Calculate the vapor pressure of water above a solution prepared by adding 24.5 g of lactose (C12H22O11) to 200.0 g of water at 338 K. (Vapor-pressure of water at 338 K 187.5 torr.)

Vapor pressure of solution → 186.3 Torr

Explanation:

To solve this problem we must apply the colligative property of vapor pressure.

ΔP = P°. Xm

Where ΔP = Vapor pressure of pure solvent - Vapor pressure of solution

P° is vapor pressure of pure solvent → 187.5 Torr

Xm is the mole fraction of solute (moles of solute / total moles)

Let's determine the mole fraction,

Moles of solute = Mass of solute / Molar mass

24.5 g / 342 g/mol = 0.0716 moles

Moles of solvent = Moles of solvent / Molar mass

200 g / 18g/mol = 11.1 moles

Total moles = 11.1 moles + 0.0716 moles → 11.1716 moles

Mole fraction of solute = 0.0716 mol / 11.1716 mol = 6.40*10⁻³

Let's apply the formula

ΔP = P°. Xm

Vapor P of pure solvent - Vapor P of solution = P°. 6.40*10⁻³

Vapor P of pure solvent - 187.5 Torr. 6.40*10⁻³ = Vapor P of solution

187.5 Torr - 187.5 Torr. 6.40*10⁻³ = Vapor P of solution

Vapor pressure of solution → 186.3 Torr