relating mole fraction to molality If the mole fraction of water in a HCl solution is 0.78 . calculate the molality of the solution?
 I don't understand how to relate mole fraction to molality.
The mole fraction is the ratio of moles of solute to moles of solvent. A mole fraction of $.78$ means that for every mole of HCl, there are $.78$ moles of water. Molality is the number of moles of solute per mass of solvant. Since HCl has a molar mass of 36.5 g/mol, we would use dimensional analysis to calculate the molality:
$$\frac{0.78 \text{ molH$_2$O}}{1\text{ mol HCl}}\cdot\frac{1 \text{ mol HCl}}{36.5\text{ g HCl}}=.021 \frac{\text{mol H$_2$O}}{\text{g HCl}}.$$
Usually, molality is given in mol/kg, so this is $21$ mol/kg.
Mole fraction of water = 0.78
Mole fraction of HCl = 1 - 0.78 = 0.22
If no. of moles of water = n1 and that of HCl = n2,
n1/(n1 + n2) = 0.78
n2/(n1 + n2) = 0.22

n1/n2 =0.78/0.22 = 3.54

Molality is no. of moles of solute in 1000g of water
No. of moles of water in 1000g of water = 1000/18 = 55.55 = n1
n2 = 55.55/3.54 = 15.69
So, molality = 15.69m