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Question: At low pressures, van der Waals' equation is written as\(\left( P + \frac{a}{V^{2}} \right)\) V = RT...

At low pressures, van der Waals' equation is written as(P+aV2)\left( P + \frac{a}{V^{2}} \right) V = RT. The compressibility factor is then equal to–

A

(1−aRTV)\left( 1 - \frac{a}{RTV} \right)

B

(1−RTVa)\left( 1 - \frac{RTV}{a} \right)

C

(1+aRTV)\left( 1 + \frac{a}{RTV} \right)

D

(1+RTVa)\left( 1 + \frac{RTV}{a} \right)

Answer

(1−aRTV)\left( 1 - \frac{a}{RTV} \right)

Explanation

Solution

V>>b⇒(P+av2)V=RTV > > b \Rightarrow \left( P + \frac{a}{v^{2}} \right)V = RT \ PV=RT−aVPV = RT - \frac{a}{V}

̃ PVRT=1aRTV=Z\frac{PV}{RT} = 1\frac{a}{RTV} = Z