Question

What is the expected freezing point of a 0.50 m solution of Na₂CO₃ in water?

1) 0.93°C
2) -0.93°C
3) -6.5°C
4) -2.8°C
5) -1.9°C

Answer 1

The expected freezing point of a 0.50 m solution of Na₂CO₃ is -2.8°C, as calculated using the formula for freezing point depression with the van't Hoff factor and the freezing point depression constant of water.

Step-by-step explanation:

The question asks to determine the expected freezing point of a 0.50 m solution of Na₂CO₃ in water. To find the freezing point depression (ΔTf), we can use the formula ΔTf = i * Kf * m, where i is the van't Hoff factor (the number of particles the solute splits into), Kf is the freezing point depression constant of the solvent (water), and m is the molality of the solution.

Sodium carbonate (Na₂CO₃) dissociates in water into 2 Na+ ions and 1 CO3^2- ion, giving us a van't Hoff factor (i) of 3. The Kf for water is 1.86°C kg/mol. Thus, the freezing point depression calculation for a 0.50 m Na₂CO₃ solution is:

ΔTf = i * Kf * m = 3 * 1.86°C kg/mol * 0.50 mol/kg = 2.79°C

The normal freezing point of water is 0°C, so the expected freezing point of the solution will be 0°C - 2.79°C = -2.8°C, which corresponds to option 4.