The compression factor (compressibility factor) for `1 mol` of a van der Waals gas at `0^(@)C` and `100 atm` pressure is found to be `0.5`. Assuming that the volume of a gas molecule is neligible, calculate the van der Waals constant `a`.

Explanation

In case of negligible molecular volume, b = 0. For 1 mole of gas `( P + (a)/(V^(2))) V = RT`
`rArr pV + (a)/(V) = RT rArr (pV)/(RT) + (a)/(VRT) = 1 [ :'(pV)/(RT) = z]`
`rArr z + (a)/(((ZRT)/(p)) RT) = 1 rArr Z + (a)/(ZR^(2) T^(2)) =1`
`rArr a = (ZR^(2) T^(2) (1 -Z))/(p) = (0.5 (0.082 xx 273)^(2) (1- 0.5))/(100), a = 1.25 atm L^(2) mol^(-2)`