Question

What is the vapor pressure of a solution of sucrose (C12H22011) prepared by
dissolving 40.0 g of sucrose in 400.0 g of water at 100°C? The vapor pressure of
pure water at 100°C is 760 Torr. Assume 3 sf.

a) 760 Torr
b) 10.00 Torr
c) 756 Torr
d) 2.00 Torr

Answer 1

The vapour pressure of the solution is 752 Torr from Raoult's law .

Mass of solute (m1) = 40.0 g

Mass of solvent(m2) = 400.0 g

Vapor pressure of solution (p)  = ?

vapor pressure of  pure water (p°) = 760 Torr

From Raoult's law

p = X p⁰

X = number of moles of solvent / number of moles of solution

number of moles of solvent, n₁ = mass in grams / molar mass = 400.0 g /18g/mol = 22.22 moles

number of moles of solute, n₂ = mass in grams / molar mass = 40.0 g/ 342.3 g/mol = 0.12 moles

total number of moles, n₁ + n₂ = 22.22 moles + 0.12 moles = 22.34 moles

moles fraction of water, X = 22.22 moles/22.34 moles = 0.99 moles

From Raoult's law;

p = p⁰ X

p = 760 Torr * 0.99 moles

p = 752 Torr

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