Question

One mole of $N_2$ gas at 0.8 atm takes 38 sec to diffuse through a pin hole, whereas one mole of an unknown compound of xenon with $F$ at 1.6 atm takes 57 sec to diffuse through the same hole. Calculate the molecular formula of the compound.

• A. $Xe{F}_4$
• B. $Xe{F}_6$
• C. $Xe{F}_2$
• D. $Xe{F}_3$

Answer 1

Answer: (B)

$Xe{F}_6$

We know,

$\frac{r_1}{r_2}=\sqrt{\frac{M_2}{M_1}}\times \frac{P_1}{P_2}$

Also we know that, $r_1=\frac{n_1}{t_1}$ and $r_2=\frac{n_2}{t_2}$

So on substituting the given values we get,

$\frac{1}{28}\times \frac{52}{1}=\sqrt{\frac{M}{28}}\times \frac{0.8}{1.6}$

$⟹M=252$

Now,

Molecular weight of $[Xe+(F{)}_x]=252$

$⟹113+19x=252⟹x=6$

Hence, the molecular formula of the compound is $Xe(F{)}_6$