`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

Answer

20

Explanation

(a) Under low pressure region `V` is high
`(V-b) ~~V rArr (P+(a)/(V^(2))) V = RT rArr PV +(a)/(V) = RT`
`rArr (PV)/(RT) +(a)/(RTV) = 1 :. Z = (PV)/(RT) = (1-(a)/(RTV))`
`Z = 1 -(20.39)/(0.0821 xx 350 xx 35) = 0.98`
(b) Under high pressure region, `P` is high,
`(P+(a)/(V^(2))) ~~ P :. P (V-b) = RT`
`rArr PV - Pb = RT rArr (PV)/(RT) -(Pb)/(RT) = 1`
`:. Z = (PV)/(RT) = 1+(Pb)/(RT)`
`Z = 1+(b)/(V) = 1+(0.1383)/(35) = 1+ 0.004 = 1.004`
by approximation `( :'(PV)/(RT)=1,(P)/(RT)=(1)/(V))`