In winter, the normal temperature in a Himalayan's valley was found to be ` - 10^(@)` C . Is a `30%` by mass of an aqueous solutions of ethylene glycol (molar mass = 62) suitable for car radiator ? `K_(f)` for water is ` 1. 86 Km^(-1)`

Answer

`T_(p) = 12.8 K, Yes`

Explanation

Mass of solution = 100 g (say)
`:. W_(B) = 30 g`
`:.` Mass of water, `W_(A) = 100 - 30 = 70 g`
0.07 kg
`M_(B) = 62 g mol^(-1)`
`K_(f) = 1 . 86 K m^(-1)`
`= 1 . 86 K kg mol^(-1)`
`Delta T_(f) = K_(f) xx (W_(B))/( M_(B)) xx (1 )/(W_(A)(kg))`
`= (1 . 86K kg mol^(-1) xx 30 kg)/( 62 g mol^(-1) xx 0 . 0 7 kg)`
`= (1 36 xx 30)/( 62 xx 7)`
`12 . 86 K = 12 . 86 ^(@) C`
`T_(f) = T_(f)^(@) - Delta T_(f) = (0 - 12 . 86)^(@) C`
`= - 12 . 86 ^(@) C `
Thus the solution will freeze at ` - 12 . 86^(@) C ` . Therefore , this solution can be used in car radiator and answer to question is Yes .