In winter, the normal temperature in Dharmshala is `- 8^(@)` C Is a `30%` by mass of an aqueous solution of ethylene glycol (molar mass = 62) suitable for car radiator . `K_(f)` for water is 1 . 86 K/m

Answer

`Delta T_(f) = 12.8 K, Yes`

Explanation

Mass of ethylane glycol `W_(B)= 30 g ` (say)
`:.` Mass of solution = 100 g
`:.` Mass of water ,` W_(A) = 100 - 30`
= 70 g = 0 . 0 7 kg
`K_(f) = 1 . 86 K//m = 1 . 86 K kg mol^(-1)`
Molar mass of ethylene glycol, `M_(B) = 62 g mol^(-1)`
`Delta T_(f) = ?`
`Delta T_(f)= K_(f) xx (W_(B))/( M_(B)) xx (1)/( W_(A) (kg))`
`=(1 . 86 K kg mol^(-1) xx 30 g)/( 62 g mol ^(-1) xx 0 . 07 kg)`
`= (186 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 remain liquid at `- 8^(@) C ` In dharmshala . The answer is yes