Question

At − 12.0 ∘ C , a common temperature for household freezers, what is the maximum mass of sorbitol (C6H14O6) you can add to 2.00 kg of pure water and still have the solution freeze? Assume that sorbitol is a molecular solid and does not ionize when it dissolves in water.

Answer 1

Answer:

2,347.8 grams

Explanation:

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

 

To still freeze at -12° C, then the molality of the solution 12/ 1.86 = 6.45 moles

 

The molecular weight of sorbitol (C6H14O6)is:

 

6 C = 6 ×12 = 72

14 H = 14 × 1 = 14

6 O = 6 × 16 = 96

...giving a total of 182

 So one mole of sorbitol has a mass of 182 grams.

 

Since there are 2 kg of water,  2 × 6.45 moles = 12.9 moles can be added to the water to get the 12° C freezing point depression. 

Therefore

grams = moles × molar mass

12.9 moles × 182 grams / mole = 2,347.8 grams of sorbitol can be added and still freeze