Question

At low pressures, the van der Waals equation is written as
$[P+\frac{a}{V^2}]V=RT$
The compressibility factor is then equal to :

• A. $[1-\frac{a}{RTV}]$
• B. $[1-\frac{RTV}{a}]$
• C. $[1+\frac{a}{RTV}]$
• D. $[1+\frac{RTV}{a}]$

Answer 1

The correct option is A $[1-\frac{a}{RTV}]$

$[P+\frac{a}{V^2}]V=RT$
$PV+\frac{a}{V}=RT$
$\frac{PV}{RT}+\frac{a}{RTV}=1$
$\frac{PV}{RT}=Z\left(compressibilityfactor\right)$
$=[1-\frac{a}{RTV}]$