Question

The vapour pressure of water at 20°C is 17 mm Hg. Calculate the vapour pressure of a solution containing 6 g of glucose in 50 g of water.

Answer 1

Given: Vapour pressure of pure water at 20°C:
`P_"water"^circ` = 17 mm Hg

Mass of glucose (C₆H₁₂O₆) = 6 g

Mass of water = 50 g

Molar mass of glucose = 180 g/mol

Molar mass of water = 18 g/mol

Moles of glucose = `6/180` = 0.0333 mol

Moles of water = `50/18` = 2.778 mol

Mole fraction of water `chi_"water" = 2.778/(2.778 + 0.0333)`

= `2.778/2.8113`

= 0.9882

By using Raoult’s law

`P_"solution" = chi_"water" xx P_"water"^circ`

= 0.9882 × 17

= 16.80 mm Hg

∴ The vapour pressure of the glucose solution at 20°C is 16.80 mm Hg.