To determine whether the solution is saturated or unsaturated, we need to compare the actual concentration of the solution (given in grams per cubic decimeter, g/dm³) with the solubility of KNO₃ at the same temperature (given in moles per cubic decimeter, mol/dm³).
First, let’s convert the given mass concentration to mol/dm³ using the molar mass of KNO₃.
Molar mass of KNO₃ = (39.10 g/mol) + (14.01 g/mol) + (3 * 16.00 g/mol) = 101.10 g/mol
Concentration in mol/dm³ = (30.3 g/dm³) / (101.10 g/mol) = 0.300 mol/dm³
Now we compare the concentration (0.300 mol/dm³) with the solubility of KNO₃ at 0°C (1.33 mol/dm³).
If the concentration is less than the solubility, the solution is unsaturated because more solute can dissolve. If the concentration is equal to the solubility, the solution is saturated because no more solute can dissolve. If the concentration is greater than the solubility, the solution is supersaturated, but this case is not relevant to our comparison.
In this case, the concentration (0.300 mol/dm³) is less than the solubility (1.33 mol/dm³). Therefore, the solution is unsaturated at 0°C because more KNO₃ can dissolve in the solution.