Question

For one mole of a van der Waals gas when $b=0$ and $T=300 K$, the $P V$ vs. $1 / V$ plot is shown below. The value of the van der Waals constant $a$ (atm.litre $^{2} mol ^{-2}$ ) is

• A. 1.0
• B. 4.5
• C. 1.5
• D. 3.0

Answer 1

Answer: (C)

van der Waals equation for 1 mole of real gas is,

$\left( P +\frac{ a }{ V ^{2}}\right)( V - b )= RT$

but, $b =0$ (given)

$\Rightarrow \left( P +\frac{ a }{ V ^{2}}\right)( V )= RT$.....(i)

$\therefore PV =- a \times \frac{1}{ V }+ RT$

$y = mx + c$

Slope $=\tan (\pi-\theta)=- a$

So, $\tan \theta= a =\frac{21.6-20.1}{3-2}=1.5$

or, $\tan \theta=\frac{24.6-20.1}{3-0}=1.5$