At –12.0 °C (a common temperature for household freezers), what is the maximum m

Question

At –12.0 °C (a common temperature for household freezers), what is the maximum mass of fructose (C6H12O6) you can add to 2.00 kg of pure water and still have the solution freeze? Assume that fructose is a molecular solid and does not ionize when it dissolves in water. Kf values are given here:

Constants for freezing-point depression and boiling-point elevation calculations at 1 atm:

(°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

Normal Freezing point of water is 0 oC.

Freezing point of the solution is -12 oC.

Depression in boiling point is 12 oC.

The Kf value for water is 1.86 oC/m.

So, molality of the solution is 12 oC / (1.86 oC/m) = 6.45 m

Molar Mass of Fructose is 180 g/mol

So, 1000 g of water contains 180 * 6.45 g = 1161 g of Fructose

2000 g of water can dissolve maximum mass of 2*1161 = 2322 g of Fructose.

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