Chemistry Practice Problems Freezing Point Depression Practice Problems Solution: What mass of salt (NaCl) should you add to 1.52 L ...

# Solution: What mass of salt (NaCl) should you add to 1.52 L of water in an ice cream maker to make a solution that freezes at -12.4 oC ? Assume complete dissociation of the NaCl and density of 1.00 g/mL for water.

###### Problem

What mass of salt (NaCl) should you add to 1.52 L of water in an ice cream maker to make a solution that freezes at -12.4 oC ? Assume complete dissociation of the NaCl and density of 1.00 g/mL for water.

###### Solution

We’re being asked to determine the mass of salt(NaCl) that must be added to 1.52 L of water to get a solution that freezes at –12.4 ˚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: Calculate for ΔTf.

Step 2: Determine the molality of the solution.

Step 3: Calculate the mass of NaCl needed.

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