Question

A certain volume of nitrogen gas at 0.8 atm takes 25 seconds to diffuse through a pin hole whereas the same volume of an unknown compound of xenon and flourine at 1.6 atm takes 37 second to diffuse through the same hole. The molecule formed can be expressed as $Xe{F}_n$. Find the value of $n$.
(Given: Molecular mass of Xe = 131 u)

Answer 1

$\frac{r_{N_2}}{r_{Xe{F}_n}}=\frac{P_{N_2}}{P_{Xe{F}_n}}\sqrt{\frac{M_{Xe{F}_n}}{M_{N_2}}}$
$\frac{r_{N_2}}{r_{Xe{F}_n}}=\frac{\frac{\text{Volume of}{N}_2}{t_{N_2}}}{\frac{\text{Volume of}Xe{F}_n}{t_{Xe{F}_n}}}=\frac{t_{Xe{F}_n}}{t_{N_2}}=\frac{37}{25}$
$\therefore \frac{37}{25}=\frac{0.8}{1.6}\sqrt{\frac{M_{Xe{F}_n}}{28}}$
$M_{Xe{F}_n}={\left(\frac{37}{25}\right)}^2\times {\left(\frac{1.6}{0.8}\right)}^2\times 28$
$=245.3$
$M_{Xe}+n{M}_F=245.3$
$131+n\times 19=245.3$
$n=6.02\approx 6$
$\therefore$ Molecular formula $=Xe{F}_6$