A solution is prepared by dissolving 2.0g of sucrose and 2.0 gurea in 100g of water at 298 K. Calculate the vapour pressure of the solution, if the vapour pressure of pure water at 298 K is 23.756 torr. (Molecular weight of urea = 60 and sucrose = 342).

Explanation

No. of moles in 100 g of water
`=(100g)/(18"g mol"^(-1))=5.55`
No. of moles in 2.0 g sucrose
`=(2g)/(342"g mol"^(-1))=5.85 xx 10^(-3)`
No. of moles in 2.0 g urea `=(2g)/(60"g mol"^(-1))=0.033`
Total no. of moles of solutes and solvents = 5.589
Mole fraction of solvent `=(5.55)/(5.589)=0.993`
Mole fraction of solute = 1 - 0.993 = 0.007
According to Raoult.s law : `(p^(0)-p)/(p^(0))=x_(2)`
or `x_(2)=(p^(0)-p)/(p^(0)) = 0.077 or (23.756-p)/(23.756)=0.007`
or `23.756-p=0.007 xx 23.756`
`p=23.756 - 0.007 xx 23.756=23.590` torr