Question #76da3

1 Answer
Jan 30, 2017

Answer:

#"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.