# Question d75c8

Apr 8, 2016

The mole fraction of ethylene glycol is 0.414.

#### Explanation:

Raoult's Law states that the vapour pressure of a solvent in a solution is directly proportional to its mole fraction:

color(blue)(|bar(ul(color(white)(a/a) P_1 = χ_1P_1^°color(white)(a/a)|)))" "

where

• ${P}_{1}$ is the vapour pressure of the solvent in the solution
• χ_1 is the mole fraction of the solvent
• P_1^° is the vapour pressure of the pure solvent

If the solvent is non-volatile, the formula can be arranged to

color(blue)(|bar(ul(color(white)(a/a)ΔP = χ_2P_1^°color(white)(a/a)|)))" "

where

• ΔP" is the vapour pressure lowering of the pure solvent
• χ_2 is the mole fraction of the solute.

The vapour pressure P_1^° of pure water at 110 °C is 1.414 atm.

Our task is to calculate the mole fraction of non-volatile solute (ethylene glycol) that will lower the vapour pressure of the solution to 1 atm at 110 °C.

ΔP = P_1^° - P_1 = "1.414 atm – 1 atm" = "0.414 atm"

ΔP = χ_2P_1^°

χ_2 = (ΔP)/P_1^° = (0.414 color(red)(cancel(color(black)("atm"))))/(1 color(red)(cancel(color(black)("atm")))) = 0.414#