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  4. A certain gas diffuses four times as quickly as oxygen. The molecular weight of the gas is

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Q. A certain gas diffuses four times as quickly as oxygen. The molecular weight of the gas is

AIIMSAIIMS 1995States of Matter

Solution:

rate of diffusion $\propto \frac{1}{\sqrt{M}}$
M = Molecular mass
$\Rightarrow \frac{r_{x}}{r_{o_{2}}} =4=\sqrt{\frac{M_{o_{2}}}{M_{x}}} $
$r_{x} $ =rate of diffusion of x (gas)
$M_{x} $ =Molecular mass of x
$\Rightarrow \frac{r_{x}}{r_{o_{2}}} =4=\sqrt{\frac{M O_{2}}{M_{x}}} $
$\Rightarrow \ 16 =\frac{32}{M_{x}}$
$ \Rightarrow M_{x}=2$