To solve this problem, we need to determine how much NaNO₃ will crystallize out of the solution when the temperature is changed from 70 °C to 20 °C.
### Step 1: Understand the given data
- At 70 °C, the solubility of NaNO₃ is 140 g per 100 g of water.
- At 20 °C, the solubility of NaNO₃ is 85 g per 100 g of water.
- We are starting with a solution that contains 200 g of NaNO₃ in 100 g of water at 70 °C.
### Step 2: Calculate the initial amount of NaNO₃ in the solution at 70 °C
Given that the solubility of NaNO₃ at 70 °C is 140 g per 100 g of water, we can assume that our 200 g of NaNO₃ is fully dissolved in the water because the solubility limit is not exceeded.
### Step 3: Calculate the final amount of NaNO₃ that remains dissolved at 20 °C
When the solution is cooled to 20 °C, the maximum solubility of NaNO₃ is 85 g per 100 g of water. Thus, the amount of NaNO₃ that can remain dissolved in the 100 g of water at 20 °C is:
[tex]\[ \text{Final amount of dissolved NaNO₃ at 20 °C} = 85 \text{ g} \][/tex]
### Step 4: Calculate the amount of NaNO₃ that will precipitate
The initial amount of NaNO₃ dissolved at 70 °C was 140 g. When cooled to 20 °C, only 85 g can remain dissolved. The difference will precipitate.
[tex]\[ \text{Amount of NaNO₃ that will precipitate} = 140 \text{ g} - 85 \text{ g} \][/tex]
[tex]\[ \text{Amount of NaNO₃ that will precipitate} = 55 \text{ g} \][/tex]
### Conclusion
When the solution is cooled from 70 °C to 20 °C, 55 grams of NaNO₃ will precipitate out of the solution.
