.7 molal Na2SO4 solutions dissociate to 70%.calculate the depression of freezing point?

To calculate the depression of the freezing point for a 0.7 molal Na2SO4 solution that dissociates to 70%, we can use the formula for freezing point depression, which is derived from colligative properties. This property depends on the number of solute particles in a solution rather than the identity of the solute itself.

Understanding Freezing Point Depression

The freezing point depression can be calculated using the formula:

ΔTf = i × Kf × m

• ΔTf = depression of the freezing point
• i = van 't Hoff factor (number of particles the solute dissociates into)
• Kf = freezing point depression constant of the solvent (for water, Kf = 1.86 °C kg/mol)
• m = molality of the solution

Step-by-Step Calculation

1. **Determine the van 't Hoff factor (i)**: For sodium sulfate (Na2SO4), it dissociates into three ions in solution: 2 sodium ions (Na⁺) and 1 sulfate ion (SO₄^2-). Therefore, the theoretical value of i is 3. However, since the solution only dissociates to 70%, we need to adjust this value:

i = 3 × 0.70 = 2.1

2. **Identify the molality (m)**: The molality of the solution is given as 0.7 molal.

3. **Use the freezing point depression constant (Kf)**: For water, Kf is 1.86 °C kg/mol.

4. **Plug the values into the formula**:

ΔTf = i × Kf × m

ΔTf = 2.1 × 1.86 °C kg/mol × 0.7 mol/kg

5. **Perform the calculation**:

ΔTf = 2.1 × 1.86 × 0.7 = 2.58 °C

Final Result

The depression of the freezing point for the 0.7 molal Na2SO4 solution that dissociates to 70% is approximately 2.58 °C. This means that the freezing point of the solution will be lowered by this amount compared to pure water.

In practical terms, if pure water freezes at 0 °C, this solution would freeze at about -2.58 °C. This principle is important in various applications, such as in antifreeze formulations and understanding how solutes affect the properties of solvents.