In A Home Ice Cream Freezer We Lower The Freezing Point Of The Water Bath?
In a home ice cream freezer we lower the freezing point of the water bath surrounding the ice cream can by dissolving NaCL in water to make a brine solution. A 15% brine solution is obseved to freeze at -10.888C.What is the van”t Hoff factor,i, for this solution
The equation for freezing point depression is,
∆T = Kf m i
where
∆T = 10.888 K (freezing point depression of H2O)
Kf = 1.858 K-kg/mol (cryoscopic constant for water)
m = molality of brine (NaCl)
i = van’t Hoff factor
To find molality:
1 kg of 15% brine solution contains 850 g water and 150 g NaCl. The MW of NaCl is 58.6 g/mole, and 150/58.6 = 2.56 moles. The molality of the solution = 2.56moles/0.850 kg water = 3.01 mol/kg.
Solving for i gives 1.96
i = 2 indicates that by using the colligative properties equations without the i factor, we’re actually calculating the molar mass of each of the Na+ and Cl- ions in solution. The molar mass of NaCl should be twice that number because it originally dissociated to produce one Na+ ion and one Cl- ion per formula unit of NaCl; the sum of the masses of the two ions should yield the mass of one formula unit of NaCl. Note that even if the mass of Na+ and Cl- weren’t equal (which is the case), we’re only calculating the average mass of the two particles using our colligative properties analysis. Hence multiplying that average number by two, we would be calculating the molar mass of NaCl.