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For minute each, at C, from two identical holes nitrogen and an unknown gas are leaked into a common vessel of litre capacity. The resulting pressure is atm and the mixture contains mole of nitrogen. What is the molar mass of unknown gas? (Use L-atm/mol-K).


Let the unknown gas be X.
Let and be the molar mass of nitrogen and the other gas respectively.
From ideal gas equation-
Given that
total no. of moles of solution
Given no. of moles of nitrogen gass
No. of moles of gas X
Now from Graham's law of diffusion,
rate of effusion
Given that
Rate of effusion of nitrogen
Rate of effusion of gas X
Further, we know that
As we know that molar mass of nitrogen gas is .
Squaring bth sides, we have
Hence the molar mass of unknown gas is .

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