The compressibility factor for definite amount of van der Waals' gas at `0^(@)C` and `100 atm` is found to be `0.5`. Assuming the volume of gas molecules negligible, the van der Waals' constant `a` for gas is

Explanation

`Z = (PV)/(RT) =0.5`
`(100 xxV)/(0.082 xx 273) = 0.5`
`V = 0.112 litre`
Now using van der Waals' equation
`[P+(a)/(V^(2))][V] =RT (:' b` is negligible)
or `[P+(a)/(V^(2))](RT)/(V)`
`:. [100 +(a)/((0.112)^(2))]= (0.082 xx 273)/(0.112) = 199.88`
`:. (a)/((0.112)^(2)) = 99.88`
`a =1.253 "litre"^(2) mo1^(-2)` atm .