A benzene solution and a water solution of acetic acid (CH₃CO₂H; molar mass = 60.05 g/mol) are both 0.50 mass percent acid. The freezing-point depression of the benzene solution is 0.205 °C, and that of the aqueous solution is 0.159 °C.

(a) Using the freezing-point depression constants in Table 12.4, calculate the molality of the solute in each of the two solutions.

(b) What are the van’t Hoff factors for the water solution and benzene solution from these experiments?

(c) Note the difference between the van’t Hoff factors, and offer an explanation for the experimental results.

Table 12.4

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TABLE 12.4 Boiling-Point Increases and Freezing-Point Depression Constants for Solvents kb (C/m) 3.07 2.53 Solvent Acetic acid Benzene Naphthalene Water Boiling Point (C) 117.90 80.10 100.00 0.512 Freezing Point (C) 16.60 5.51 80.2 0.00 k (C/m) 3.90 4.90 6.8 1.86