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A solution of glycerol (C-(3)H(8)O(3) , ...

A solution of glycerol `(C-(3)H_(8)O_(3)` , molar mass = 92 g `mol^(-1)` iin water was prepared by dissolving some glycero 500 g of water. This solution has a boiling point of `100.42^(@)C`. What mass of glycerol was dissolved to make this solution ? `K_(b)` for water=` 0.512 k kg mol^(-1).`

Text Solution

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The correct Answer is:
37.7 g
`DeltaT_(b)=(100.42^(@)C-100)^(@)C=0.42^(@)C=0.42" K",`
`M_(B)=92" g mol"^(-1),W_(A)=500 g =0.5" kg",`
`K_(b)=0.152" k kg mol"^(-1)`
`W_(B)=(M_(B)xxDeltaT_(b)xxW_(A))/(K_(b))=((92g mol^(-1))xx(0.42K)xx(0.5kg))/((0.512" k kg mol"^(-1)))=37.7 g`.
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