How to find vapor pressure?

Question

Water has a vapor pressure of 18.0 torr and a density of 0.997 g/mL. Methanol (CH₃OH) has a vapor pressure of 126.8 torr and a density of 0.791 g/mL. Assuming a mixture of the two behaved ideally and followed Raoult's Law, what would you predict to be the vapor pressure (in torr) of a solution containing 525 mL of water and 255 mL of methanol?

Answer 1

So what we want to do initially is to find the mole fraction of water and of methanol because the vapor pressure of the final solution will depend on these values.

mols H2O = 525 ml x 0.997 g / ml x 1 mol H2O / 18 g = 20.08 mols H2O

mols CH3OH = 255 ml x 0.791 g / ml x mol CH3OH / 32.04 g = 6.295 mols CH3OH

TOTAL moles = 20.08 mols + 6.295 mols = 26.38 mols

Mole fraction H2O = 20.08 mol / 26.38 mol = 0.761

Mole fraction CH3OH = 6.295 mol / 26.38 mol = 0.239

Vapor pressure H2O = 0.761 x 18.0 torr = 13.7 torr

Vapor pressure CH3OH = 0.239 x 126.8 = 30.3 torr

Vapor pressure of solution = 13.7 torr + 30.3 torr = 44.0 torr