Final answer:
The freezing point of the solution is calculated using the formula for freezing point depression and the given molality. It is found to be -3.72°C, which is answer option (a).
Step-by-step explanation:
The question requires an understanding of the concept of freezing point depression in solutions, which is governed by the formula ΔTf = i * Kf * m, where i is the van 't Hoff factor (number of particles the solute splits into), Kf is the cryoscopic constant of the solvent (for water it is 1.86 °C/m), and m is the molality of the solution. Since LiBr splits into two ions, Li+ and Br-, its van 't Hoff factor (i) is 2.
The molality of the solution is calculated as moles of solute per kilogram of solvent. Here, the molality (m) is 0.5 mol / 0.5 kg = 1 mol/kg. Next, we use the formula above: ΔTf = 2 * 1.86 °C/m * 1 m = 3.72 °C.
Therefore, the freezing point of the water will decrease by 3.72 °C. Since the normal freezing point of water is 0.0 °C, the new freezing point will be 0.0 °C - 3.72 °C = -3.72 °C. Thus, the correct answer is (a) -3.72 °C.