Question

One mole of nitrogen gas at 0.8 atm takes 38 s to diffuse through a pinhole, whereas 1 mol of an unknown compound of xenon with fluorine at 1.6 atm takes 57 s to diffuse through the same hole. The formula of the compound is XeF${}_n$. What is the value of n?

Answer 1

From Graham's law of diffusion, we know that for the same volume moles diffused,

$Timetaken\propto \sqrt{M}\times \frac{1}{P}$

$\therefore \frac{t_{gas}}{t_{nitrogen}}=\frac{P_{nitrogen}}{P_{gas}}\sqrt{\frac{M_{gas}}{M_{nitrogen}}}$

or $\frac{57}{38}=\frac{0.8}{1.6}\sqrt{\frac{M_{gas}}{28}}$

or $M_{gas}=252$

Let the formula of xenon fluoride be $Xe{F}_n$:

$\therefore M=131.29+n\left(19\right)=252$

$n=6.35\approx 6$

Thus $n=6$