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# Solution: When 0.81 g of an unknown non-electrolyte is dissolved in 50.0 g of benzene, the freezing point decreased by 0.41 degrees C.If the Kfp of the solvent is 5.12 K/m, calculate the molar mass of the unkno

###### Problem

When 0.81 g of an unknown non-electrolyte is dissolved in 50.0 g of benzene, the freezing point decreased by 0.41 degrees C.If the Kfp of the solvent is 5.12 K/m, calculate the molar mass of the unknown solute.

a. 20.23 g/mol
b. 202.3 g/mol
c. 2023 g/mol
d. not enough information is given

###### Solution

We’re being asked to determine the molar mass of an unknown solute present in 50.0 g benzene to get a change in freezing point of 0.41˚C.

Recall that the freezing point of a solution is lower than that of the pure solvent and the change in freezing point (ΔT­f) is given by:

The change in freezing point is also related to the molality of the solution:

$\overline{){{\mathbf{\Delta T}}}_{{\mathbf{f}}}{\mathbf{=}}{{\mathbf{imK}}}_{{\mathbf{f}}}}$

where:

i = van’t Hoff factor

m = molality of the solution (in m or mol/kg)

Kf = freezing point depression constant (in ˚C/m)

Recall that the molality of a solution is given by:

For this problem, we need to do the following:

Step 1: Determine the molality of the solution.

Step 2: Calculate the moles of the unknown solute.

Step 3: Calculate the molar mass of the unknown solute.

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