Question

A solution of lactose containing 8.45 g of lactose in 100 g of water has a vapour pressure of 4.559 mm of Hg at 0°C. If the vapour pressure of pure water is 4.579 mm of Hg, calculate the molecular weight of lactose.

Answer 1

Given: Mass of lactose = 8.45 g

Mass of water = 100 g = 0.1 kg

Vapour pressure of pure water = 4.579 mm Hg

Vapour pressure of solution = 4.559 mm Hg

Molar mass of water = 18 g/mol

ΔP = 4.579 − 4.559

= 0.20 mm Hg

By using Raoult’s law

`(Delta P)/P_0 = n_"solute"/(n_"solvent" + n_"solute") ≈ n_"solute"/n_"solvent"`    ...[Since solute is small]    ...(i)

`(Delta P)/P_0 = 0.020/4.579` ≈ 0.00437    ...(ii)

Number of moles in solvent (water):

`n_"water" = 100/18`

≈ 5.56 mol

Number of moles of solute (lactose):

`n_"solute"/n_"solvent" = 0.00437`    ...[From (ii) and (ii)]

`n_"solute" = 0.00437 xx 5.56`

≈ 0.0243 mol

Molar mass of lactose = `8.45/0.0243`

≈ 348 g/mol

∴ The molecular weight of lactose is 348 g/mol.