Question

One mole of $N_2$ gas at $0.8atm$ takes $38sec$ to diffuse through a pin hole, whereas one mole of an unknown compound of Xenon with $F$ at $1.6atm$ takes $57sec$ to diffuse through the same hole. Calculate the molecular formula of the compound. (At. wt. $Xe=138,F=19)$.

Answer 1

$\frac{diffusionrate1}{diffusionrate2}=\sqrt{\frac{M_2}{M_1}}\times \frac{P_1}{P_2}$

$diffusionrate=\frac{n_1}{t_1}\times \frac{n_2}{t_2}$

moles are same for both compounds so,

$\frac{57}{38}=\sqrt{\frac{M_2}{28}}\times \frac{.8}{1.6}$

$M_2=252$

$131+19x=252$ or $x=6$

The formula of compound is $Xe{F}_6$