Final answer:
To find the freezing point of a 0.015 molal aqueous solution of MgSO₄, multiply the molal freezing point depression constant (1.86 °C m-1) by the molality of the solution and the expected van't Hoff factor (i = 2) to get the freezing point depression. Then subtract this from the normal freezing point of water to find the solution's freezing point.
Step-by-step explanation:
To determine the freezing point of a 0.015 molal aqueous solution of MgSO₄, we need to consider the van't Hoff factor (i), which accounts for the number of particles the solute dissociates into in solution. Since MgSO₄ dissociates into one Mg2+ ion and one SO42- ion, we expect the van't Hoff factor to be i = 2 under ideal conditions. However, in real solutions, especially at higher concentrations, the interactions between ions reduce the effective number of particles and thus the value of i can slightly deviate from ideal.
The equation for calculating freezing point depression (ΔTf) is:
ΔTf = i × Kf × m
Where Kf is the molal freezing point depression constant of the solvent (water in this case, which is 1.86 C m-1), and m is the molality of the solution.
Assuming the ideal van't Hoff factor for MgSO₄ (i = 2), the calculation will be:
ΔTf = 2 × 1.86 C m-1 × 0.015 m = 0.0558 C
Since this value is the depression of the freezing point, we subtract it from the normal freezing point of pure water (0°C):
Freezing point of the solution = 0°C - ΔTf = 0°C - 0.0558°C = -0.0558°C
Therefore, the freezing point of the 0.015 molal aqueous solution of MgSO₄ is approximately -0.056°C at atmospheric pressure at sea level.