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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

Verified by Experts

`342 g` in `1000 g` of `H_(2)O=1 m`
Weight of solution = `1342 g`
`1342 g` contains =`1000 g `of `H_(2)O`
`1000 g` contains =`1000/1342 xx(1000)=745.156 g` of `H_(2)O`
Let `x g` of water remains in liquid state.
`x g` of `H_(2)O` dissolves in 1 mol solute.
`745.15 g` of `H_(2)O` dissolves =`1/x xx(745.156)` mol of solute
`DeltaT_(f)=K_(f)xxm`
`3.534=1.86 xx(745.156)/(x)`
`x=392.18 g`
Amount of water separates as ice
`=745.156 -392.18`
`=352.98 g`
Alternate method
`1 m=342 g per 100g ` of `H_(2)O`
Find sugar in `1000 g` of solution.
1342 g solution=342 g sugar
1000 g solution =`(342 xx 1000)/(254.85 g)`
Mass of `H_(2)O` per `1000 g` solution `= 1000-254.85`
= `745.15 g`
`DeltaT_(f)=(K_(f)xx1000xx"grams of sucrose")/(Mw_("sugar")xx"grams" of H_(2)O "left")`
=`(K_(f)xxW_(2)xx1000)/(Mw_(2)xxW_(1))`
`=(1.86xx254.84xx1000)/(3.534xx342)`
`=392.2 g H_(2)O`
Ice separates out=`745.15-392.2`
`=352.95 g`
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