The freezing point and boiling point of a solution can be calculated using the following formula:
Freezing Point = Kf x molality
Boiling Point = Kb x molality
where Kf and Kb are the freezing and boiling point constants respectively.
The molality of a solution is the number of moles of solute (NaNO3) in 1 kg of solvent (water). For this solution, the mass of the solute (NaNO3) is 5.5%, and the mass of the solvent (water) is 94.5%.
Therefore, the mass of NaNO3 = 5.5g/100g = 0.055g
The molar mass of NaNO3 = 85.0 g/mol
Therefore, the number of moles of NaNO3 = 0.055g/85.0 g/mol = 0.000647 mol
The mass of water = 94.5g/100g = 0.945g
Therefore, the molality of the solution = 0.000647 mol/0.945 kg = 0.000682 mol/kg