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If the boiling point of an aqueous solut...

If the boiling point of an aqueous solution containing a non-volatile solute is `100.1^(@)C`. What is its freezing point? Given latent heat of fusion and vapourization of water `80 cal g^(-1)` and `540 cal g^(-1)`, respectively.

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For a given aqueous solution,
`DeltaT_(f) = K_(f) xx m …(i)`
`DeltaT_(b) = K_(b) xx m …(ii)`
`(K_(f) = RT_(f)^(2)) /( 1000 l_(f)) …(iii)`
`(K_(b) = RT_(b)^(2)) /( 1000 l_(v)) …(iv)`
Dividing Eq.(iii) by Eq. (iv),
`(K_(f))/(K_(b))=(T_(f)^(2)xxl_(v))/(T_(b)^(2)xxl_(f))`
`:. (DeltaT_(f))/(DeltaT_(b)) = (K_(f)^(2) xx l_(v))/(K_(b)^(2) xx l_(f))`
`T_(f) = 0 + 273 = 273 K`
, `T_(b) = 100 + 273 = 373 K`
`l_(f) = 80 cal g^(-1), l_(v) = 540 cal g^(-1)`
`:. (DeltaT_(f))/0.15 = (273 xx 273 xx 540) / (373 xx 373 xx 80)
or `DeltaT_(f) = (273 xx 273 xx 540)/(373xx373xx80)xx0.15 = 0.542`
`:.T_(f) = 0 - 0.542 = -0.542^(@)C`.
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