Question

Question #d75c8

Answer 1

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`