1000gm of sucrose solution in water is cooled to `-0.5^(@)C`. How much of ice would be separated out at this temperature, if the solution started to freeze at `-0.38^(@)C`. Express your answer in gram.
`(K_(f)H_(2)O=1.86K "mol"^(-1)kg)`

Explanation

`w_(A)+w_(B)=1000`……………i
`DeltaT_(f)=(K_(f)xxw_(B)xx1000)/(M_(B)xxw_(A))`
or `0.38=(1.86xx1000xxw_(B))/(342xxw_(A))`
`(w_(B))/(w_(A))=0.07`………….ii
By i and ii
`w_(B)=65.42gm` and `w_(A)=934.58gm`
Atg `-0.5^(@)C` some water separate out as ice and solute exist as 65.42 gm
`0.5=(1.86xx65.42xx1000)/(342xxw_(A))`
`W_(A)=711.58gm`
`:.` separated ice `=934.58 gm -711.58gm =223 gm`.