If the boiling point of an aqueous solution containing a non-volatile solute is `100.15^(@)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.

Explanation

For given aqueous soltion .
`Delta T_(f) = k_(f) xx m" "……(i)`
`DeltaT_(b) = k_(b) xx m" "…………(ii)`
`k_(f) = (RT_(f)^(2))/(1000 l_(f)) " " and " "………..(iii)`
`K_(b) = (RT_(b))/(1000l_(v))" "......(iv)`
Dividing eq.(iii) by eq.(iv)
`(K_(f))/(k_(b)) = (T_(f)^(2) xx l_(v))/(T_(b)^(2) xx l_(f))`
`therefore " "(Delta T_(f))/(Delta T_(b)) = (T_(f)^(2) xx l_(v))/(T_(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_(b) = 100.15 - 100 =0.15`
`therefore " " (Delta T_(f))/(0.15) = (273 xx 273 xx 540)/(373 xx 373 x 80)`
or `" " Delta T_(f) = (273 xx 273 xx 540)/(373 x 373 xx 80) xx 0.15 = 0.542`
`therefore " " T_(f) = 0-0.542 = - 0.542^(@)C`