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′.
We know that,
Z=PVRT
0.5=100×V0.0821×273
V=0.112 litre
According to van der Waals' equation,
(P+aV2)(V−b)=RT for 1 mole
[100+a(0.112)2][0.112−0]−0.0821×273
On solving, we get a=1.253 L2mol−2atm.