Question

At low pressures (For 1 mole), the van der Waals equation is written as $[p+\frac{a}{V^2}]V=RT$ The compressibility factor is then equal to:

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

Answer 1

The correct option is D $(1-\frac{a}{RTV})$

At low pressure,
$(P+\frac{a}{V^2})\left(V\right)=RT$
$PV+\frac{a}{V}=RT$
$\therefore \frac{PV}{RT}=1-\frac{a}{VRT}$