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
Jan 4, 2016

Answer:

#"45.9 g"#

Explanation:

So, you know that potassium nitrate, #"KNO"3#, has a solubility of #"155 g"# per #"100 g"# of water at #75^@"C"# and of #"38.0 g"# at #25^@"C"#.

What that means is that at #75^@"C"#, you can dissolve as much as #"155 g"# of solid potassium nitrate in water without the solution becoming saturated.

Once you hit that #"155 g"# mark, the solution becomes saturated, which means that the solution can't dissolve any more solid.

Now, the same thing can be said for the solution at #25^@"C"#. At this temperature, dissolving less than #"38.0 g"# of potassium nitrate per #"100 g"# of water will result in an unsaturated solution.

At the #"38.0 g"# mark, the solution will become saturated.

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

http://www.mts.net/~alou/Chemistry%2011/Unit%204%20-%20Solutions%20Lessons/Lesson%203%20-%20Factors%20Affecting%20Solubility.htm

So, you are starting with #"100 g"# of saturated solution at #75^@"C"#. Mind you, you have #"100 g"# of 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 #"100 g"# of water. Calculate how much water you have in this initial solution

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

Next, determine how much potassium nitrate can be dissolved in #"39.22 g"# of water at #26^@"C"# in order to make a 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 #75^@"C"# to #25^@"C"#, the amount of water that it contained will only hold #"14.9 g"# of dissolved potassium nitrate.

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.