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Solution: The freezing point of t-butanol is 25.50°C and Kf is 9.1°C • kg/mol. Usually t-butanol absorbs water on exposure to air. If the freezing point of a 10.0-g sample of t-butanol is 24.59°C, how many grams of water are present in the sample?

Problem

The freezing point of t-butanol is 25.50°C and Kf is 9.1°C • kg/mol. Usually t-butanol absorbs water on exposure to air. If the freezing point of a 10.0-g sample of t-butanol is 24.59°C, how many grams of water are present in the sample?

Solution

We’re being asked to determine the mass of water present in a 10.0 g sample of t-butanol with a freezing point of 24.59°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:


ΔTf=Tf, pure solvent-Tf, solution


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


ΔTf=imKf


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:


molality=moles solutekg solvent



To solve this problem, we shall follow these steps

Step 1: Calculate for ΔTf.

Step 2: Determine the molality of the solution.

Step 3: Calculate the mass of H2O.


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