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Determine the theoretical melting temperature (in °C) of an aqueous solution of 1.55 m CaCl2, given that [tex]K_f = 2.31 \, \text{K/m}[/tex].

Answer :

Final answer:

The theoretical melting temperature of a 1.55 m CaCl2 aqueous solution is calculated using freezing point depression and the Van't Hoff factor. It's found to be -11.14°C.

Explanation:

The theoretical melting temperature of an aqueous solution of 1.55 m CaCl2 can be determined using the concept of freezing point depression. When a solute is added to a solvent, it decreases the freezing point of the solvent. This is calculated using the formula ΔTf = Kf * m * i. Here, Kf is the cryoscopic constant of water (1.86 K/m), m is the molality of the solution, and i is the van 't Hoff factor (number of ions produced per formula unit of the solute).

In the case of CaCl2, it dissociates into three ions (one Ca2+ and two Cl-), therefore, i = 3. Applying the values to the formula gives ΔTf = 2.31 K/m * 1.55 m * 3 = 11.14°C. The theoretical melting temperature of the solution is then 0 °C - ΔTf, which gives a theoretical melting temperature of -11.14 °C.

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