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Answer :
Final answer:
Freezing point depression data in a benzene solution suggests a molar mass calculation error in the given options, as the correct result approximately 132 g/mol does not match the proposed answers in the question. The formula for freezing point depression and molar mass calculation was used to find the correct answer.
Explanation:
To find the molar mass of a nonionizing solute from the given freezing point depression in benzene, we use the formula ΔTf = Kf * m, where ΔTf is the freezing point depression, Kf is the molal freezing point depression constant of the solvent, and m is the molality of the solution. First, calculate the freezing point depression (ΔTf) by subtracting the freezing point of the solution from that of the pure solvent. Then, the molality (m) is determined by dividing the freezing point depression by the constant Kf of benzene. Finally, to calculate the molar mass, you divide the mass of solute in kilograms by the number of moles, which is the product of molality and the mass of solvent in kilograms.
Using the provided information, the ΔTf = 5.5 °C - 3.34 °C = 2.16 °C. Now, using Kf for benzene, which is 5.12 °C/m, the molality of the solution can be calculated as m = ΔTf / Kf = 2.16 °C / 5.12 °C/m = 0.4219 m. The molar mass (M) of the solute can then be calculated with the formula M = (mass of solute / (molality * mass of solvent)). Plugging in the values M = (1.365 g / (0.4219 m * 0.02416 kg)) gives the molar mass of approximately 132 g/mol, which is not matching any of the proposed answers (A-D).
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