How many grams of naphthalene needs to be added to 500.0 mL of hexane for the vapor pressure of the solution to be 100. mmHg at 25ºC. The vapor pressure and density of pure hexane at 25ºC is 150.5 mmHg and 0.6548 g/mL respectively. (The MW of naphthalene (C10H8) is 128.18 amu, and the MW of hexane (C6H14)is 86.20 amu.)
I'm rounding everything to three places but since the numbers are better than that you should recalculate and use at least 4 places or 5 places as appropriate.
Psoln = Xhexane*Po hexane
100 mm = Xhexane*150.5 and Xhexane = 0.664
Since Xhexane + Xnaph = 1.00, then
Xnaph = 1.00 - 0.664 = 0.336
How many grams hexane do you have? That's
mass = volume x density
mass = 500 mL x 0.655 g/mL = 328 g,
How many moles is that ?
moles = g/molar mass = 328/86.2 = 3.80 moles hexane.
Xhexane = mols hexane/total moles
0.664 = 3.80/total mols and total moles = 3.80/0.664 = 5.72
total mols = mols hexane + moles naphthalene = 5.72
5.72 = 0.664 + moles naphthalene and mols naph = 5.72 - 0.664 = 5.06
grams naph = mols naphthalene x molar mass naph = 5.06 x 128 = ?
NOTE: Check this very carefully. I've checked it but the answer just doesn't look right to me; however, if there is an error I don't see it.