What is the freezing point of radiator fluid that is 50% antifreeze by mass? kf for water is 1.86 ∘c/m. express your answer to three significant figures and include the appropriate units.

-30.0 ºC

Explanation:

The freezing point depression of a solution is given by the relation:

ΔT = - Kf m, where Kf is the  molal freezing point constant  of water, and m is the molality of the solute.

The molality, in turn, is given by:

m = mol solute / Kg solvent

We are not given in this question the identity of the  solute, but the most typical component in antifreeze  is ethylene glycol, and that is what we are going to use here.

We now have all the information required to solve this question.

In 100 grams of fluid we have:

Molar mass ethylene glycol = 62.07 g/mol

mol ethyle glycol = 50 g / 62.07 g/mol = 0.81 mol

Kg solvent = 50 g/ 1000 g/ Kg = 0.050 Kg

m = 0.81 mol / 0.050 Kg = 16.1 m

ΔT = - Kf m = -1.86 ºC/m x 16.1 m = -30.0 ºC