Question

High temperature and high pressure.The compression factor (compressibility factor) for one mole of a Van der Waals gas $0^{o}C$ and $100$ atmosphere pressure is found to be $0.5$ Assuming that the volume of a gas molecule is negligible. Calculate the Van der Waals constant ${}^{\prime }{a}^{\prime }$.

Answer 1

Compressibilty factor $Z=\frac{PV}{RT}$

$\Rightarrow 0.5=\frac{100\times V}{0.082\times 273}$

$\therefore V=0.1117L$

Assuming volume of a gas is negligible,

$(P+\frac{a}{V^2})(V-0)=RT$

or, $PV=RT-a/V$

or, $a=RTV-P{V}^2$

$=(0.082\times 0.1117\times 273)-(100\times {0.1117}^2)$

$=1.253atm{L}^{2}mo{l}^{-2}$