A rock salt (NaCl), ice, and water mixture is used to cool milk and cream to make homemade ice cream. How many grams of rock salt must be added to water to lower the freezing point 12.6°C?

Answer 1

∆T = imK

∆T = change in temperature = 12.6º (normal freezing point of water is 0ºC)

i = van't Hoff factor = 2 for NaCl (Na⁺ and Cl^-; 2 particles)

m = molality = moles of NaCl / kg water

K = freezing point constant for water = 1.86º/m

Solving for m, we have...

12.6 = (2)(m)(1.86)

m = 12.6 / (2)(1.86)

m = 3.387 moles NaCl / kg water

Molar mass NaCl = 58.4 g / mol

3.387 mols x 58.4 g / mol = 198 g NaCl added to 1 kg of water will lower the freezing point 12.6ºC