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A solution `M` is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixture is `0.9` Given: Freezing point depression constant of water `(K_(f)^(water)=1.86 K kg mol^(-1))` Freezing point depression constant to ethanol `(K_(f)^(ethanol))=2.0 K kg mol^(-1))` Boiling point elevation constant of water `(K_(b)^(water))=0.52 K kg mol^(-1))` Boiling point elevation constant of ethanol `(K_(b)^(ethanol))=1.2 K kg mol^(-1))` Standard freezing point of water = `273 K ` Standard freezing point of ethanol = `155.7 K ` Standard boiling point of water = `373 K ` Standard boiling point of ethanol = `351.5 K ` Vapour pressure of pure water =`32.8 mm Hg` Vapour pressure of pure ethanol =`40 mm Hg` Molecular weight of water =`18 g mol^(-1)` Molecular weight of ethanol =`46 g mol^(-1)` In anwering the following questions consider the solutions to be ideal dilute solutions and solutes to be non-volatile and non-dissociative. The freezing point of the solution `M` isA. `268.7 K`B. `268.5 K`C. `150.9 K`D. `268.7 K`

Answer» `chi_("Ethanol")=0.9`
` chi_("water")=0.1`
`("Solvent" =-B)`
`("Solvent" =-A)`
`DeltaT_(f)=K_(f) .m=K_(f) . (chi_(B))/(1-chi_(B)) xx (1000)/(Mw_(A))`
`=2 xx 0.1/0.9 xx 1000/46=4.86 K`
`T_(f)=T_(f)^(@)-DeltaT_(f)=155.7 + 4.83 =150.87 K`


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