A motor vehicle raditor was filled with `8 L`of water to which `2 L`of methyl alcohol `(density 0.8 g mL^(-1))` was added. What is the lowest temperature at which the vehicle can be parked outdoors without the danger that the water in the raditor will freeze? Given that `K_(f)` for water is `1.86 K kg mol^(-1)`

Explanation

Let us calculate the depression caused by the addition of methyl alcohol .
`Delta T_(f) = (K_(f) xx 1000 xx w_(B))/(w_(A) xx M_(B))`
`w_(A) = 2000 xx 1.0 = 8000 g ` (Density of water = 1 g/ml)
`w_(B) = 2000 xx 0.8 = 1600 g`
`M_(B) = 32`
`Delta T_(f) = (1.86 xx 1000 xx 1600)/(8000 xx 32)`
` = 11.625`
Freezing point = 0-11 .625
` = - 11.625^(@)C` .
`therefore ` Vehicle may be parked outdoor not below `- 11.625^(@)C` temperature .