The freezing point of an aqueous solution of MgBr2 was found to be -3.0 °C. Calculate the boiling point of an aqueous solution of AlCl3 that has the same molality as the MgBr2 solution.

Given:
- $ K_f $ for water = 1.86 °C/m
- $ K_b $ for water = 0.512 °C/m

Possible answers:
A. 101.1 °C
B. 99.9 °C
C. 101.5 °C
D. 102.1 °C
E. 100.5 °C

To calculate the boiling point of an aqueous solution of AlCl3 with the same molality as the MgBr2 solution, we use the formula ΔTb = Kb × m. Given the freezing point depression of the MgBr2 solution and the molal boiling point elevation constant for water, we can find the molality of the MgBr2 solution. Using the molality, we can then calculate the change in boiling point for the AlCl3 solution and add it to the boiling point of pure water to find the boiling point of the AlCl3 solution.

Explanation:

To find the boiling point of an aqueous solution of AlCl3 with the same molality as the MgBr2 solution, we can use the formula:

ΔTb = Kb × m

Where ΔTb is the change in boiling point, Kb is the molal boiling point elevation constant for water, and m is the molality of the solution.

Given that the freezing point depression of the MgBr2 solution is -3.0 °C and the molal boiling point elevation constant for water is 0.512 °C/m, we can calculate the molality of the MgBr2 solution:

ΔTf = Kf × m

Therefore:

m = ΔTf / Kf = -3.0 °C / 1.86 °C/m = -1.61 m

Now we can calculate the change in boiling point for the AlCl3 solution using the same molality and the molal boiling point elevation constant for water:

ΔTb = Kb × m = 0.512 °C/m × -1.61 m = -0.824 °C

To find the boiling point of the AlCl3 solution, we add the change in boiling point to the boiling point of pure water (100 °C):

Boiling point = 100 °C + (-0.824 °C) = 99.17 °C

Therefore, the boiling point of an aqueous solution of AlCl3 with the same molality as the MgBr2 solution is approximately 99.17 °C.

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