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 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
Now, potassium nitrate's solubility is given per #"100 g"# of water. Calculate how much water you have in this initial solution
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
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
The answer is rounded to three sig figs. |