Question

Ideal gas obey $P V=n R T$ at all the conditions of $P$ and $T$. At STP all the gases deviate from ideal behaviour. All gases are thus real gases, however they behave ideally at Boyle's temperature $T_B=\frac{a}{R b}$. van der Waals' suggested a modified gas equation to describe the behaviour of real gases over wider range of pressure and temperature. The van der Waals' equation for one mole of gas is written as:
$\left(P+\frac{a}{V^2}\right)(V-b)=R T$
If $n$ moles of gas are present in volume $V$; the volume of one mole of gas would be $\frac{V}{n}$. So, van der Waals' equation changes to
$\left(P+\frac{n^2 a}{V^2}\right)(V-n b)=n R T$
where, $P, V$ and $T$ are the observed pressure, volume and temperature for the gas under study. ${ }^{\prime} a^{\prime}$ and ${ }^{\prime} b^{\prime}$ are van der Waals' parameters, (i.e., constant of attraction and constant of volume respectively) which vary from gas to gas. The parameters $a$ and $b$ take care of the intermolecular forces and size of the molecules respectively.
At high pressure, the van der Waals' equation is reduced to

• A. $\left(P+\frac{n^2 a}{V^2}\right)=n R T$
• B. $P(V-b)=n R T$
• C. $P(V-n b)=n R T$
• D. $P V=n R T$

Answer 1

Answer: (C)

$\left[P+\frac{n^2 a}{V^2}\right](V-n b)=n R T$
At high pressure, volume of molecules being appreciably significant in comparison to volume of gas as well as gases show positive deviations which is possible only when
$P[V-n b]=n R T$
or $P V=n R T+P b$
or $P V>n R T$
or $Z>1\left[Z=1+\frac{P b}{R T}\right]$