Question

The critical volume of oxygen is 2.35 cm${}^{-3}$ g${}^{-1}$. If the molecular diameter is $2.7\times {10}^{-x}cm$,then the value of $x$ is_______.

Answer 1

The critical volume of a Van Der Walls gas, in terms of Van Der Walls constant b, is given by $V_C=3b$

Hence $b=0.78{cm}^{-3}{g}^{-1}$

Also, b is the effective volume of one gram of gas molecules, hence,

$4X\frac{6.022X{10}^{23}}{32}X\frac{4}{3}\pi r^3=0.78$

Hence, $d=2r=2.7X{10}^{-8}cm$

Hence $x=8$