During an diffusion experiment, it took 75 seconds for a certain number of moles of an unknown gas
to pass through a tiny hole. Under the same conditions, the same number of moles of oxygen gas
passed through the hole in 30 seconds. What is the molar mass of the unknown gas?

Question

During an diffusion experiment, it took 75 seconds for a certain number of moles of an unknown gas 
to pass through a tiny hole.  Under the same conditions, the same number of moles of oxygen gas 
passed through the hole in 30 seconds.  What is the molar mass of the unknown gas?

jfraser · Answer

In general, the heavier a gas molecule is, the slower it moves, and the longer it takes to effuse (escape through a tiny hole in a barrier). Graham's Law describes the relationship between the molar mass of a gas and its relative rate of effusion.$$\frac {R_1}{R_2} = \sqrt{\frac{MM_2}{MM_1}}$$
You know that gas 1 passed through the hole in 75 seconds, and that gas 2 took only 30 seconds. You also know that gas 2 is oxygen gas \O_2.  Oxygen gas has a molar mass of 32g/mol. The only thing missing is MM1.

Plug and solve