Vapor Pressure Please help!?

The vapor pressure of pure methanol, CH3OH, at 30 °C is 160 torr. How many grams of the nonvolatile solute glycerol, C3H5(OH)3, must be added to 146 g of methanol to obtain a solution with a vapor pressure of 117 torr? (Do not include units in your answer.)

Answer:
Raoult's Law is required to solve for the mole fraction of the methanol in this solution. The actual pressure = (mole fraction of the solvent)(pressure of the pure solvent).

117 torr = (mole fraction of methanol)(160 torr)
mole fraction of methanol = 0.731

mole fraction of CH3OH = moles CH3OH / (moles CH3OH + moles glycerol)

146g CH3OH (1 mole CH3OH / 32.04 g CH3OH) = 4.56 moles CH3OH

mole fraction = 0.731 = 4.56 / (4.56 + moles glycerol)
moles of glycerol = 1.68 moles
molar mass of glycerol = 92.09 g/mol

mass of glycerol needed = 1.68 moles (92.09 g / mol) = 155g glycerol

= 155
Use Raoult's law, p = p* x, where p* is the equilibrium vapor pressure of the pure substance and x is the mole fraction. You are given p* in the problem statement, 160 torr. Calculate the x you need, then you can calculate how many grams of glycerol you need to obtain that x.

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