Unknown gas diffuses at a speed one-quarter of that of helium. What is the molar mass of the uknown gas?(He=4)
Answers
Around 64 g/mol.
You can start from any expression for the speed. The RMS speed is a fine choice:
vRMS=√3RTM,
where R and T are from the ideal gas law, and M is the molar mass of the gas in kg/mol.
The ratio of two speeds v is directly proportional to the ratio of the gas diffusion rates z (the 3RT cancels out):
vRMS,BvRMS,A=zBzA=√MAMB
which is Graham's law of diffusion; the gas with more mass per particle diffuses more slowly. (In this case, the molar mass can now be in g/mol and it won't matter.)
Since helium is known to diffuse 4 times as fast as unknown gas B, then off the top of my head, helium is probably 42=16 times as light (one-sixteenth the molar mass of B).
Let's check mathematically.
zBzA=√MAMB
If we assign helium as A, then the unknown gas is B and zBzA=14.
⇒14=√4.0026MB
⇒116=4.0026MB
⇒MB=4.0026×16≈64 g/mol
So the unknown gas has about 16 times higher of a molar mass.