# Question #76da3

##### 1 Answer

#### Explanation:

The first thing to do here is to figure out how much potassium nitrate you can dissolve in water at **saturated solution**.

You already know that at **for every**

In other words, you get

#"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 *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

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

Now, when you cool the solution to **for every**

You know that this solution contains *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

#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

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.