The molecular weight of a gas which diffuse through a porous plug at 1/6 th of the speed of hydrogen under identical conditions is :

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Solution

The correct option is D 72
Hydrogen
Molecular weight of $H_{2} = M_{1} = 2$
Rate of diffusion of $H_{2} = r_{1} = r$
Unknown gas
Molecular weight of unknown gas $= M_{2} = x = ?$
Rate of diffusion of unknown gas $= r_{2} = r / 6$
$\frac{r_{1}}{r_{2}} = \sqrt{\frac{M_{2}}{M_{1}}} \Rightarrow \frac{r}{r / 6} = \sqrt{\frac{M_{2}}{2}}$
$\Rightarrow 6 = \sqrt{\frac{x}{2}} \Rightarrow 36 = \frac{x}{2} \Rightarrow x = 72$

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