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

delta T = i*Kf*m

2.43 = 3*1.86*m
solve for m.

To calculate the molal concentration of an aqueous calcium chloride solution, we need to use the freezing point depression equation. The equation is as follows:

ΔT = K_f * molality

Where:
ΔT is the freezing point depression
K_f is the molal freezing point depression constant for the solvent (water in this case)
molality is the molal concentration of the solute (calcium chloride)

First, we need to find the freezing point depression (ΔT). The given freezing point is -2.43 degrees Celsius. Since the freezing point of pure water is 0 degrees Celsius, the freezing point depression is calculated by subtracting the given freezing point from the freezing point of pure water:

ΔT = 0°C - (-2.43°C)
ΔT = 2.43°C

Next, we need to find the molal freezing point depression constant (K_f) for water. The molal freezing point depression constant for water is 1.86°C/m.

Finally, we can rearrange the freezing point depression equation to calculate the molal concentration (molality):

molality = ΔT / K_f
molality = 2.43°C / 1.86°C/m
molality ≈ 1.31 mol/kg

To determine the molal concentration of the aqueous calcium chloride solution, we need to use the freezing point depression equation.

The freezing point depression (ΔTf) is given by the formula:
ΔTf = Kf * m

Where:
- ΔTf is the change in freezing point (in degrees Celsius)
- Kf is the cryoscopic constant (freezing point depression constant) of the solvent
- m is the molal concentration of the solute (in mol/kg)

In this case, the freezing point depression (ΔTf) is -2.43 degrees Celsius. We need to find the molal concentration (m) of calcium chloride.

Calcium chloride (CaCl2) is a strong electrolyte that dissociates into three ions in water: Ca2+ and two Cl-. Therefore, the effective concentration of calcium chloride is three times the actual concentration.

Next, we need to find the cryoscopic constant (Kf) of the solvent, which is water in this case. The cryoscopic constant for water is approximately 1.86 degrees Celsius·kg/mol.

Using the formula with the given values:
-2.43 = (1.86 * 3) * m

Simplifying the equation:
-2.43 = 5.58 * m

Now, solve for the molal concentration (m):
m = -2.43 / 5.58
m ≈ -0.436 mol/kg

The molal concentration of the aqueous calcium chloride solution is approximately -0.436 mol/kg. Note that the negative sign indicates a decrease in the freezing point compared to pure water.