At −11.0 ∘C , a common temperature for household freezers, what is the maximum mass of sucralose (C12H19Cl3O8) you can add to 1.50 kg of pure water and still have the solution freeze?

Answer 1

I'm guessing the question really means to ask how much sucralose you can add and still have the solution NOT freeze. But if it really is "still have the solution freeze", then it would be 10 g less (using sig, figs.) or any amount less than that calculated if not interested in sig. figs.

molar mass sucralose = 397.6 g/mol

The change in the freezing point of water can be determined from

∆T = imK

∆T = change in freezing point = 11º

i = van't Hoff factor = 1 for sucralose since it is a non electrolyte

m = molality = moles solute/kg water = ?

K = freezing point constant for water = 1.86 º/m

Solving for m, we have...

m = 11º/((1)(1.86º/m) = 5.91 molal

This means 5.91 moles sucralose/kg water, but since we have 1.50 kg we can find moles present:

5.91 moles/kg x 1.50 kg = 8.87 moles of sucralose

mass of sucralose = 8.87 moles x 398 g/mol = 3530 g