Question

The gases which strictly follow the general equation $(PV=nRT)$ are called ideal or perfect gases. Actually, there is no gas which is perfect or ideal. A real gas is one which actually exists, whether it obeys gas laws strictly or not. Under ordinary conditions, only those gases nearly behave as ideal or perfect which have very low boiling points such as nitrogen, hydrogen, etc. The most easily liquefiable and highly soluble gases such as ammonia, carbon dioxide, sulphur dioxide show large deviations.
A very convenient method of studying deviation of real gases from ideal behaviour is through a compressibility factor $\left(Z\right)$.
$Z=\frac{PV}{nRT}$
(i) $Z=1$, for ideal gases.
(ii) $Z\ne 1$, for real gases.

The behaviour of a real gas is usually depicted by plotting compressibility factor $Z$ versus pressure $P$ at a constant temperature. At high temperature and pressure, $Z$ is usually more than one. This fact can be explained by Van der Waals' equation when :

• A. the constant ${}^{\prime }{a}^{\prime }$ is negligible but not ${}^{\prime }{b}^{\prime }$
• B. the constant ${}^{\prime }{b}^{\prime }$ is negligible but not ${}^{\prime }{a}^{\prime }$
• C. both the constant ${}^{\prime }{a}^{\prime }$ and ${}^{\prime }{b}^{\prime }$ are negligible
• D. both the constant ${}^{\prime }{a}^{\prime }$ and ${}^{\prime }{b}^{\prime }$ are not negligible

Answer 1

The correct option is A the constant ${}^{\prime }{a}^{\prime }$ is negligible but not ${}^{\prime }{b}^{\prime }$

The behaviour of a real gas is usually depicted by plotting comprehensibility factor Z versus pressure P at a constant temperature. At high temperature and pressure, Z is usually more than one. This fact can be explained by van der Waals' equation.

In option $A$, The constant ′a′ is negligible but not ′b′
In such cases, the van der Waals' equation reduces to $PV=nRT+nPb$

$Z=\frac{PV}{nRT}$

$Z=\frac{nRT+nPb}{nRT}$

$Z=1+\frac{Pb}{RT}>1$

Hence, te correct option is $\text{A}$