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)

$\tt 0.1\times 32+0.9\times M=3.2+0.9M$

Graham's Law :

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