Question

A graph is plotted between $P{V}_m$ along Y-axis and $P$ along X-axis at particular temperature, 300 K, where $V_m$ is the molar volume of $N_2$ gas. Calculate the intercept along Y-axis. (Take $R=0.0083{\text{kJ K}}^{-1}{\text{mol}}^{-1}$)

Answer 1

We know, the van der Waal equation (for one mole) of a real gas is:
$(P+\frac{a}{V_m^2})(V_m-b)=RT$
$\Rightarrow P{V}_m-Pb+\frac{a}{V_m}-\frac{ab}{V{m}^2}=RT$
$\Rightarrow P{V}_m=RT+Pb-\frac{a}{V_m}+\frac{ab}{V{m}^2}$
To calculate the intercept $P\to 0$, hence $V_m\to \infty$, due to which the terms $\frac{a}{V_m}\text{and}\frac{ab}{V{m}^2}$ can be neglectred.

$\therefore P{V}_m=RT+Pb$
Thus the intercept along Y axis is
$=RT=0.0083\times 300=2.49{\text{kJ mol}}^{-1}$