Question

The critical temperature and pressure of $C{O}_2$ gas are $304.2K$ and $72.9atm$ respectively. what is the radius of $C{O}_2$ molecules assuming it to behave as Vander Waal's gas?

Answer 1

Given critical temperature $T_c=304.2$K

Given critical pressure $P_c=72.9K$atm

Critical volume $V_c=3b=3\frac{R{T}_C}{8P_C}$

$V_c=4N\frac{4}{3}\pi r^3$

where N=Avogadro constant

r=Radius

$4\times 6.022\times {10}^{23}\times \frac{4}{3}\times \frac{22}{7}\times r^3=\frac{3\times 0.0821\times 304.2}{8\times 72.9}$

$r^3=4.25\times {10}^{-30}$

$r=1.62A$