Molality problem?

Question

Ok, so i did out this problem, but in the answer booklet, i have no idea where this number comes from.
So the problem asks:
HF<-->H+ + F-
a. 40 g HF and 2kg water, determine mass of each substance which is needed to make max quantity of .1 molal HF solution.
i figured this out to be 4 g (0.2 mol) HF and 2 kg water.
the next part asks:
Determine the molality of F- ions and the molality of HF molecules in the solution prepared as directed in part a.
what the book does is, it says that the molality of all dissolved particles is equal to the sum of the molalites of H+ ions, F- ions, and HF molecules.
mH+mF+mHF=0.108 <<<---Where does that number come from/?????
it then explains, per kg solvent, let x=mol HF dissociated=mol H+formed=mol F- formed
0.1 - x = mHF
x+x+(0.1-x)=0.108
x=0.008
Now what confuses me is where the 0.108 came from?!?!?!?
it says no where how it comes from or where they got it?
possible explanation please?

well theres another part of the question that asks for the percent ionization, which i found to be 8%.
also, it is given that 0.1 m solution of HF in water gives freezing point of -0.201 C.
it doesnt say anything else (or give any more information)

Answer 1

I have not worked it all out, but HF is not a strong acid; it is a weak acid. That means that it is not completely dissociated into H+ and F- ions. There is a certain constant Ka = [H+][F-] The 0.108 factor has something to do with Ka. Can you look back and see if there is something among the given?

Answer 2

its relatively simple if you go by units... molarity = concentration in volume molality = concentration in mass so you have molarity which is in essence is mol/volume(which ever units in this case lets use m^3) and you have density which is kg/m^3 (in this example) just divide molarity by density to give: mol*m^3/(m^3*kg) = mol / kg