## Solid Solubility and Temperature

Solubility often depends on temperature; the solubility of many substances increases with increasing temperature.

### Learning Objectives

Recall the relationship between solubility and temperature

### Key Takeaways

#### Key Points

• For many solids dissolved in liquid water, the solubility increases with temperature.
• The increase in kinetic energy that comes with higher temperatures allows the solvent molecules to more effectively break apart the solute molecules that are held together by intermolecular attractions.
• The increased vibration (kinetic energy) of the solute molecules causes them to dissolve more readily because they are less able to hold together.

#### Key Terms

• solubility: The amount of a substance that will dissolve in a given amount of a solvent to give a saturated solution under specified conditions.
• kinetic energy: The energy possessed by an object because of its motion, equal to one half the mass of the body times the square of its velocity.

### Solid Solubility and Temperature

The solubility of a given solute in a given solvent typically depends on temperature. Many salts show a large increase in solubility with temperature. Some solutes exhibit solubility that is fairly independent of temperature. A few, such as cerium(III) sulfate, become less soluble in water as temperature increases. This temperature dependence is sometimes referred to as retrograde or inverse solubility, and exists when a salt’s dissolution is exothermic; this can be explained because, according to Le Chatelier’s principle, extra heat will cause the equilibrium for an exothermic process to shift towards the reactants.

Solubility Versus Temperature: This chart shows the solubility of various substances in water at a variety of temperatures (in degrees Celsius). Notice how NaCl’s solubility is relatively constant regardless of temperature, whereas Na2SO4’s solubility increases exponentially over 0–35 degrees Celsius and then abruptly begins to decrease.

### Theoretical Perspective

As the temperature of a solution is increased, the average kinetic energy of the molecules that make up the solution also increases. This increase in kinetic energy allows the solvent molecules to more effectively break apart the solute molecules that are held together by intermolecular attractions.

The average kinetic energy of the solute molecules also increases with temperature, and it destabilizes the solid state. The increased vibration (kinetic energy) of the solute molecules causes them to be less able to hold together, and thus they dissolve more readily.

### Application in Recrystallization

A useful application of solubility is recrystallizaton. During recrystallization, an impure substance is taken up in a volume of solvent at a temperature at which it is insoluble, which is then heated until it becomes soluble. The impurities dissolve as well, but when the solution is cooled, it is often possible to selectively crystallize, or precipitate, the desired substance in a purer form.

## Gas Solubility and Temperature

Solubility of a gas in water tends to decrease with increasing temperature, and solubility of a gas in an organic solvent tends to increase with increasing temperature.

### Learning Objectives

Recall the relationship between gas solubility and temperature

### Key Takeaways

#### Key Points

• Gases dissolved in water become less soluble with increasing temperature.
• Gases dissolved in organic solvents become more soluble with increasing temperature.
• Dissolved oxygen in water is important to the survival of fish, so increasing temperature (and therefore less dissolved oxygen in water) can cause problems for fish.

#### Key Terms

• solubility: The amount of a substance that will dissolve in a given amount of a solvent to give a saturated solution under specified conditions.

Several factors affect the solubility of gases: one of these factors is temperature. In general, solubility of a gas in water will decrease with increasing temperature: colder water will be able to have more gas dissolved in it.

Solubilities of Gases in Water: Methane, oxygen, carbon monoxide, nitrogen, and helium all have different solubilities in water, but all of them become less soluble with increasing temperature.

### Consequences of Gas Solubility Temperature Dependence

When the temperature of a river, lake, or stream is raised abnormally high, usually due to the discharge of hot water from some industrial process, the solubility of oxygen in the water is decreased.

Because fish and other organisms that live in natural bodies of water can be sensitive to the concentration of oxygen in water, decreased levels of dissolved oxygen may have serious consequences for the health of the water’s ecosystems. In severe cases, temperature changes can result in large-scale fish kills.

### Gas Solubility In Organic Solvents

The trend that gas solubility decreases with increasing temperature does not hold in all cases. While it is in general true for gases dissolved in water, gases dissolved in organic solvents tend to become more soluble with increasing temperature.

There are several molecular reasons for the change in solubility of gases with increasing temperature, which is why there is no one trend independent of gas and solvent for whether gases will become more or less soluble with increasing temperature.

## Solubility and Pressure

Increasing pressure will increase the solubility of a gas in a solvent.

### Learning Objectives

Recognize the relationship between pressure and the solubility of a gas

### Key Takeaways

#### Key Points

• For condensed phases ( solids and liquids ), the pressure dependence of solubility is typically weak and is usually neglected in practice.
• William Henry, an English chemist, showed that the solubility of a gas increased with increasing pressure.
• The increase in solubility based on pressure will depend on which gas is being dissolved and must be determined experimentally for each gas.

#### Key Terms

• solubility: The amount of a substance that will dissolve in a given amount of a solvent to give a saturated solution under specified conditions.
• equilibrium: The state of a reaction in which the rates of the forward and reverse reactions are the same.
• 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.

### The Effect of Pressure on Solubility

For solids and liquids, known as condensed phases, the pressure dependence of solubility is typically weak and is usually neglected in practice. However, the solubility of gases shows significant variability based on pressure. Typically, a gas will increase in solubility with an increase in pressure. This effect can be mathematically described using an equation called Henry’s law.

### Henry’s Law

When a gas is dissolved in a liquid, pressure has an important effect on the solubility. William Henry, an English chemist, showed that the solubility of a gas increased with increasing pressure. He discovered the following relationship:

$\text{C}= \text{k}*\text{P}_{\text{gas}}$

In this equation, C is the concentration of the gas in solution, which is a measure of its solubility, k is a proportionality constant that has been experimentally determined, and Pgas is the partial pressure of the gas above the solution. The proportionality constant needs to be experimentally determined because the increase in solubility will depend on which kind of gas is being dissolved.

William Henry: The discoverer of Henry’s law, which states that the solubility of a gas in a solvent is directly proportional to the pressure of the gas.

There are some things to remember when working with this law:

• Henry’s law only works if the molecules are at equilibrium and if the same molecules are present throughout the solution.
• Henry’s law does not apply to gases at extremely high pressures.
• Henry’s law does not apply if there is a chemical reaction between the solute and the solvent. For example, HCl (g) reacts with water in the dissociation reaction and affects solubility, so Henry’s law cannot be used in this instance.
• If Henry’s law is used to denote how the concentration will change with pressure, the following equation is used: $\frac{\text{P}_1}{\text{C}_1} =\frac{\text{P}_2}{\text{C}_2}$

### Example

If 2.5 atm of pressure is applied to a carbonated beverage, what is the concentration of the dissolved CO2, given k = 29.76 $\frac{\text{atm}}{\text{M}}$ for CO2?

$\text{P} = \text{k} \times \text{C}$

$2.5 \text{atm} = 29.76 \frac{\text{atm}}{\text{M}} \times \text{C}$

Solving for C, we find that the concentration of the dissolved CO2 is 0.088 M.

### Applications of Gas Solubility

In order for deep-sea divers to breathe underwater, they must inhale highly compressed air in deep water, resulting in more nitrogen dissolving in their blood, tissues, and joints. If a diver returns to the surface too rapidly, the nitrogen gas diffuses out of the blood too quickly, causing pain and possibly death. This condition is known as “the bends.”

To prevent the bends, a diver must return to the surface slowly, so that the gases will adjust to the partial decrease in pressure and diffuse more slowly. A diver can also breathe a mixture of compressed helium and oxygen gas, since helium is only one-fifth as soluble in blood as nitrogen.

Underwater, our bodies are similar to a soda bottle under pressure. Imagine dropping the bottle and trying to open it. In order to prevent the soda from fizzing out, you open the cap slowly to let the pressure decrease. On land, we breathe about 78 percent nitrogen and 21 percent oxygen, but our bodies use mostly the oxygen. When we’re underwater, however, the high pressure of water surrounding our bodies causes nitrogen to build up in our blood and tissues. Like in the case of the bottle of soda, if we move around or come up from the water too quickly, the nitrogen will be released from our bodies too quickly, creating bubbles in our blood and causing “the bends.”

Scuba diver: Solubility and pressure are very relevant to scuba divers, who are susceptible to “the bends.” As divers swim deeper, the pressure increases the amount of nitrogen dissolved in their blood. Unless they ascend slowly, the nitrogen can diffuse out of their blood too quickly, causing pain and even death.