At −11.5 ∘C , a common temperature for household freezers, what is the maximum mass of sucralose (C12H19Cl3O8) you can add to 1.00 kg of pure water and still have the solution freeze?

Question

Assume that sucralose is a molecular solid and does not ionize when it dissolves in water.

Answer 1

Let's use the formula ∆T = imK

∆T = change in the freezing point = 11ºC (normal freezing point is 0º, so -11º is a change of 11º)

i = van't Hoff factor = 1 since sucralose does not ionize

m = molality of sucralose (see below)

K = freezing constant for water = 1.86º/m

Now we will solve the equation for m (molality of sucralose)

11 = (1)(m)(1.86)

m = 5.91 moles/kg water

Since we have 1 kg of water, the maximum moles of sucralose would be 5.91 moles.

The question asks for mass of sucralose, so we can now easily calculate that.

Molar mass sucralose = 12x12 + 19x1 + 3x35.5 + 16x8 = 398 (rounded to 3 sig.figs.)

mass of sucralose =5.91 moles x 398 g / mole = 2352 g = 2350 g Sucralose (3 sig.figs.)