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The freezing point of cyclogexane is 279...

The freezing point of cyclogexane is 279.65 K. A solution of 14.75 g of a solute in 500 g of cyclohexane has a freezing point of 277.33 K. Calculate the molar mass of the solute. (Given `K_(f)`=20.2 K kg `mol^(-1)`)

Text Solution

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The correct Answer is:
258.77 g `mol^(-1)`
`DeltaT_(f)=T_(f)^(@)-T_(f)=279.65 K-277.33=2.33 K`
`K_(f)=20.2" K kg mol"^(-1)=20.2Km^(-1)`
`"Molality, m"=(DeltaT_(f))/K_(f)=(2.23K)/(20.2Km^(-1))=0.115 m`
Mass of solvent = 500 g = 0.5 kg
`"Moles of solute" = "molality"xx"mass of solvent in kg" =0.115" kg mol"^(-1)xx0.5" kg "=0.057" moles"`
`"Molar mass of solute"=("Mass of sovent")/("Moles of solute")=(14.75 g)/(0.057" moles")=258.77" g mol"^(-1)`.
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