It takes 32 seconds for a certain number of moles of H2 to effuse through a leak in a tank. An unknown gas was later places under the same conditions; it took 1:39 for the same number of moles to effuse. Find the molecular mass of the gas.
I set it up like this:
rate of effusion H2 (32 s)/ rate of effusion unknown (99 s) = (molar mass unknown/molar mass H2 (2.02))^.5
and ended up with
molar mass unknown^.5= .459
molar mass unknown= .211
What's wrong with what I did?
The time is not the rate. rate is L/time, or in this case, mols/time. You don't have mols so just assume any number, for example, one. Let us know if you still have problems.
Ok, I understand that. So if I were to use 1 mol, what I would have is
(1 mol/32 s)/(1 mol/99 s)= (molar mass unknown/molar mass H2)^.5
Should I get the same answer regardless of what number I use for moles, as long as I set it up like that?
right.
(1/32) and (1/99) would be the rates. It doesn't matter what number of mols you use as long as you use the same for both gases. Is that 1 min and 39 seconds; if so then that is 99 seconds.
Sorry. I see the 99 now.
No problem! It's important to have all the correct values when setting up the equation. So now you can continue solving the equation as you mentioned before:
(1 mol/32 s)/(1 mol/99 s) = (molar mass unknown/molar mass H2)^0.5
To find the molecular mass of the unknown gas, you need to solve for molar mass unknown. Let's simplify the equation:
(99 s/32 s) = (molar mass unknown/molar mass H2)^0.5
Now, you can square both sides of the equation to get rid of the square root:
(99 s/32 s)^2 = (molar mass unknown/molar mass H2)
Simplifying further:
(99/32)^2 = (molar mass unknown/molar mass H2)
Now, to get the value of (molar mass unknown), you can rearrange the equation:
molar mass unknown = (99/32)^2 * molar mass H2
By plugging in the molar mass of H2 (2.02 g/mol), you can calculate the molecular mass of the unknown gas:
molar mass unknown = (99/32)^2 * 2.02 g/mol
Evaluating this expression will give you the answer.