A certain salt is known to have a solubility in water of 25.2g/100g water at 100°C and 11.4g/100g water at 20°C. The salt is dissolved in 240 g of water at 100°C until no more solid will dissolve. How much salt will crystallize out when the solution is cooled to 20°C?
How much will dissolve in 240 g H2O at 100 C? That will be
25.2 x (240/100) = ?
How much will dissolve when cooled? That will be
11.4 x 240/100 = ? g in solution.
Then grams at 100 (from above calcn) - g in soln at 20 = grams that will crystallize.
To calculate the amount of salt that will crystallize out when the solution is cooled to 20°C, you need to compare the solubility of the salt at the two temperatures.
First, calculate the maximum amount of salt that can dissolve in 240 g of water at 100°C.
Solubility at 100°C = 25.2 g/100g water
Maximum amount of salt at 100°C = (Solubility at 100°C) x (mass of water)
Maximum amount of salt at 100°C = (25.2/100) x 240 g = 60.48 g
Since the solution has been saturated at 100°C, it means that 60.48 g of salt was dissolved in the 240 g of water.
Now, calculate the maximum amount of salt that can dissolve in 240 g of water at 20°C.
Solubility at 20°C = 11.4 g/100g water
Maximum amount of salt at 20°C = (Solubility at 20°C) x (mass of water)
Maximum amount of salt at 20°C = (11.4/100) x 240 g = 27.36 g
Since the solution is now cooled to 20°C, the maximum amount of salt that can remain dissolved in 240 g of water is 27.36 g.
To find out the amount of salt that will crystallize out, subtract the maximum amount of salt that can remain dissolved at 20°C from the amount of salt initially dissolved at 100°C.
Salt crystallized out = Initial dissolved salt - Remaining dissolved salt
Salt crystallized out = 60.48 g - 27.36 g = 33.12 g
Therefore, 33.12 grams of salt will crystallize out when the solution is cooled to 20°C.
To find out how much salt will crystallize out when the solution is cooled to 20°C, we need to calculate the difference between the amount of salt that can dissolve at 100°C (the initial temperature) and the amount of salt that can dissolve at 20°C (the final temperature).
Step 1: Calculate the maximum amount of salt that can dissolve at 100°C.
Given that the solubility of the salt at 100°C is 25.2g/100g water, we can calculate the mass of salt that can dissolve in 240g of water at 100°C:
Mass of salt dissolved at 100°C = (25.2g/100g water) * 240g water
Mass of salt dissolved at 100°C = 60.48g
Step 2: Calculate the maximum amount of salt that can dissolve at 20°C.
Given that the solubility of the salt at 20°C is 11.4g/100g water, we can calculate the mass of salt that can dissolve in 240g of water at 20°C:
Mass of salt dissolved at 20°C = (11.4g/100g water) * 240g water
Mass of salt dissolved at 20°C = 27.36g
Step 3: Calculate the amount of salt that will crystallize out when cooled from 100°C to 20°C.
The difference between the amount of salt dissolved at 100°C and 20°C will represent the amount of salt that will crystallize out:
Salt crystallized out = Mass of salt dissolved at 100°C - Mass of salt dissolved at 20°C
Salt crystallized out = 60.48g - 27.36g
Salt crystallized out = 33.12g
Therefore, when the solution is cooled from 100°C to 20°C, approximately 33.12 grams of salt will crystallize out.