`100 g` of water contains `1.0 g` urea and `2.0 g` sucrose at `298 K`. The vapour pressure of water at `298 K` is `0.3 atm`. Calculate the vapour pressure of the solution. (Molecular weight of urea =`60`, Molecular weight of sucrose = `342`)

Explanation

The given values are
`{:(W_(H_(2)O)=100g,,,Mw_(H_(2)O)=18 "g mol"^(-1)),(W_("urea")=10g,,,Mw_("urea")=60"g mol"^(-1)),(W_("sucrose")=2g,,,Mw_("sucrose")=342"g mol"^(-1)):}`
`P_(H_(2)O)^(@)=0.3 atm`
Amount fraction of solvent
`= ("Amount of solvent")/("Amount of (solvent + solute")`
`(100//18)/(100//18+1//60+2//342)`
`= (5.556)/(5.577) = 0.99`
According to Raoult's law,
`P_(A) = P_(A).^(@)chi_(A)`
`:.` Vapour pressure of solution `= 0.3 xx 0.99 = 0.29 atm`