## Solubility and Pressure

#### Learning Objective

• Recognize the relationship between pressure and the solubility of a gas

#### 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.

#### Terms

• solubilityThe amount of a substance that will dissolve in a given amount of a solvent to give a saturated solution under specified conditions.
• equilibriumThe state of a reaction in which the rates of the forward and reverse reactions are the same.
• Henry’s lawStates 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:

$C= k*P_{gas}$

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.

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: $\frac{P_1}{C_1} =\frac{P_2}{C_2}$

## 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 $\frac{atm}{M}$ for CO2?

$P = k \times C$

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

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.”