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15.0 g of an unknown molecular material ...

`15.0 g` of an unknown molecular material was dissolved in `450 g` of water. The resulting solution was found to freeze at `-0.34 ^(@)C`. What is the the molar mass of this material. (`K_(f)` for water `= 1.86 K kg mol^(-1)`)

Text Solution

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Here ` w^(2) = 15 g, w_(1) = 450 g, K_(f) = 1.86" K kg "mol^(-1)`
` M_(2) `=?
`DeltaT_(f) = 0 - (-0.34) = 0.34^(@)C or 0.34" K "`
Using the formula,
`Delta T_(f) = K_(f) m = K_(f) xx (w_(2) xx 1000)/ (M_(2) xx w_(1))`
` 0.34 = (1.86 xx 15 xx 1000)/(M_(2) xx 450)`
` :. " " M_(2) = (1.86 xx 15xx 1000)/(0.34 xx 450) = (186 xx 100)/(34 xx 3)`
` = (18600)/102 = 182.35" g "mol^(-1)`
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