Calculate the vapor pressure at 35ºC of a solution made by dissolving 20.2 g of sucrose (C12H22O11) in 60.5 g of water. The vapor pressure of pure water at 35ºC is 42.2 mmHg. What is the vapor-pressure depressionof the solution (in units of mmHg) ? (Sucrose is nonvolatile)

P' = 41.4 mmHg → Vapor pressure of solution

Explanation:

ΔP = P°. Xm

ΔP = Vapor pressure of pure solvent (P°) - Vapor pressure of solution (P')

Xm = Mole fraction for solute (Moles of solvent / Total moles)

Firstly we determine the mole fraction of solute.

Moles of solute → Mass. 1 mol / molar mass

20.2 g. 1 mol / 342 g = 0.0590 mol

Moles of solvent → Mass. 1mol / molar mass

60.5 g. 1 mol / 18 g = 3.36 mol

Total moles = 3.36 mol + 0.0590 mol = 3.419 moles

Xm = 0.0590 mol / 3.419 moles → 0.0172

Let's replace the data in the formula

42.2 mmHg - P' = 42.2 mmHg. 0.0172

P' = - (42.2 mmHg. 0.0172 - 42.2 mmHg)

P' = 41.4 mmHg