What is the minimum mass of glycerol (c3h8o3) that must be dissolved in 928 mg of water to prevent the solution from freezing at −15.0°c? (assume ideal

In order to have a freezing point of −15.0°c means we need a depression in freezing point to be −15.0°c

we know that depression in freezing point is a colligative property which depends on molality as

depression in freezing point  = Kf X molality

Kf = 1.86 °C/m

molality = moles of solute / mass of solvent in Kg

15 = 1.86 °C/m X molality

molality = 8.065

molality = moles of glycerol / mass of water in Kg

moles of glycerol = 8.065 X 928 X 10^-6

moles = 0.00748

moles = mass / molar mass

mass = moles X molar mass = 0.00748 X 92 = 0.688 grams = 688 mg

so this is the minimum mass required