Potassium sulfate has a solubility of 15g/100g water at 40 celsius. a solution is prepared by adding 39.0g of potassium sulfate to 225g water, carefully heating the solution, and cooling it to 40 celsius. a homogeneous solution is obtained. is this solution saturated, unsaturated, or supersaturated? the beaker is shaken and precipitation occurs. how many grams of potassium sulfate would you except to crystallize out?

To determine the state of saturation of the solution, we calculate the mass of solute per mass of water for the given amounts and compare this value to the solubility. If the value is less than the solubility, then the solution is unsaturated. If it is greater than solubility, then it is supersaturated. If it is equal to the solubility, then it is saturated.

mass solute / mass water  = 39.0 grams K2SO4 / 225 grams H2O = 0.173 g K2SO4/ g H2O
solubility = 15 g /100 g = .15 g/g

Therefore, the solution is supersaturated. When it is shaken, some of the solute would precipitate out. 

mass of solute soluble to water = .15 g K2SO4/ g water ( 225 g water ) = 33.75 g K2SO4
mass of K2SO4 that would crystallize = 39.0 - 33.75 = 5.25 g K2SO4