A storage battery contains a solution of `H_(2)SO_(4) 38%` by weight. At this concentration, the Vant't Hoff factor is `2.50`. At what temperature will the battery contents freeze? `(K_(f)=1.86^(@) mol^(-1) kg)`

Explanation

Weight of `H_(2)SO_(4) (w_(B)) = 38 g`
Weight of water `(w_(A)) = 100-38 = 62 g`
Calculated `Delta T_(f) `
`Delta T_(f) = (1000 xx K_(f) xx w_(B))/( w_(A) xx M_(B))`
` = (1000 xx 1.86 xx 38)/(62 xx 98) = 11.633^(@)`
Van.t Hoff factor `i=("Observed" Delta T_(f))/("Calculated" DeltaT_(f))`
`therefore ` Observed `Delta T_(f) = i xx "Calculated" Delta T_(f)`
`= 2.5 xx 11.633 = 29.08^(@)`
`therefore` Freezing point of battery content ` = 273-29.08`
` = 243.92 K`