Question

A vessel of volume 100ml contains 10% of oxygen and 90% of an unknown gas. The gases diffuses in 86 second through a small hole of vessel.

If pure oxygen under similar
conditions and diffuses in 75 second, find the molecular weight of unknown gas?​

Answer 1

The molecular weight of unknown gas : 23.46 g/mol

Further explanation

Given

A vessel contains 10% of oxygen and 90% of an unknown gas.

diffuses rate of mixed gas = 86 s

diffuses rate of O₂ = 75 s

Required

the molecular weight of unknown gas (M)

Solution

The molecular weight of mixed gas :(M O₂=32 g/mol)

`\tt 0.1* 32+0.9* M=3.2+0.9M`

Graham's Law :

`\tt (r_(O_2))/(r_(mixed~gas))=\sqrt{(M_(mixed))/(M_(O_2)) }\\\\(75)/(86)=\sqrt{(3.2+0.9M)/(32) }\\\\0.76=(3.2+0.9M)/(32)\\\\24.32=3.2+0.9M\\\\21.12=0.9M\rightarrow M=23.46~g/mol`