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17.5: Solubility Graphs

Created by: CK-12

Lesson Objectives

The student will:

  • define unsaturated solution and saturated solution.
  • interpret a solubility graph in terms of temperature and saturation points.

Vocabulary

  • saturated solution
  • unsaturated solution

Introduction

Solubility graphs are an excellent way of organizing and displaying data for interpretation. In this lesson, we will learn how to read and analyze a solubility graph in order to extract the relevant data.

Saturated and Unsaturated Solutions

A saturated solution is one in which a given amount of solvent has dissolved the absolute maximum amount of solute at that temperature. Two teaspoons of table salt in one cup of water is probably the maximum amount of salt that can be dissolved in water. If you then try to dissolve three teaspoons, some of the table salt would probably sit on the bottom of the glass. Once a solution becomes saturated, if more solute is added to a saturated solution, the excess solute remains undissolved and simply sits on the bottom of the cup. In comparison, if only one teaspoon was placed in the glass, the solution would be said to be unsaturated. An unsaturated solution is one that contains less than the maximum amount of solute that is possible in a given amount of solvent.

Reading and Interpreting Solubility Graphs

As we already know, solubility is the amount of solute that will dissolve in a given amount of solvent at a particular temperature. The latter part of this statement is significant since, for many solutes, the solubility will increase as the temperature is increased. There are exceptions, of course, such as sodium chloride (table salt). Sodium chloride will dissolve to the extent of about 36 \ \mathrm{g} in 100 \ \mathrm{g} of water at 25^\circ\mathrm{C}, and there is little change as the temperature increases. As another example, the solubility of cesium sulfate actually decreases as temperature increases. For the most part, however, the vast majority of ionic solids that are solutes do increase their solubility with temperature.

To display the different solubilities at different temperatures, a solubility graph is drawn to show the data in a more coherent manner. Having a solubility graph allows us to read the data about a particular solute or to compare solutes at a particular temperature quickly and easily. Let’s look at a typical solubility graph and see how it works.

What kind of information does this graph tell us? You can see that the solubility of three of the four solids increases with increasing temperature. In addition to general trends in the solubility of a substance, you can also get detailed facts from a solubility graph. For example, we can see that at 30^\circ\mathrm{C}, 95 \ \mathrm{g} of sodium nitrate (\mathrm{NaNO}_3) will dissolve, but at 60^\circ\mathrm{C}, 120 \ \mathrm{g} will dissolve in 100 \ \mathrm{g} of \mathrm{H}_2\mathrm{O}. At these same two temperatures, only 50 \ \mathrm{g} of \mathrm{Na}_2\mathrm{SO}_4 and 113 \ \mathrm{g} of potassium nitrate (\mathrm{KNO}_3) will dissolve in 100 \ \mathrm{g} of \mathrm{H}_2\mathrm{O}.

Example:

Answer the following questions using the solubility graph above.

  1. How much sodium nitrate will dissolve at 30^\circ\mathrm{C}?
  2. Which solid is most soluble at 60^\circ\mathrm{C}?
  3. Which solid is least soluble at 40^\circ\mathrm{C}?
  4. At what temperature will 60 \ \mathrm{g} of sodium sulfate dissolve in 100 \ \mathrm{g} of water?

Solution:

  1. Looking at the solubility graph below, you draw a line up (vertically) from 30^\circ\mathrm{C} until it hits the \mathrm{NaNO}_3 line. Following this, carry the line over (horizontally) to find the amount of \mathrm{NaNO}_3 that dissolves. Therefore, approximately 95 \ \mathrm{g} of \mathrm{NaNO}_3 will dissolve in 100 \ \mathrm{g} of water at 30^\circ\mathrm{C}.

  1. The highest line at 60^\circ\mathrm{C} is the green line (\mathrm{NaNO}_3), therefore it is the most soluble at 60^\circ\mathrm{C}.
  2. The lowest line at 40^\circ\mathrm{C} is the purple line (\mathrm{NaCl}), therefore \mathrm{NaCl} is the least soluble at 40^\circ\mathrm{C}.
  3. Looking at the solubility graph below, you draw a line over (horizontally) from 60 \ \mathrm{g} until it hits the \mathrm{Na}_2\mathrm{SO}_4 line. Following this, carry the line down (vertically) to find the temperature at which 60 \ \mathrm{g} of \mathrm{Na}_2\mathrm{SO}_4 will dissolve. Therefore, 60 \ \mathrm{g} of \mathrm{Na}_2\mathrm{SO}_4 will dissolve in 100 \ \mathrm{g} of water at 50^\circ\mathrm{C}.

Look at the solubility graph below, which shows more common ionic compounds. The lines on the solubility curves represent the amounts that dissolve in the given amount of solvent at a specific temperature. Look at the line for \mathrm{NH}_3. According to the graph, \mathrm{NH}_3 is the only substance of this group that decreases in solubility as the temperature is increased. We can also see that the most soluble substance at room temperature (25^\circ\mathrm{C}) is \mathrm{NH}_3 because it is the line highest up on the graph at 25^\circ\mathrm{C}. The highest point on the solubility curve is at approximately y = 92. We can say then that the most soluble substance at 0^\circ\mathrm{C} is ammonia with a solubility of approximately 92 \ \mathrm{g} in 100 \ \mathrm{g} of water.

All of this information can be obtained from reading the solubility graph. What other information can you obtain from a solubility graph? You could do a number of different types of calculations. For example, if you were doing an experiment in the lab (at room temperature) and needed a saturated solution of potassium chloride dissolved in 35 \ \mathrm{g} of water, how much \mathrm{KCl} would you need?

At 25^\circ\mathrm{C} (room temperature), approximately 35 \ \mathrm{g} of \mathrm{KCl} will dissolve in 100. \ \mathrm{g} of water. For 35 \ \mathrm{g} of water:

 \frac {x \ \mathrm{g \ KCl}} {35 \ \mathrm{g \ H}_2\mathrm{O}} = \frac {35 \ \mathrm{g \ KCl}} {100. \ \mathrm{g \ H}_2\mathrm{O}}
x = 12 \ \mathrm{g \ KCl}

Another type of problem that can be solved using a solubility graph is determining whether a solution is saturated or not. For example, you have a solution of potassium chlorate that you know is 76 \ \mathrm{g} dissolved in 250 \ \mathrm{g} of water. You want to know if this solution is saturated or unsaturated when your solution is being heated at 80^\circ\mathrm{C}.

Looking at the solubility graph, at 80^\circ\mathrm{C}, 44 \ \mathrm{g} of \mathrm{KClO}_3 will dissolve in 100. \ \mathrm{g} of \mathrm{H}_2\mathrm{O}. Therefore, we can use the same type of equation as used previously to determine how much would dissolve in 250 \ \mathrm{g} of \mathrm{H}_2\mathrm{O}.

 \frac {x \ \mathrm{g \ KClO}_3} {250. \ \mathrm{g \ H}_2\mathrm{O}} = \frac {44 \ \mathrm{g \ KClO}_3} {100. \ \mathrm{g \ H}_2)}
x = 110. \ \mathrm{g \ KClO}_3

Since it is possible to dissolve 110 \ \mathrm{g} of \mathrm{KClO}_3 in 250 \ \mathrm{g} of \mathrm{H}_2\mathrm{O} and our solution only has 76 \ \mathrm{g} dissolved in 250 \ \mathrm{g} of \mathrm{H}_2\mathrm{O}, the solution is unsaturated.

Lesson Summary

  • A saturated solution holds the maximum amount of solid at a specific temperature.
  • An unsaturated solution does not have the maximum amount of solute dissolved at that temperature in a given amount of solvent.
  • A solubility graph is drawn to display the solubility at different temperatures.
  • From reading a solubility graph, one can determine the mass of solute that can dissolve at specific temperatures, whether or not a solution is saturated, and compare solubilities of different substances at specific temperatures.

Further Reading / Supplemental Links

This website details some of the factors that affect solubility.

Review Questions

  1. Using the graph below, determine:
    1. How much ammonia will dissolve at 30^\circ\mathrm{C}?
    2. What solid is more soluble at 50^\circ\mathrm{C}?
    3. What solid is least soluble at 60^\circ\mathrm{C}?
    4. At what temperature will 50 \ \mathrm{g} of ammonium chloride dissolve in 100 \ \mathrm{g} of water?

  2. Why are solubility graphs useful?
  3. Define solubility and solubility graph.
  4. How many grams of \mathrm{NaCl} are in 450 \ \mathrm{g} of water at 30^\circ\mathrm{C} if the solubility is 39.8 \ \mathrm{g} per 100 \ \mathrm{g} of water?
    1. 8.84 \ \mathrm{g}
    2. 39.8 \ \mathrm{g}
    3. 100 \ \mathrm{g}
    4. 179 \ \mathrm{g}
  5. How many moles of ammonium chloride are in 225 \ \mathrm{g} of water at 40^\circ\mathrm{C} if the solubility is 45.8 \ \mathrm{g} per 100 \ \mathrm{g} of water?
    1. 0.86 \ \mathrm{mol}
    2. 1.92 \ \mathrm{mol}
    3. 20.3 \ \mathrm{mol}
    4. 103 \ \mathrm{mol}
  6. How many moles of potassium chloride are in 500 \ \mathrm{g} of water at 80^\circ\mathrm{C} if the solubility is 51.3 \ \mathrm{g} per 100 \ \mathrm{g} of water?
    1. 0.140 \ \mathrm{mol}
    2. 0.688 \ \mathrm{mol}
    3. 3.44 \ \mathrm{mol}
    4. 10.3 \ \mathrm{mol}
  7. Plot the following data (see Table below) on a solubility graph and then answer the questions below.
    1. Which substance is the most soluble at 50^\circ\mathrm{C}?
    2. Which substance is the least soluble at 90^\circ\mathrm{C}?
    3. What is the solubility of \mathrm{NH}_4\mathrm{ClO}_4 at 30^\circ\mathrm{C}?
    4. How many grams of \mathrm{NH}_4\mathrm{ClO}_4 would dissolve in 250 \ \mathrm{mL} at 30^\circ\mathrm{C}?
    5. At what temperature will 20 \ \mathrm{g} potassium sulfate dissolve in 100 \ \mathrm{g} of water?
Table for Problem 7
Temp (^\circ\mathrm{C}) \mathrm{g} \ \mathrm{NH}_4\mathrm{Br}/100 \ \mathrm{g} \ \mathrm{H}_2\mathrm{O} \mathrm{g} \ \mathrm{NH}_4\mathrm{ClO}_4 /100 \ \mathrm{g} \ \mathrm{H}_2\mathrm{O} \mathrm{g} \ \mathrm{NaClO}_3/100 \ \mathrm{g} \ \mathrm{H}_2\mathrm{O}
0 60.0 13.0 80.0
20 75.5 23.5 98.0
40 92.0 36.8 118.0
60 107.8 51.5 143.0
80 126.0 67.9 172.0
100 146.0 87.0 207.0
  1. Plot the following data (see Table below) on a solubility graph and then answer the questions below.
    1. Which substance is the most soluble at 50^\circ\mathrm{C}?
    2. Which substance is the least soluble at 90^\circ\mathrm{C}?
    3. What is the solubility of \mathrm{CuSO}_4 at 30^\circ\mathrm{C}?
    4. At what temperature will 20 \ \mathrm{g} potassium sulfate dissolve in 100 \ \mathrm{g} of water?
Table for Problem 8
Temp (^\circ\mathrm{C}) \mathrm{g} \ \mathrm{NaCl}/100 \ \mathrm{g} \ \mathrm{H}_2\mathrm{O} \ \mathrm{g} \mathrm{K}_2\mathrm{SO}_4/100 \ \mathrm{g} \ \mathrm{H}_2\mathrm{O} \mathrm{g} \ \mathrm{CuSO}_4/100 \ \mathrm{g} \ \mathrm{ H}_2\mathrm{O}
0 35.7 7.4 14.3
20 36.0 11.1 20.7
40 36.5 14.8 28.7
60 37.3 18.2 40.0
80 38.1 21.4 56.0
100 39.2 24.1  80.0

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