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1000 g of 1 molal aqueous solution of s...

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)`)

Text Solution

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Source is a non-electrolyte
Molecular weight of sucrose `C_(12)H_(2)O_(11)=M=342 gm "mol"^(-1)`
Molality of the solution `0.75m`
`=0.75"mol" kg^(-1)` solvent `=256.5` gm Sourcose per kg solvent
Hence weight of 1 molal solution `(256.5)/(1256.5)xx1000=204.14 gm`
Weight of solvent `(H_(2)O)` present in 1kg solution `=1000-204.14 gm`
Since depressionnin freezing point.
`DeltaT_(t)=K_(t)xx(W)/(m)xx(1000)/(W)` where W= weight of solvent
W= weight of the solute
or `4=1.86xx(256.5)/(342)xx(1000)(W)`
`:.W=348.75gm`
i.e., weight of solvent required to maintain this solution at `-4^(@)C`
`W=348.75 gm`
Hence rest weight of `H_(2)O` will convert into ice
Hence amount of ince formed `=795.86-348.477.11 gm`
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