What is the molal concentration of an aqueous calcium chloride solution that freezes at -2.43 degrees C?

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To determine the molal concentration of an aqueous calcium chloride solution that freezes at a specific temperature, you need to use the concept of freezing point depression and the colligative properties of solutions.

Freezing point depression occurs when a solute is added to a solvent, which lowers the freezing point of the solvent. In this case, calcium chloride (CaCl2) is the solute, and water is the solvent.

The equation for freezing point depression is given by:

ΔT = Kf * m,
where ΔT is the change in freezing point temperature, Kf is the cryoscopic constant (a characteristic property of the solvent), and m is the molality of the solute.

First, you need to find the change in freezing point temperature (ΔT) by subtracting the freezing point of the solution from the freezing point of pure water:

ΔT = Tpure water - Tsolution

In this case, the solution freezes at -2.43 degrees C, and the freezing point of pure water is 0 degrees C. Therefore:

ΔT = 0 - (-2.43)
ΔT = 2.43 degrees C

Next, you need to determine the cryoscopic constant (Kf) for water. The cryoscopic constant for water is 1.86 degrees C/m.

Now, you can rearrange the freezing point depression equation to solve for molality (m):

m = ΔT / Kf
m = 2.43 / 1.86

Calculating the molality:

m ≈ 1.31 mol/kg (rounded to two decimal places)

Therefore, the molal concentration of the aqueous calcium chloride solution is approximately 1.31 mol/kg.