A 1.00-L gas sample at 100.°C and 611 torr contains 50.0% helium and 50.0% xenon by mass. What are the partial pressures of the individual gases?

Answer 1

Assume any mass you wish.
moles He = grams/molar mass
moles Xe = grams/molar mass.
total moles = moles He + moles Xe.

mole fraction He = moles He/total moles.
mole fraction Xe = moles Xe/total moles.

PHe = mole fraction He x 611.
PXe = moles fractiion Xe x 611.
Note: You may think this strange that you may use any convenient number for mass Xe and mass He but you can check this if you wish with the following:
Use PV = nRT and calculate n = total number moles. (But you don't know how to divide that since it's percent by mass and not percent by moles.)
After you have gone through the mole fraction and calculated the PHe and PXe, then use PV = nRT, and plug in P, V, R, an T and solve for n for EACH, then add the moles He and moles Xe and you will come out with the same number as total moles from the original PV = nRT.