Final answer:
The solubility of potassium nitrate in water at 20°C is not specified in the given information, but generally, solubility curves are used to determine the maximum amount of a solute like KNO3 that can be dissolved in a solvent at a specific temperature.
Step-by-step explanation:
The solubility of potassium nitrate (KNO3) in water varies with temperature. Solubility curves provide information about how much solute can be dissolved in a solvent at a specific temperature, indicating whether a solution is saturated or unsaturated. At 20°C, the specific solubility for potassium nitrate is not provided in the given information. However, by understanding solubility curves, one can determine that if a solution at 20°C is saturated with KNO3, it will contain the maximum amount of solute that can be dissolved in the solvent at that temperature. The remaining undissolved KNO3 will crystallize out of the solution if no additional solvent is added, just as it was shown in the given scenarios where 32 g of KNO3 remained undissolved at 30°C and 66 g would crystallize out when the temperature is lowered to 0°C.