Question

At relatively high pressure, van der Waals equation reduces to

• A. $PV=RT$
• B. $PV=RT+\frac{q}{V}$
• C. $PV=RT+Pb$
• D. $PV=RT-\frac{a}{V^2}$

Answer 1

The correct option is C $PV=RT+Pb$

The van der Waals equation is given by
$(P+\frac{a{n}^2}{V^2})(V-nb)=nRT$
For one mole of a real gas, this can be reduced to
$(P+\frac{a}{V^2})(V-b)=RT$
At relatively high pressure, the volume of the gas is very small.
Hence, we cannot neglect the term $nb$ but we can neglect the term $\left(\frac{a}{V^2}\right)$ as it is negligible when compared with the value of $P$.
$\Rightarrow P(V-b)=RT$
$\Rightarrow PV=RT+Pb$
Thus, option (c) is the correct answer.