Ethylene glycol `(C_(2) H_(6) O _(2))` can be used as an antifreeze in the radiator of a car. Calculate the temperature when ice will begin to separate from a mixture with 20 mass percent of glycol in water used in the car radiator. `K_(f)` for water `= 1.86 K kg mol^(-1)` and molar mass of ethylene glycol is `62 g mol ^(-1).`

Explanation

Weight of solute `(W_(2))=20` mass percent of solution means 20g of ethylene glycol Weight of solvent (water) `W_(1) = 100 -20=80g`
`Delta T_(f) = K _(f) m = (K _(f) xx W_(2) xx 1000)/( M _(2) xx W _(1)) = (1. 86 xx 20 xx 1000)/(62 xx 80) = 7.5 K`
The temperature at which the ice will begin to separate is the freezing of water after the addition of solute i.e. `7.5K` lower than the normal freezing point of water `(273 - 7.5) K = 265.5K`