behaves similar to an ideal gas in the limit of large molar volumes
behaves similar to an ideal gas in the limit of large pressures
is characterised by van der Waals' coefficients that are dependent on the identity of the gas but are independent of the temperature
has the pressure that is lower than the pressure exerted by the same gas behaving ideally
Solution
The gas described by van der Waals' equation in the limit of large molar volume, in the intermediate range of pressure experience balancing by two factors.
$
\left(p+\frac{a}{V^2}\right)(V-b)=R T \Rightarrow p V=\frac{a}{V}-p b+\frac{a b}{V^2}=R T
$
(We can neglect the product of two very small constants, $\frac{a b}{V^2}$ )
So,
$
p V+\frac{a}{V}-p b=R T
$
As
$
\frac{a}{V}=p b
$
The gas behaves ideally, $p V=R T$
- The van der Waals' constants ' $a$ ' and ' $b$ ' are characteristics of the gas. The value of these constants are determined by the critical constants of the gas
$
a=3 p_C V_C^2=3 p_C\left(\frac{3 R T_C}{8 p_C}\right)^2=\frac{27\left(R T_C\right)^2}{64 p_C} ; b=\frac{1}{3}\left(\frac{3 R T_C}{8 p_C}\right)=\frac{R T_C}{8 p_C}
$
Question is based on description by van der Waals' equation, that's why we have to ignore the effect of temperature on $a$ and $b$. Actually, the so-called constant varies to some extent with temperature and this shows that the van der Waals' equation is not a complete solution of the behaviour of real gas