First, you can use the ideal gas law to calculate the average molar mass of the gas mixture:
PV = n RT
Since n = mass / molar mass
PV = (mass/molar mass) RT
Since density = mass/V, you can rearrange the equation to give:
molar mass = (density)RT / P
Using the values in the problem (and converting everything to the correct units)
molar mass = (0.518 g/L) (0.0821 Latm/molK) (298K) / 0.9487 atm
molar mass = 13.35 g/mol
Now, let x = mole fraction of He and 1-x = mole fraction of O2, Then:
13.35 g/mol = 4(x) + 32(1-x)
Once you solve for x, just multiply it by 100 to get the percent of helium in the gas mixture.
