At –13.5 °C (a common temperature for household freezers), what is the maximum

Question

At –13.5 °C (a common temperature for household freezers), what is the maximum mass of sucrose (C12H22O11) you can add to 2.50 kg of pure water and still have the solution freeze? Assume that sucrose is a molecular solid and does not ionize when it dissolves in water. Kf values are given here.

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

depression in freezing point dT = 0-(-13.5) = 13.5 ,

dT = Kf x m , where m=molality , kf = 1.86,

m = dT/kf = 13.5/1.86 = 7.258 molal,

molality = 7.258 = moles of sucrose /2.5 ,

moles of sucrose = 18.145,

mass of sucrose max can be added = 18.145 x 342 = 6205.6 gm = 6.2056 Kg

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