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Question

The rate of diffusion of methane at a given temperature is twice that of gas $$X$$. The molecular mass of gas $$X$$ is :


A
64.0
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B
32.0
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C
4.0
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D
8.0
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Solution

The correct option is C $$64.0$$
The rate of diffusion of methane at a given temperature is twice that of gas X.
$$\displaystyle   {r_{CH_4}} = 2{r_X}$$
The rate of diffusion is inversely proportional to the square root of its molar mass.

$$\displaystyle \dfrac {r_{CH_4}}{r_X}=\sqrt {\dfrac {M_X}{M_{CH_4}}}$$
$$\displaystyle \dfrac {2r_X}{r_X}=\sqrt {\dfrac {M_X}{ 16}}$$
$$\displaystyle 4= \dfrac {M_X}{ 16} $$
The molecular mass of gas $$X$$ is $$\displaystyle M_X = 64.0$$  g/mol

Hence, the correct option is A.

Chemistry

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