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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.