Final answer:
The molar mass of the nonionizing solute is calculated using the freezing point depression formula. After determining the change in freezing point and calculating the molality of the solution, the moles of solute are found, which are then used to determine the molar mass to be 126.91 g/mol.
Step-by-step explanation:
The question is asking to determine the molar mass of a nonionizing solute based on its impact on the freezing point of benzene. To calculate the molar mass, we use the freezing point depression formula ΔTf = Kf × m, where ΔTf is the change in freezing point, Kf is the freezing point depression constant for benzene (-5.12 °C/m), and m is the molality of the solution.
The initial freezing point of benzene is 5.5 °C, and the new freezing point after adding the solute is 3.08 °C. Thus, the depression in freezing point (ΔTf) is 5.5 °C - 3.08 °C = 2.42 °C. Now we calculate the molality (m) using the formula:
m = ΔTf / Kf = 2.42 °C / (-5.12 °C/m) = -0.47266 m (the negative sign indicates the direction of change, but for calculation purposes, we use the absolute value).
Since molality (m) is moles of solute per kilogram of solvent, we have to find the moles of solute. 1.33 grams of the solute dissolved in 22.18 grams (0.02218 kg) of benzene gives us a molality of 0.47266 m, which means 0.47266 moles of solute per kilogram of benzene. Now we can calculate the moles of solute in the actual solution:
0.47266 moles/kg × 0.02218 kg = 0.01048 moles.
Finally, we find the molar mass of the solute by dividing the mass of the solute by the moles of solute:
Molar mass = mass of solute / moles of solute = 1.33 g / 0.01048 moles = 126.91 g/mol.