On dissolving 0.5 g of non-volatile, non-ionic solute to 39 g of benzene, its vapour pressure decreases from 650 mm of Hg to 640 mm of Hg. The depression of freezing point of benzene (in K) upon addition of the solute is __________.
(Given data: Molar mass & molar freezing point depression is 78 g `mol^(-1) & 5.12 K kg mol^(-1)`]

Explanation

`(p^(@) - p)/(p^(@)) = (n_(2))/(n_(1) + n_(2)) ~~ (n_(2))/(n_(1))`
`n_(2) = (0.5)/(M_(2)) , n_(1) = (39)/(78)`
`(650-640)/(650) = (0.5 xx 78)/(M_(2) xx 39)`
`(10)/(650) = (0.5 xx 78)/(M_(2) xx 39)`
or `" "M_(2) = (0.5 xx 78 xx 650)/(10 xx 39) = 65 g mol^(-1)`
Now `DeltaT_(f) = (k_(f) xx 1000 xx w_(2))/(w_(1) xx M_(2))`
` = (5.12 xx 1000 xx 0.5)/(39xx65) = 1.01 K`