# The solubility of #KNO_3# is 155 g per 100 g of water at 75° Cand 38.0 g at 25°C. What mass (in grams) of #KNO_3# will crystallize out of solution if exactly 100.0 g of its saturated solution at 75° C is cooled to 25°C?

##### 1 Answer

#### Explanation:

So, you know that *potassium nitrate*,

What that means is that at **without** the solution becoming **saturated**.

Once you hit that **saturated**, which means that the solution can't dissolve any more solid.

Now, the same thing can be said for the solution at **less** than **unsaturated solution**.

At the **saturated**.

Now, take a look at how the *solubility graph* for potassium nitrate looks like

So, you are starting with **saturated solution** at **solution** that contains **as much dissolved potassium nitrate as possible**.

This solution will contain

#100.0 color(red)(cancel(color(black)("g solution"))) * "155 g KNO"_3/((155 + 100)color(red)(cancel(color(black)("g solution")))) = "60.78 g KNO"_3#

Now, potassium nitrate's solubility is given per

#m_"water" = "100.0 g" - "60.78 g" = "39.22 g"#

Next, determine how much potassium nitrate can be dissolved in **saturated solution**, i.e. have the *maximum amount* of dissolved potassium nitrate possible

#39.22 color(red)(cancel(color(black)("g water"))) * "38.0 g KNO"_3/(100color(red)(cancel(color(black)("g water")))) = "14.9 g KNO"_3#

This means that when the initial solution is cooled from

The rest will crystallize out of solution

#m_"crystallize" = "60.78 g" - "14.9 g" = color(green)("45.9 g")#

The answer is rounded to three sig figs.