Question

One mole of nitrogen gas at $0.8atm$ takes $38$ second to diffuse through a pin hole whereas one mole of an unknown compound of xenon with fluorine at $1.6atm$ takes $57$ second to diffuse through the same hole.

Calculate the molecular formula of the compound :

Answer 1

$\frac{r_{N_2}}{r_{Xe{F}_n}}=\frac{P_{N_2}}{P_{Xe{F}_n}}\sqrt{\frac{M_{Xe{F}_n}}{M_{N_2}}}$

$\frac{r_{N_2}}{r_{Xe{F}_n}}=\frac{\frac{Molarvolume}{t_{N_2}}}{\frac{Molarvolume}{t_{Xe{F}_n}}}=\frac{t_{Xe{F}_n}}{t_{N_2}}=\frac{57}{38}$

$\therefore \frac{57}{38}=\frac{0.8}{1.6}\sqrt{\frac{M_{Xe{F}_n}}{28}}$
$M_{Xe{F}_n}={\left(\frac{57}{38}\right)}^2\times {\left(\frac{1.6}{0.8}\right)}^2\times 28$

$=252$

$Xe+nF=252$

$131+n\times 19=252$

$n=6$

Molecular formula $=Xe{F}_6$.