1000 g of 1 molal aqueous solution of sucrose is cooled and maintained at `-3.534^(@)C`. Find out how much ice will separate out at this temperature. `(K_(f)` for water `=1.86 k m^(-1)`)

Answer

`=353g`

Explanation

Sucrose is a non-electrolyte hence, `i=1`
`m,` (mol.wt. of solute) `=342g "mol"^(-1)`
Molality of the solution `=1 "mol" kg^(-1)` solvent
`=342g` sucrose `kg^(-1)` solvent `(H_(2)O))~
Hence, weight of `1` molal solution `=1000+342=1342g`
Sucrose present in `1kg` solution `=(342)/(1342)xx1000=254.84g`
Solvent `(H_(2)O)` present in `1kg` solution `=1000-254.84=745.16g`
Depression in f.p. `(DeltaT)_(f)=(1000K_(f)w_(1))/(m_(1)w_(2))(i)`
Weight of solvent required to maintain this solution at `-3.534^(@)C`
`w_(2)=(1000xx1.86xx254.84xx1)/(342xx3.534)=392.18g`
hence, amount of ice formed `=745.16-392.18=352.98=353g`