Vapour pressure of pure water at `298 K ` is `23.8 mm Hg`. `50g` of urea `(NH_(2)CONH_(2))` is dissolved in `850g` of water. Calculate the vapour pressure of water for this solution and its relative lowering.

Answer

`233.4mm, 0.017`

Explanation

Given`:`
`p_(H2O)^(@)=23.8mm,W_(2)=50g,Mw_(2)(urea)=60gmol^(-1)`
`W_(1)=850g,Mw_(2)(H_(2)O)=18g mol^(-1)`
Applying Raoult's law and using another relation `:`
`(p^(@)-p_(s))/(p_(s))=(n_(2))/(n_(1))=(W_(2)//Mw_(2))/(W_(1)//Mw_(1))=(50//60)/(850//18)=0.17`
Substituting the value of `p^(@)=23.8mm`
`(23.8-p_(S))/(p_(S))=0.017`
or `23.8-p_(S)=0.017p_(S)implies1.017p_(S)=23.8`
or `p_(S)=(23.8)/(1.017)23.4mm`
Thus, the vapour pressure of water in the solution `=23.4mm.`