Question

Question #76da3

Answer 1

`"252 g KNO"_3`

Explanation:

The first thing to do here is to figure out how much potassium nitrate you can dissolve in water at `75^@"C"` in order to have `"550.0 g"` of saturated solution.

You already know that at `75^@"C"`, a saturated solution of potassium nitrate holds `"155 g"` of solute for every `"100 g"` of water.

In other words, you get `"155 g"` of potassium nitrate for every

`"155 g KNO"_3 + "100.0 g H"_2"O" = "255 g solution"`

You can now use this as a conversion factor to figure out how much potassium nitrate you get in `"550 g"` of saturated solution

`550.0 color(red)(cancel(color(black)("g solution"))) * "155 g KNO"_3/(255color(red)(cancel(color(black)("g solution")))) = "334.3 g KNO"_3`

You can now say that at `75^@"C"`, `"550.0 g"` of saturated solution contain `"334.3 g"` of potassium nitrate and

`"550.0 g solution " - " 334.3 g KNO"_3 = "215.7 g H"_2"O"`

Now, when you cool the solution to `25^@"C"`, you decrease the solubility of the solute to `"38.0 g"` for every `"100.0 g"` of water.

You know that this solution contains `"215.7 g"` of water, so use the known solubility of potassium nitrate at `25^@"C"` to calculate how much solute you can get in a saturated solution at this temperature

`215.7 color(red)(cancel(color(black)("g H"_2"O"))) * "38.0 g KNO"_3/(100.0color(red)(cancel(color(black)("g H"_2"O")))) = "81.97 g KNO"_3`

This means that your solution can hold a maximum of `"81.97 g"` of potassium nitrate at `25^@"C"`. The rest of the solute will crystallize out of solution.

`m_"crystallize" = "334.3 g" - "81.97 g"`

`m_"crystallize" = "252.3 g KNO"_3`

Rounded to three sig figs, the answer will be

`m_"crustallize" = color(darkgreen)(ul(color(black)("252 g KNO"_3)))`

Therefore, you can say that `"550.0 g"` of saturated potassium nitrate solution will hold `"334.3 g"` of potassium nitrate at `75^@"C"` and `"81.97 g"` at `25^@"C"`.

The difference between these two values will crystallize out of solution as a result of the decrease in solubility associated with the decrease in temperature.