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Freezing point depression is one of the colligative properties. Its equation is
[tex] T_{F,solvent} - T_{F,solution} =molality*i* K_{F,solvent} [/tex]
where the solvent is water. Thus, TF,solvent = 0 degrees Celsius and Kf is 1.86 kg/mol-C. i is the vant Hoff factor and TF,solution is -29 degrees = -33.9 degrees Celsius. Substituting,
For i = 3,
[tex]0 - -33.9 =molality*3* 1.86[/tex]
molality = 6.08 mol CaCl2/kg water
For i=2.6
[tex]0 - -33.9 =molality*2.6* 1.86[/tex]
molality = 7 mol CaCl2/kg water
We compare the values of the molalities to the solubility. Molecular weight of CaCl2 = 111 g/mol.
Solubility = (74.5 g/100g)(1 mol /111g)(1000 g/1 kg)
Solubility = 6.71 mol CaCl2/kg water
Since at 7 mol CaCl2/kg water (when i=2.6) is greater than the solubility, then it will not be possible.