A sample of methane (CH4) gas contains a small amount of helium. Calculate the volume percentage of helium if the density of the sample is 0.70902 g/L t 273K and 1.00 atm.

Question

I know that the sample is at STP and that the 1 mole of gas under these conditions occupies 22.4L, but how do I use the density to find the fractional volumes that each gas inhabits?

Answer 1

The general gas formula of PV = nRT can be rearranged for molar mass of
P*M = density*RT
M = dRT/P = about 15.9 but you need to do it for a more accurate answer.
Then let X = fraction CH4
and 1-X = fraction He
Then molar mass CH4*X + molar mass He*(1-x) = molar mass from above.

Solve for X (and 1-X if needed) and convert to percent.
Note: Since the density is contains 5 significant figures I would use R = 0.082057 and use at least 5 places for CH4 and He AND I would carry everything out to 6 places before rounding.
I obtained about 98.7% but that's only a close estimate.

Answer 2

Thanks