Question

The critical temperature and pressure of $C{O}_2$ gas are 304.2 K and 72.9 atm respectively.Calculate the radius of $C{O}_2$ molecule assuming it to behave van der Waal's gas.

Answer 1

$T_C=\frac{8a}{27bR}$ and $P_C=\frac{a}{{27b}^2}$

$\therefore b=\frac{R}{8}\times \frac{T_C}{P_C}$

$=\frac{0.0821}{8}\times \frac{304.2}{72.9}=0.428lit{mol}^{-1}$

now, $n={4N}_0\frac{4}{3}{\Pi r}^3$

$\Rightarrow 0.0428=4\times 6.023\times {10}^{23}\times \frac{4}{3}\times \Pi \times r^3$

$\Rightarrow r=2.37\times {10}^{-9}dm$