Question

What is the minimum mass (in mg) of glycerol (C3H8O3) that must be dissolved in 11.0 mg water to prevent the solution from freezing at –25 oC? Round your answer to the hundredths digit.

Answer 1

Mass of water = 11 mg = 0.011 g = 11*10^-6 kg

Freezing point of water = 0^oC

To prevent the freezing, the Freezing point of solution should be minimum 25^oC = t

Since glycerol is a non-electrolyte. So, it will not dissociate in solution and i = 1

Now, T = i*m*K_f

Where K_f =molal depression cofficient = 1.86^oC/m

so, 25^oC = 1*m*1.86

m = 13.44

Now, Molality =Moles of Glycerol/ Mass of water in kg

13.44 = Mass of glycerol / (Molar mass of glycerol*Mass of water in kg)

13.44 *11*10^-6 kg *92.09382 g/mol= Mass of glycerol [ molar mass of glycerol = 92.09382 g/mol]

Mass of glycerol = 0.0136 g

Thus, Minimum mass of glycerol that must be dissolved = 13.6 mg