Crystallization problem

[gmg12]

The solubility of KNO3 is 155g per 100g of water at 75C and 38g at 25C. What mass in grams of KNO3 will crystallize out of a solution if exactly 100g of its saturated solution at 75C is cooled to 25C? 

My chemistry book does not have a formula to figure this out and I tried looking online for help. I'm just not sure where to even start.
Thanks.

[kingchemist]

At 75C there will be 155g KNO3 in 100g of water, making a total mass of 255g for the solution.

So find the mass that will be in 100g of solution at this temperature ((155/255) x 100) = 60.78g KNO3.
Find the volume of the water in this solution (this will be 'same' as the mass of water as (solution mass - KNO3 mass) 100-60.78 = 39.32g of water = 32.32 mL of water

At 25C you have 35g in 100g making 35g/135g of solution. Use the volume of water in the previous step to find the mass of KNO3 that can dissolve in this at 25C. 100g H2O contain 35g KNO3 so 39.32g will contain 13.76g KNO3

The difference in the two mass will be the mass of solute that crystallises 60.78 - 13.76 = 47.02 g (does this make sense? check it through

[gmg12]

Thanks. Im not understanding where the 32.32 mL of water comes from based on the calculation you have?

[kingchemist]

OOps it should have been 39.32g of water = 39.32 mL of water

Sorry