Question

Show that the compressibility factor can be as
$z \: = \frac{V \: real }{V \: Ideal }$
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Answer 1

Answer

Z=1−VRTa

The van der Waals equation is as given below.

(P+V2n2a)(V−nb)=nRT

For n=1, the equation becomes,

(P+V2a)(V−b)=RT

At low pressure,  V > > b

Hence, the equation becomes,

(P+V2a)V=RT

Rearrange above equation

PV+Va=RT

PV=RT−Va

Dividing both sides by RT

RTPV=1−VRTa

z=1−VRTa.

Thus, if Z is a compressibility factor, van der waals equation at low pressure can be written as Z=1−VRTa.

Answer 2

you r answer is in aatchment