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  4. The rate of diffusion of methane at a given temperature is twice of a gas X. The molar mass of the gas X is:

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Q. The rate of diffusion of methane at a given temperature is twice of a gas X. The molar mass of the gas X is:

KEAMKEAM 2001

Solution:

Relation between rate of diffusions and molar masses of the gases X and
$ C{{H}_{4}} $ is $ \frac{{{r}_{x}}}{{{r}_{C{{H}_{4}}}}}=\sqrt{\frac{{{M}_{C{{H}_{4}}}}}{{{M}_{x}}}} $
Let the rate of diffusion of gas
$ X=a $ $ \therefore $
$ \frac{a}{2a}=\sqrt{\frac{16}{{{M}_{X}}}} $
( $ \because $ $ C{{H}_{4}}=12.4=16 $ )
$ \therefore $ $ \frac{1}{2}=\sqrt{\frac{16}{{{M}_{X}}}} $
$ \therefore $ $ {{M}_{X}}=16\times 4=64 $
So, the molar mass of gas X is 64.