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Speed of Efflux

360 cm3 of ...

Question

$360 c m^{3}$ of $C H_{4}$ gas diffused through a porous membrane is $15$ minutes. Under similar conditions, $120 c m^{3}$ of another gas diffused in $10$ minutes. Find the molar mass of the gas.

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Solution

Rate of different $r = \frac{V}{f}$
$r = \frac{1}{\sqrt{M}}$
therefore,
$\frac{r_{C H_{4}}}{r_{g}} = \sqrt{\frac{M_{g}}{M_{C H_{4}}}} = \frac{V_{C H_{4}} \times t_{g}}{V_{g} \times t_{C H_{4}}}$
$\sqrt{\frac{M_{g}}{16}} = \frac{360 \times 10}{120 \times 15}$
$\sqrt{\frac{M_{g}}{16}} = 2$
$M_{g} = 64$ .

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