Okay, well my initial thoughts are how to approach this question. If one were to derive the expression:
Kf = (M·R·Tf2)/ΔHfus (1), then one could quite easily solve for Kf.
Using the given information, the heat of fusion for water can be derived as such:
ΔHfus = ΔHsub - ΔHvap
Therefore, the heat of fusion for water is 6.01 kJ/mol.
For (1), we additionally need to know the molar weight and normal freezing point for water, as well as the universal gas constant (8.315).
Using the mole fraction of glucose in a 1-molal solution of the solute, we can derive the molar weight for water using
1 = nglucose/(MWwater·nwater), and 0.0177 = nglucose/(nglucose + nwater)...
We find it to be 0.01802 kg/mol.
I finally tried to find the normal freezing point of water using the saturated vapour pressure piece of information. I tried to use the Clausius-Clapeyron relation, but it didn't seem to be valid...
If the question assumes that we know the normal freezing point of water, then it should be pretty straightforward...
I would be interested to see your solution for how this question should be solved, Borek.