Question

# For 10 minute each, at 0∘C, from two identical holes nitrogen and an unknown gas are leaked into a common vessel of 4 litre capacity. The resulting pressure in the vessel is 2.8 atm and the mixture contains 0.4 mole of nitrogen. What is the molar mass of unknown gas ?

A
448 g mol1
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B
224 g mol1
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C
226 g mol1
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D
None of these
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Solution

## The correct option is A 448 g mol−1The rate of effusions through the hole for the gases N2 and X in this case is directly proportional to the number of moles of the respective gases in the mixture. So, Graham's law equation can be applied in terms of number of moles. nN2nX=√MXMN2 ...(i) PTVT=nTRT ...(ii) nT=2.8×40.0821×273=0.5 nX+nN2=0.5 As nN2=0.4 (Given) so, nX=0.1 From (i) : 0.40.1=√MX28 ; MX=448 g mol−1

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