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Standard XII

Chemistry

Real Gases

A certain vol...

Question

A certain volume of argon gas (Mol. Wt. 40) requires $45 s$ to effuse through a hole at a certain pressure and temperature. The same volume of another gas of unknown molecular weight requires $60 s$ to pass through the same hole under the same conditions of temperature and pressure. The molecular weight of the gas is:

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120

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Solution

The correct option is C 71
Rate of diffusion of a gas $(r)$ = $\frac{V o l u m e o f g a s c o m i n g o u t}{T i m e t a k e n} \propto \sqrt{\frac{1}{M o l a r m a s s o f g a s}}$
Therefore, under identical conditions, the time taken for diffusion (t) is directly proportional to the molar mass of the gas $(M)$ .
Consider the time taken to for $A r$ gas to diffuse to be $t_{1}$ and for unknown gas to be $t_{x}$ .
$\frac{t_{1}}{t_{x}} = \sqrt{\frac{M_{1}}{M_{x}}}$

According to the given conditions,
= $\frac{45}{60} = \sqrt{\frac{40}{M_{x}}}$
= $M_{x}$ = $\frac{12^{2}}{9^{2}} \times 40$
$\Rightarrow M_{x} = 71.11$

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