From a certain apparatus, the diffusion rate ...

Kinetic Theory

Question : 12 of 14

Marks: +1, -0

From a certain apparatus, the diffusion rate of hydrogen has an average value of

28.7\,\mathrm{cm}^3\,\mathrm{s}^{-1}

. The diffusion of another gas under the same conditions is measured to have an average rate of

7.2\,\mathrm{cm}^3\,\mathrm{s}^{-1}

. Identify the gas.

Solution:

According to Graham’s law of diffusion,

\frac{r_{1}}{r_{2}} = \sqrt{\frac{M_{2}}{M_{1}}}

where,

r_{1} =

diffusion rate of hydrogen

= 28.7\,\mathrm{cm}^3\,\mathrm{s}^{-1}

r_{2} =

diffusion rate of unknown gas

= 7.2\,\mathrm{cm}^3\,\mathrm{s}^{-1}

M_{1} =

molecular mass of hydrogen

=2\,\mathrm{u}

M_{2} = ?

\therefore \frac{28.7}{7.2} = \sqrt{\frac{M_{2}}{2}}

M_{2}= \left( \frac{28.7}{7.2} \right)^{2} \times 2

=31.78 \approx 32

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