Question

The compressibility factor $(Z)$ of one mole of a van der Waals gas of negligible $‘a’$ value is

• A. $1$
• B. $\frac{bp}{RT}$
• C. $1+\frac{bp}{RT}$
• D. $1-\frac{bp}{RT}$

Answer 1

Answer: (C)

van der Waals' equation is
$\left(p+\frac{a}{V^{2}}\right)(V-b)=R T\,\,\,$(for 1 mole)
If $a$ is negligible, $p+\frac{a}{V^{2}} \approx p$
$p(V-b)=R T $
$\Rightarrow p V-p b=R T $
or $\frac{p V}{R T}-\frac{p b}{R T}=1 $
$\Rightarrow \frac{p V}{R T}=1+\frac{p b}{R T}$