Question

If 240 ml, of a gas $x$ diffuses through a porous membrane in 20 min whereas the same volume of methane diffuses in 10 min at the same temperature and pressure, the molar mass in g mol${}^{-1}$ of gas $x$ is:

• A. 8
• B. 64
• C. 32
• D. 128

Answer 1

The correct option is B 64

Rate of diffusion, $R\propto \frac{1}{\sqrt{M}}\propto \frac{1}{t}\Rightarrow t\propto \sqrt{M}$

$t_1/t_2=\sqrt{M_x/M_2}$

$\sqrt{M_x/M_2}=20/10$

$M_2$ = Molar mass of methane = 16

$\sqrt{M_x/16}=20/10$

$\sqrt{M_x/16}=2$

$\sqrt{M_x}=4\times 2$

$\sqrt{M_x}$= 8

$M_x$ = 64
Molar mass of $x=64$ g/mol