Question

The compression factor (compressibility factor) for one mole of a Vander Waals gas at $0^{o}C$ and $100$ atmospheric pressure is found to be $0.5$. Assuming that the volume of a gas molecule is negligible, calculate the Van der Waals constant $a$.

Answer 1

The compressibity factor is given by,

$Z=\frac{PV}{RT}0.5=\frac{100\times V}{0.082\times 273}V=0.0117L$

Vanderwaals equation,

$(P+\frac{a}{v^2})(V-0)=RTPV=RT-\frac{a}{V}ora=RTV-{PV}^2$

$substitutingtheabovevalues,A=(0.082\times 0.1119\times 273)-(100\times 0.1119\times 0.1119)$

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