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# 16.1: Solubility

Difficulty Level: At Grade Created by: CK-12

## Lesson Objectives

• List examples of solutions made from different solute-solvent combinations.
• List and explain three factors that affect the rate of dissolving of a solid solute in a liquid solvent.
• Explain solution equilibrium and distinguish between saturated, unsaturated, and supersaturated solutions.
• Explain the effects of temperature on the solubility of solids and gases. Use a solubility curve to determine the solubilities of substances at various temperatures.
• Use Henry’s law and explain the effect of pressure on the solubility of gases.

## Lesson Vocabulary

• Henry’s law
• recrystallization
• saturated solution
• solubility
• solution equilibrium
• supersaturated solution
• unsaturated solution

### Recalling Prior Knowledge

• What is a solvent and what is a solute?
• How does a liquid solvent dissolve a solid solute?

Solutions are of great importance in chemical reactions. In this lesson, you will learn about the factors which affect the solubility of substances and the rate of dissolving.

## Solution Components

The focus in the chapter Water was on water and its role in the formation of aqueous solutions. We examined the primary characteristics of a solution, how water is able to dissolve solid solutes, and we differentiated between a solution, a suspension, and a colloid. There are many examples of solutions that do not involve water at all, or that involve solutes that are not solids. Table below summarizes the possible combinations of solute-solvent states, along with examples of each.

Solute-Solvent Combinations
Solute State Solvent State Example
liquid gas water in air
gas gas oxygen in nitrogen (gas mixture)
solid liquid salt in water
liquid liquid alcohol in water
gas liquid carbon dioxide in water
solid solid zinc in copper (brass alloy)
liquid solid mercury in silver and tin (dental amalgam)

Our air is a homogeneous mixture of many different gases and therefore qualifies as a solution. Solid-solid solutions such as brass, bronze, and sterling silver are called alloys. Fish depend on oxygen gas that is dissolved in the water found in oceans, lakes, and rivers (Figure below). While solid-liquid and aqueous solutions comprise the majority of solutions encountered in the chemistry laboratory, it is important to be aware of the other possibilities.

Large aquariums like this salt-water tank have air continually bubbled into the water so that the fish have enough dissolved oxygen to breathe.

## Rate of Dissolving

We know that the dissolving of a solid by water depends upon the collisions that occur between the solvent molecules and the particles in the solid crystal. Anything that can be done to increase the frequency of those collisions and/or to give those collisions more energy will increase the rate of dissolving. Imagine that you were trying to dissolve some sugar in a glassful of tea. A packet of granulated sugar would dissolve faster than a cube of sugar. The rate of dissolving would be increased by stirring, or agitating the solution. Finally, the sugar would dissolve faster in hot tea than it would in cold tea.

### Surface Area

The rate at which a solute dissolves depends upon the size of the solute particles. Dissolving is a surface phenomenon, since it depends on solvent molecules colliding with the outer surface of the solute. A given quantity of solute dissolves faster when it is ground into small particles than if it is in the form of a large chunk, because more surface is exposed. The packet of granulated sugar exposes far more surface area to the solvent and dissolves more quickly than the sugar cube.

### Agitation of the Solution

Dissolving sugar in water will occur more quickly if the water is stirred. The stirring allows fresh solvent molecules to continually be in contact with the solute. If it is not stirred, then the water right at the surface of the solute becomes saturated with dissolved sugar molecules, meaning that is more difficult for additional solute to dissolve. The sugar cube would eventually dissolve because random motions of the water molecules would bring enough fresh solvent into contact with the sugar, but the process would take much longer. It is important to realize that neither stirring nor breaking up a solute affect the overall amount of solute that dissolves. It only affects the rate of dissolving.

### Temperature

Heating up the solvent gives the molecules more kinetic energy. The more rapid motion means that the solvent molecules collide with the solute with greater frequency and the collisions occur with more force. Both factors increase the rate at which the solute dissolves. As we will see in the next section, a temperature change not only affects the rate of dissolving, but it also affects the amount of solute that can be dissolved.

## Types of Solutions

Table salt (NaCl) readily dissolves in water. Suppose that you have a beaker of water to which you add some salt, stirring until it dissolves. Then you add more, and that dissolves as well. If you keep adding more and more salt, eventually you will reach a point at which no more of the salt will dissolve, no matter how long or how vigorously you stir it. Why? On the molecular level, we know that action of the water causes the individual ions to break apart from the salt crystal and enter the solution, where they remain hydrated by water molecules. What also happens is that some of the dissolved ions collide back again with the crystal and remain there. Recrystallization is the process of dissolved solute returning to the solid state. At some point, the rate at which the solid salt is dissolving becomes equal to the rate at which the dissolved solute is recrystallizing. When that point is reached, the total amount of dissolved salt remains unchanged. Solution equilibrium is the physical state described by the opposing processes of dissolution and recrystallization occurring at the same rate. The solution equilibrium for the dissolving of sodium chloride can be represented by one of two equations.

\begin{align*}\text{NaCl}{(s)} \rightleftharpoons \text{NaCl}{(aq)}\end{align*}

While this shows the change of state back and forth between solid and aqueous solution, the preferred equation also shows the dissociation that occurs as an ionic solid dissolves.

\begin{align*}\text{NaCl}{(s)} \rightleftharpoons \text{Na}^+{(aq)}+\text{Cl}^-{(aq)}\end{align*}

When the solution equilibrium point is reached and no more solute will dissolve, the solution is said to be saturated. A saturated solution is a solution that contains the maximum amount of solute that is capable of being dissolved. At 20°C, the maximum amount of NaCl that will dissolve in 100. g of water is 36.0 g. If any more NaCl is added past that point, it will not dissolve, because the solution is saturated. What if more water is added to the solution instead? Now, more NaCl would be capable of dissolving, since there is additional solvent present. An unsaturated solution is a solution that contains less than the maximum amount of solute that is capable of being dissolved. Figure below illustrates the above process and shows the distinction between unsaturated and saturated.

When 30.0 g of NaCl is added to 100 mL of water at 20°C, it all dissolves, forming an unsaturated solution. When 40.0 g is added, 36.0 g dissolves and 4.0 g remains undissolved, forming a saturated solution.

How can you tell if a solution is saturated or unsaturated? If more solute is added and it does not dissolve, then the original solution was saturated. If the added solute dissolves, then the original solution was unsaturated. A solution that has been allowed to reach equilibrium but still has extra undissolved solute at the bottom of the container must be saturated (Figure below).

A saturated solution of salt (sodium chloride) with undissolved solute remaining at the bottom of the measuring cup.

### Solubility Values

The solubility of a substance is the amount of that substance that is required to form a saturated solution in a given amount of solvent at a specified temperature. Solubility is often measured as grams of solute per 100 g of solvent. The solubility of sodium chloride in water is 36.0 g per 100 g water at 20°C. The temperature must be specified because solubility varies with temperature. For gases, the pressure must also be specified. Solubility is specific for a particular solvent. In other words, the solubility of sodium chloride would be different in another solvent. For the purposes of this text, the solubility of a substance will refer to aqueous solubility unless otherwise specified. Solubilities for different solutes have a very wide variation, as can be seen by the data presented in Table below.

Solubility of Solutes at Different Temperatures (in g/100 g H
Substance 0°C 20°C 40°C 60°C 80°C 100°C
AgNO3 122 216 311 440 585 733
Ba(OH)2 1.67 3.89 8.22 20.94 101.4
C12H22O11 179 204 238 287 362 487
Ca(OH)2 0.189 0.173 0.141 0.121 0.07
KCl 28.0 34.2 40.1 45.8 51.3 56.3
KI 128 144 162 176 192 206
KNO3 13.9 31.6 61.3 106 167 245
LiCl 69.2 83.5 89.8 98.4 112 128
NaCl 35.7 35.9 36.4 37.1 38.0 39.2
NaNO3 73 87.6 102 122 148 180
CO2 (1 atm) 0.335 0.169 0.0973 0.058
O2 (1 atm) 0.00694 0.00537 0.00308 0.00227 0.00138 0.00

## Factors Affecting Solubility

The solubility of a solid or liquid solute in a solvent is affected by the temperature, while the solubility of a gaseous solute is also affected by both the temperature and the pressure of the gas. We will examine the effects of temperature and pressure separately.

### Temperature

The solubility of the majority of solid substances increases as the temperature increases. However, the effect is difficult to predict and varies widely from one solute to another. The temperature dependence of solubility can be visualized with the help of a solubility curve, which is a graph of the solubility vs. temperature. Examine the solubility curves shown in Figure below.

A solubility curve is a graph of the solubility of a substance as a function of temperature.

Notice how the temperature dependence of NaCl is fairly flat, meaning that an increase in temperature has relatively little effect on the solubility of NaCl. The curve for KNO3, on the other hand, is very steep; an increase in temperature dramatically increases the solubility of KNO3.

Several substances listed on the graph – HCl, NH3, and SO2 – have solubilities that decrease as the temperature increases. These substances are all gases over the indicated temperature range when at standard pressure. When a solvent with a gas dissolved in it is heated, the kinetic energy of both the solvent and solute increases. As the kinetic energy of the gaseous solute increases, its molecules have a greater tendency to escape the attraction of the solvent molecules and return back to the gas phase. As a result, the solubility of a gas decreases as the temperature increases. This has some profound environmental consequences. Industrial plants situated near bodies of water often use that water as a coolant, returning the warmer water back to the lake or river. This increases the overall temperature of the water, which lowers the quantity of dissolved oxygen, affecting the survival of fish and other organisms.

Solubility curves can be used to determine if a given solution is saturated or unsaturated. Suppose that 80 g of KNO3 is added to 100 g of water at 30°C. According to the solubility curve, approximately 48 g of KNO3 will dissolve at 30°C. This means that the solution will be saturated, since 48 g is less than 80 g. We can also determine that there will be 80 – 48 = 32 g of undissolved KNO3 remaining at the bottom of the container. Now, suppose that this saturated solution is heated to 60°C. According to the curve, the solubility of KNO3 at 60°C is about 107 g. The solution is now unsaturated, since it still contains only the original 80 g of solute, all of which is now dissolved. Then, suppose the solution is cooled all the way down to 0°C. The solubility at 0°C is about 14 g, meaning that 80 – 14 = 66 g of the KNO3 will recrystallize.

Some solutes, such as sodium acetate, do not recrystallize easily. Suppose an exactly saturated solution of sodium acetate is prepared at 50°C. As it cools back to room temperature, crystals do not immediately appear in the solution, even though the solubility of sodium acetate is lower at room temperature. A supersaturated solution is a solution that contains more than the maximum amount of solute that is capable of being dissolved at a given temperature. The recrystallization of the excess dissolved solute in a supersaturated solution can be initiated by the addition of a tiny crystal of solute, called a seed crystal. The seed crystal provides a nucleation site on which the excess dissolved crystals can begin to grow. Recrystallization from a supersaturated solution is typically very fast.

This video shows the rapid recrystallization that occurs after a sodium acetate seed crystal is added to a supersaturated solution http://www.youtube.com/watch?v=0wifFbGDv4I (1:07).

### Pressure

Pressure has very little effect on the solubility of solids or liquids, but it has a significant effect on the solubility of gases. Gas solubility increases as the partial pressure of a gas above the liquid increases. Suppose a certain volume of water is in a closed container with the space above it occupied by carbon dioxide gas at standard pressure. Some of the CO2 molecules come into contact with the surface of the water and dissolve into the liquid. Now suppose that more CO2 is added to the space above the container, causing a pressure increase. More CO2 molecules are now in contact with the water, so more of them dissolve. Thus the solubility increases as the pressure increases. As with a solid, the CO2 that is undissolved reaches an equilibrium with the dissolved CO2, represented by the following equation.

\begin{align*}\text{CO}_{2}{(g)} \rightleftharpoons \text{CO}_{2}{(aq)}\end{align*}

At equilibrium, the rate of gaseous CO2 dissolving is equal to the rate of dissolved CO2 coming out of the solution.

When carbonated beverages are packaged, they are done so under high CO2 pressure so that a large amount of carbon dioxide dissolves in the liquid. When the bottle is open, the equilibrium is disrupted because the CO2 pressure above the liquid decreases. Immediately, bubbles of CO2 rapidly exit the solution and escape out of the top of the open bottle. The amount of dissolved CO2 decreases. If the bottle is left open for an extended period of time, the beverage becomes “flat” as more and more CO2 comes out of the liquid.

The relationship of gas solubility to pressure is described by Henry’s Law, named after English chemist William Henry (1774-1836). Henry’s Law states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. Henry’s Law can be written as follows:

\begin{align*}\mathrm{\dfrac{S_1}{P_1}=\dfrac{S_2}{P_2}}\end{align*}

S1 and P1 are the solubility and partial pressure of a certain gas at an initial set of conditions; S2 and P2 are the solubility and partial pressure of the same gas under a different set of conditions. Solubilities of gases are typically reported in g/L, as seen in Sample Problem 16.1.

Sample Problem 16.1: Henry's Law

The solubility of a certain gas in water is 0.745 g/L at standard pressure. What is its solubility when the pressure of the gas present above the solution is raised to 4.50 atm? The temperature is constant at 20°C.

Step 1: List the known quantities and plan the problem.

Known

• S1 = 0.745 g/L
• P1 = 1.00 atm
• P2 = 4.50 atm

Unknown

• S2 = ? g/L

Substitute into Henry’s law and solve for S2.

Step 2: Solve.

\begin{align*}\mathrm{S_2=\dfrac{S_1 \times P_2}{P_1}=\dfrac{0.745 \ g/L \times 4.50 \ atm}{1.00 \ atm}=3.35 \ g/L}\end{align*}

The solubility is increased to 4.5 times its original value, which makes sense for a direct relationship.

Practice Problem
1. The solubility of a gas is 1.67 g/L at a pressure of 1230 mmHg. At what pressure will the solubility be 1.12 g/L?

## Lesson Summary

• Solutions can consist of solutes and solvents that are solids, liquids, or gases.
• The rate at which a solid solute dissolves in a liquid solvent increases when the surface area of the solute is increased, the mixture is agitated, or the temperature is raised.
• The maximum amount of solute capable of dissolving in a solvent is called its solubility. Solutions can be unsaturated, saturated, or supersaturated, depending on the amount of solute dissolved relative to its solubility at the given temperature.
• Solubility is dependent on temperature. For solids, solubility generally increases with an increase in temperature. For gases, solubility decreases with an increase in temperature.
• Henry’s Law describes the direct relationship between the solubility of a gas in a liquid and the pressure of the gas.

## Lesson Review Questions

### Reviewing Concepts

1. What determines how fast a substance will dissolve in a given solvent?
2. What is the requirement for reaching solution equilibrium?
3. What are two things that you could do to change an unsaturated solid/liquid solution into a saturated solution?
4. A given solution is clear and colorless. A single crystal of solute is added to the solution. Describe what happens in each of the following situations.
1. The original solution was saturated.
2. The original solution was unsaturated.
3. The original solution was supersaturated.
5. Explain how a supersaturated solution must be prepared.
6. Under which set of conditions is the solubility of a gas in a liquid the greatest?
1. low temperature and low pressure
2. low temperature and high pressure
3. high temperature and low pressure
4. high temperature and high pressure

### Problems

1. List the original states (solid, liquid, or gas) of the solute and solvent that are combined to make each of the following solutions.
1. an alloy
2. salt water
3. carbonated water
4. oil in gasoline

Use the solubility curve from the text (Figure above) to answer questions 8-10.

1. How many grams of NH4Cl are required to make a saturated solution in 100 g of water at 70°C?
2. How many grams of NH4Cl could be dissolved in 200 g of water at 70°C?
3. At what temperature is a solution of 50 grams of KNO3 dissolved in 100 grams of water a saturated solution?
4. Which 2 substances in the above graph have the same solubility at 85°C?
5. How many grams of NaNO3 can be dissolved in 100 grams of water to make a saturated solution at 25°C?
6. How much KI can be dissolved in 5 grams of water at 20°C to make a saturated solution?
2. An exactly saturated solution of KClO3 is prepared at 90°C using 100 grams of water. If the solution is cooled to 20°C, how many grams of KClO3 will recrystallize?
3. Indicate whether the following solutions are unsaturated, saturated, or supersaturated. Assume that all three could potentially form a supersaturated solution.
1. 22 grams of KClO3 is dissolved in 100 g of water at 50°C.
2. 60 grams of KNO3 is dissolved in 100 g of water at 50°C.
3. 50 grams of NaCl is dissolved in 100 g of water at 50°C.
4. The solubility of a gas in water is 3.28 g/L at 304 kPa. What is its solubility at standard pressure?

## Points to Consider

Solutions are prepared by dissolving a certain amount of solute in a certain amount of solvent. The concentration of a solution is a quantitative measure of how much solute has been dissolved.

• What are the ways in which the concentration of a solution can be calculated?
• What happens to the concentration of a solution when additional solvent is added?

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