Problem: In ice-cream making, the ingredients are kept below 0.0°C in an ice-salt bath.(a) Assuming that NaCl dissolves completely and forms an ideal solution, what mass of it is needed to lower the melting point of 5.5 kg of ice to –5.0°C?(b) Given the same assumptions as in part (a), what mass of CaCl2 is needed?

FREE Expert Solution

Recall that the melting point is the same temperature as the freezing point.

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:

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Problem Details

In ice-cream making, the ingredients are kept below 0.0°C in an ice-salt bath.

(a) Assuming that NaCl dissolves completely and forms an ideal solution, what mass of it is needed to lower the melting point of 5.5 kg of ice to –5.0°C?
(b) Given the same assumptions as in part (a), what mass of CaCl2 is needed?