Question

Ideal gas obey $PV=nRT$ 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 $T_B=\frac{a}{Rb}$. 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:
$\left(P+\frac{a}{V^2}\right)(V-b)=RT$
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
$\left(P+\frac{n^{2}a}{V^2}\right)(V-nb)=nRT$
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. $\left(P+\frac{n^{2}a}{V^2}\right)=nRT$
• B. $P(V-b)=nRT$
• C. $P(V-nb)=nRT$
• D. $PV=nRT$

Answer 1

Answer: (C)

$\left[P+\frac{n^{2}a}{V^2}\right](V-nb)=nRT$
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
$P[V-nb]=nRT$
or $PV=nRT+Pb$
or $PV>nRT$
or $Z>1\left[Z=1+\frac{Pb}{RT}\right]$