Question

At −15.0 ∘C , a common temperature for household freezers, what is the maximum mass of sucrose (C12H22O11) you can add to 1.50 kg of pure water and still have the solution freeze? Assume that sucrose is a molecular solid and does not ionize when it dissolves in water.

Answer 1

Answer: The maximum mass of sucrose you can add is 4158.95 grams.

Explanation:

This is an example of freezing point depression. The formula for calculating this is the following:

ΔT = Kf . b . i

ΔT is the temperature depression

Kf is the cryoscopic constant that is unique for each solvent

b is the molality of the solution (moles of solute per kg of solvent)

i is the Vant Hoff factor

The freezing point of water is 0°C. ΔT equals inicial temperature - final temperature, so it's 0°- (-15°)= 273K - 258K = 15K

The Kf for water is known to be 1.853 K. Kg /mol

i is the number of particles the molecule is split to when ionized. Because sucrose doesn't ionize, its Vant Hoff factor is 1.

If we clear b from the ecuation:

b = ΔT/ Kf . i

b = 15K/ 1.853 K. Kg/mol . 1

b= 8.1 mol/kg

If we can add 8.1 moles to a kg of water before it freezes, we use cross multiplication to calculate how many we can add to 1.5 kg. The answer is 12.15.

The weight of a mole of sucrose is 342.3 grams. So the weight of 12.15 moles of sucrose is 4158.95g.