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Question

The compression factor (compressibility factor) for 1 mole of a van der Waals' gas at 0 C and 100 atmospheric pressure is found to be 0.5. Assuming that the volume of a gas molecule is negligible, calculate the van der Waals' constant 'a' (in L2mol1atm)

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Solution

Given,
Moles of gas=1 mol
T=0 C=273 K
P=100 atm
Z=0.5
We know that,
Z=PVRT
0.5=100×V0.082×273
V = 0.112 L
Accoording to van der Waals' equation,
(P+aV2)(Vb)=RT for 1 mole
As volume of a gas moecule is negligible so b=0
[100+a(0.112)2][0.1120]=0.0821×273
On solving, we get a=1.253 L2 mol2atm

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