A \(80^\circ \text{C}\), \(100\text{ g} \) of \(\ce{KNO_3}\) saturated solution is cooled to \(20^\circ \text{C}\). What is the mass of \(\ce{KNO_3}\) in grams that will separate out from the solvent?
Details and Assumptions:
Separate out: when it used to have some mass dissolved in a saturated solution but as the temperature decrease, the solubility decrease so some of the solute cannot remain dissolve and will return as solid/liquid state until it reaches the solubility within the new temperature.
Solubility of \(\ce{KNO_3}\) at \(80^\circ\text{C}\): \(169\text{ g}/100\text{ g}\) water.
Solubility of \(\ce{KNO_3}\) at \(20^\circ \text{C}\): \(31.6\text{ g}/100\text{ g}\) water.