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

Question

One mole of nitrogen gas at 0.8 atm takes 38 seconds to diffuse through a pinhole, whearas one mole of an unknown compound of xenon with fluorine at 1.6 atm takes 57 seconds to diffuse through the same hole. Calculate the molecular mass of the compound.

(A) 252

(B) 525

(C) 262

(D) 380

Answer 1

$\begin{array}{l}\text { } \frac{r_1}{r_2}=\sqrt{\frac{M_2}{M_1}} \times \frac{P_1}{P_2} \text { or } \frac{n_1}{t_1} \times \frac{t_2}{n_2}=\sqrt{\frac{M_2}{M_1}} \times \frac{P_1}{P_2} \\\text { or } \frac{1}{38} \times \frac{57}{1}=\sqrt{\left(\frac{M_{\text {gas }}}{28}\right)} \times \frac{0.8}{1.6} \\\therefore M_{\text {gas }}=\left[\frac{57}{38} \times \frac{1.6}{0.8}\right]^2 \times 28 \Rightarrow M_{\text {gas }}=252 \\\end{array}$

So, The correct option is  (A).