`1 mol` of `C Cl_(4)` vapours at `77^(@)C` occupies a volume of `35.0 L`. If van der Waals constants are `a=20.39 L^(2) atm mol^(-2)` and `b=0.1383 L mol^(-1)`, calculate compressibility factor `Z` under
(`a`) Low pressure region
(`b`) High pressure region

Explanation

(`a`) Under low pressure region, `V` is high
`(V-b)~~V`
`(P+(a)/(V^(2)))V=RT`
`PV+(a)/(V)=RT`
`:. Z=(PV)/(RT)=(1-(a)/(RTV))`
`=1-(20.39)/(0.0821xx350xx35)=0.98`
(`b`) Under high pressure region, `P` is high
`(P+(a)/(V^(2)))V~~P`
`:.P(V-b)=RT` or `PV-Pb=RT`
or `(PV)/(RT)-(Pb)/(RT)=1`
`implies Z=(PV)/(RT)=1+(Pb)/(RT)`
`=1+(b)/(V)` by approximation(`:' (PV)/(RT)=1`, `(P)/(RT)=(1)/(V))`
`=1+(0.1383)/(35)=1+0.004=1.004`