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17.5: Solubility Graphs

Difficulty Level: At Grade 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.

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.

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 $(^\circ\mathrm{C})$ $\mathrm{g} \ \mathrm{NaCl}/100 \ \mathrm{g} \ \mathrm{H}_2\mathrm{O} \ \mathrm{g}$ $\mathrm{K}_2\mathrm{SO}_4/100 \ \mathrm{g} \ \mathrm{H}_2\mathrm{O}$ $\mathrm{g} \ \mathrm{CuSO}_4/100 \ \mathrm{g} \ \mathrm{ H}_2\mathrm{O}$
$0$ $35.7$ $7.4$ $14.3$
$20$ $36.0$ $11.1$ $20.7$
$40$ $36.5$ $14.8$ $28.7$
$60$ $37.3$ $18.2$ $40.0$
$80$ $38.1$ $21.4$ $56.0$
$100$ $39.2$ $24.1$ $80.0$

Feb 23, 2012

Jan 07, 2015