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Question: At low pressures (For 1 mole), the Vander Waal’s equation is written as \[\left\lbrack p + \frac{a}...

At low pressures (For 1 mole), the Vander Waal’s equation is written as

[p+aV2]V=RT\left\lbrack p + \frac{a}{V^{2}} \right\rbrack 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

(P+aV2)\left( P + \frac{a}{V^{2}} \right) (V) = RT

PV + aV\frac{a}{V} = RT

PVRT=1−aVRT\frac{PV}{RT} = 1 - \frac{a}{VRT}