How do you find the molality of an unknown solution?
That depends on just how "unknown" it is.
Then use the following equation to solve for molality:
There is one constant for freezing point change and one for boiling point change. Every solvent has its own unique values.
The van't Hoff factor is essentially the number of particles a unit or molecule breaks into when it is dissolved. For example, sodium chloride (NaCl) breaks into 2 ions, so its van't Hoff factor is 2. Calcium chloride (CaCl2) would have a factor of 3. Molecular substances such as sucrose or glucose do not ionize, so their factor is 1.
For ionic substances the equation above becomes less accurate as the concentration increases due to attractive interactions of the ions.
If you don't know the identity or molecular nature of the solute, you could use the same procedure to find the "total molality" of the solution. This would simply be
There are similar ways to determine molality by measuring changes in vapor pressure and osmotic pressure of solutions as compared to a pure solvent. They use other equations, but I hope this answer has helped.
A number of examples that illustrate the point on this page http://www.chemteam.info/Solutions/FP-depression-probs11-to-25.html