Using relative effusion rates to find an unknown molar mass

Question

A gas made up of homonuclear diatomic molecules escapes through a pinhole 0.325 times as fast as He gas. Write the chemical formula of the gas.

Answer 1

Graham's law of Effusion:

rate gas 1 / rate gas 2 = √MW gas 2 / √MW gas 1

Let gas 1 be He and rate = 1. MW = 4

Gas 2 is G and rate is 0.325 MW = x

1/0.325 = √x / √4

3.08 = √x / 2

√x = 6.16

x = 37.9

Since the gas is diatomic and homonuclear, we look in the periodic table and find the most likely gas to be F (fluorine)

Answer 2

Effusion == diffusion; rate is inversely proportional to (square root(molecular weight)). Guess you could divide the mass of helium by the square of that given ratio value, hmm? (Square the diffusion proportion to get the first order ratio of molecular weights!) (Divide, so that you get a larger number for desired mass!) Round to integer, divide by 2 ("diatomic" specified!), look up elemental mass on the Periodic Table? (Prepare results for evaluation!)

So, where is the lack of know-how to attack this problem? Is it in knowing how/why to look up the law for diffusion? Is it in translating that equation into an equation for your given problem? Is it in performing a calculation (any calculator can do that)? Is it in checking for the reasonableness of your answer, given your intuitions of the magnitude of the data involved? If you have to answer "yes" to any of these, then you need some more basic tutoring. You have to know how to apply tools as well as which tools to apply, to solve any problem.

-- Cheers, --Mr. d.