Freezing Point Depression

Freezing point depression is a colligative property, which means it depends on the number of solute particles present in a solution, rather than the nature of the solute particles. It is the phenomenon where the freezing point of a solvent is lowered when a non-volatile solute is added to it.

Colligative Properties

Colligative properties are those properties of a solution that depend on the concentration of solute particles, but not on their identity. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.

Formula for Freezing Point Depression

The formula to calculate the freezing point depression (ΔTf) is:

ΔTf = Kf * m

where ΔTf is the change in freezing point, Kf is the cryoscopic constant (a characteristic property of the solvent), and m is the molality of the solution (moles of solute per kilogram of solvent).

Percent Dissociation

Percent dissociation is a measure of the extent to which a solute dissociates into ions when dissolved in a solvent. It is calculated by dividing the number of dissociated particles by the total number of particles present in the solution, and then multiplying by 100.

Calculation

To calculate the percent dissociation of the salt in water, we need to know the freezing point depression (ΔTf) and the cryoscopic constant (Kf) for water.

Given:
- Freezing point depression (ΔTf) = -2.4°C
- Mass of solvent (water) = 1 kg

Find:
- Percent dissociation of the salt in water

Step 1: Calculate Molality (m)

Molality (m) is defined as the moles of solute per kilogram of solvent. In this case, since we have 1 mole of the salt dissolved in 1 kg of water, the molality can be calculated as:

m = 1 mole / 1 kg = 1 mol/kg

Step 2: Calculate Cryoscopic Constant (Kf)

The cryoscopic constant (Kf) for water is 1.86°C/m.

Step 3: Calculate Change in Freezing Point (ΔTf)

We can use the formula for freezing point depression to calculate the change in freezing point:

ΔTf = Kf * m
ΔTf = 1.86°C/m * 1 mol/kg
ΔTf = 1.86°C

Step 4: Calculate Percent Dissociation

The salt (type mx) dissociates into m moles of cations (m+) and m moles of anions (x-) in water. Therefore, the total number of particles in the solution is 3m (1 mole of salt dissociates into 1 mole of cations and 1 mole of anions).

The percent dissociation can be calculated as:

Percent dissociation = (m / 3m) * 100
Percent dissociation = 1/3 * 100
Percent dissociation = 33.33%

Conclusion

The percent dissociation of the salt (type mx