Question

At a moderate pressure, the van der Waals' equation is written as
$\left[p+\frac{a}{V^{2}}\right] V=R T$
The compressibility factor is equal to

• A. $\left(1-\frac{a}{R T V}\right)$
• B. $\left(1-\frac{R T V}{a}\right)$
• C. $\left(1+\frac{a}{R T V}\right)$
• D. $\left(1+\frac{R T V}{a}\right)$

Answer 1

Answer: (A)

From the given equation
${\left[p+\frac{a}{V^{2}}\right] V=R T} $
$p V+\frac{a}{V}=R T$
$\frac{p V}{R T}+\frac{a}{R T V}=1 $
$\frac{p V}{R T}=Z \text { (Compressibility factor) }=\left(1-\frac{a}{R T V}\right)$