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

`Z=(PV)/(nRT), i.e., 0.5=(100xxV)/(1xx0.082xx273)" or "V=0.1119" L"`
`(P+(a)/(V^(2)))(V-b)=RT` for 1 mol
Neglecting b, `(P+(PV)/(V^(2)))V=RT " or "PV+(a)/(V)=RT" or " (PV)/(RT)+(a)/(VRT)=1`
or `" " a=(1-(PV)/(RT))VRT=(1-0.5)0.1119xx0.082xx273=1.252" atm "L^(2)mol^(-2)`