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Question

A gaseous mixture of He & CH4 gases with mole ratio 2 : 1 respectively is placed in a container and allowed to effuse through a small orifice. Xml of the He gas effuses in 5 seconds. The time required to effuse same volume of CH4 gas is:

A
5 sec
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B
20 sec
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C
40 sec
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D
10 sec
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Solution

The correct option is A 40 sec
The rate of effusion is directly proportional to the mole fraction and inversely proportional to the square root of molar mass.
rr=VV×tt=XX×MM
Here, r,V,t,X and M are the rate of diffusion, volume diffused, time for diffusion, mole fraction and the molar mass for He respectively
and r,V,t,X and M are the rate of diffusion, volume diffused, time for diffusion, mole fraction and the molar mass for methane respectively
XX×t5=21×164
t=40sec
Hence, the time required to effuse same volume of methane gas is 40 sec.

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