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.
