Molality (m) = moles of solute / kilograms of solvent
Given:
Mass of calcium chloride (CaCl2) = 250 g
Molar mass of CaCl2 = 110.98 g/mol
Volume of water = 1000 g (assuming the density of water is 1 g/mL)
Convert the volume of water to kilograms:
Mass of water = Volume × Density = 1000 g × 1 g/mL = 1000 g = 1 kg
Now, calculate the moles of CaCl2:
Moles of CaCl2 = Mass / Molar mass = 250 g / 110.98 g/mol ≈ 2.25 mol
Finally, calculate the molality:
Molality (m) = 2.25 mol / 1 kg = 2.25 mol/kg
The freezing point depression (ΔTf) of a solution is directly proportional to the molality of the solution and the freezing point depression constant (Kf) of the solvent. The freezing point depression constant of water (Kf) is 1.86 °C/mol/kg.
ΔTf = Kf × m = 1.86 °C/mol/kg × 2.25 mol/kg ≈ 4.20 °C
Therefore, the freezing point of the solution would be approximately 4.20 °C lower than the freezing point of pure water (0 °C). Thus, the freezing temperature of the solution would most likely be between -4.20 °C and 0 °C.