# 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?

###### FREE Expert 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:

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:

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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###### Problem Details

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?