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Hydrogen gas diffuses from two different vessels $X$ and $Y .$
Vessel $X$ has a circular orifice while vessel $Y$ has a square orifice
of length equal to the radius of the orifice of vessel $X$ . Assuming
same temperature and pressure, the ratio of the rates of diffusion
of gas from vessel $X$ to vessel $Y$ is :

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$\frac{1}{π}$

$1 : 1$

$1 : 2$

$π .$

answer is D.

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Detailed Solution

Let r = radius of the orfice of vessel X.

We know : rate of diffusion is directly proportional to the area of orfice.

So for vessel X with circular orifice $r_{x} \propto {πr}^{2} \dots (i);$

for square vessel Y length=r ; orifice = $r_{y} \propto r^{2}$

Ratio of rates of diffusion of X and Y ;

$\frac{r_{x}}{r_{y}} = \frac{{πr}^{2}}{r^{2}} or \frac{r_{x}}{r_{y}} = π$

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