low pressures, all gases have Z less than 1.

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Compressibility Factor -

at very high pressure, all gases have Z greater than 1.

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Compressibility Factor -

for hydrogen and helium, Z is  greater than 1 even at low pressures.

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we know $compression \:\:factor\:\: z\:\:= 1+\frac{pb}{RT}$  , at T=Constant

$slop \propto \:b$   ( volume of molecules )

order of radii of element $Xe>Kr>Ar>Ne$

b value of Xe will be higher so , the graph will be steepest .

Option 1)

Xe

Option 2)

Kr

Option 3)

Ne

Option 4)

Ar

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