chemistry question

Question

At –13.5 °C (a common temperature for household freezers), what is the maximum mass of sucralose (C12H19Cl3O8) you can add to 3.00 kg of pure water and still have the solution freeze? Assume that sucralose is a molecular solid and does not ionize when it dissolves in water. Kf values are given here.

Answer 1

The freezing point depression of water is 1.86° C / molal.

 

To still freeze at -13.5° C, the molality of the solution has to be no more than 13.5 / 1.86 = 7.26 m.

 

The molecular weight of sucralose is:

 

12 C = 12 *12 = 144

19 H = 19 * 1 = 19

3 Cl = 3 * 35.45 = 106.35

8 O = 8 * 16 = 128

 

...for a total of 397.35.  So one mole of sucralose has a mass of 397.35 grams.

 

Since there are 3 kg of water, you can add 3 * 7.26 moles (= 21.78 moles) to the water to get the 13.5° C freezing point depression.  That's 21.78 moles * 397.35 grams / mole = 8654.28 grams, or 8.654 kg.

 

That seems like a lot, but that's how the numbers seem to come out.