At –14.0 °C (a common temperature for household freezers), what is the maximum m

Question

At –14.0 °C (a common temperature for household freezers), what is the maximum mass of sucralose (C12H19Cl3O8) you can add to 1.00 kg of pure water and still have the solution freeze? Assume that sucralose is a molecular solid and does not ionize when it dissolves in water. Kf values are given here.

(°C/m)

Normal freezing

point (°C)

(°C/m)

Normal boiling

point (°C)

Solvent Formula Kf value*

(°C/m)

Normal freezing

point (°C)

Kb value

(°C/m)

Normal boiling

point (°C)

water H2O 1.86 0.00 0.512 100.00 benzene C6H6 5.12 5.49 2.53 80.1 cyclohexane C6H12 20.8 6.59 2.92 80.7 ethanol C2H6O 1.99 –117.3 1.22 78.4 carbon
tetrachloride   CCl4 29.8 –22.9 5.03 76.8 camphor   C10H16O 37.8 176

Explanation / Answer

freezing point = - 14 oC

Kf of water = 1.86

delta Tf = Kf x m

0 - (- 14) = 1.86 x m

m = 7.53

molality = 7.53 m

molality = moles / mass of solvent

7.53 = moles / 1

moles = 7.53

mass of sucralose = 7.53 x 397.64

mass of sucralose added = 2993 g

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