Question

For one mole of a van der Waals' gas when $b=0$ and $T=300K$. the $pVvs1/V$ plot is shown below. The value of the van der Waals' constant a (atm $Lmo{l}^{-2}$)

• A. 1.0
• B. 4.5
• C. 1.5
• D. 3.0

Answer 1

Answer: (C)

The van der Waals equation of state is
$\left(p+\frac{n^a}{V^2}\right)(V-nb)=nRT$
For one mole and when $b=0$, the above equation condenses to $\left(p+\frac{n^a}{V^2}\right)V=RT$
$\Rightarrow pV=RT-\frac{a}{V}\dots (i)$
Eq. (i) is a straight equation between $pV$ and $\frac{1}{V}$ whose slope is - - $a$'. Equating with slope of the straight line given in the graph.
$-a=\frac{20.1-21.6}{3-2}=-1.5$
$\Rightarrow a=1.5$