Henry’s Law and Gas Solubility

Henry’s law states that at a constant temperature the amount of a gas that dissolves in a liquid is directly proportional to the partial pressure of that gas above the liquid: C = kH × P. In brief: doubling the pressure of carbon dioxide above a drink doubles the dissolved CO2, and at 25 °C with 4.0 atm of CO2 a soda holds about 0.14 mol/L.

Henry’s law explains why a bottle of soda fizzes when it is opened, why divers can suffer decompression sickness and how oxygen enters water for fish. It is one of the simplest laws of solution chemistry. This article states the law, gives values of the Henry’s law constant, solves examples and explains how temperature affects gas solubility.

What does Henry’s law say?

The concentration of a dissolved gas is proportional to its partial pressure in the gas phase:

C = kH × P, or C1/P1 = C2/P2

Here C is the concentration of the dissolved gas (mol/L), P is its partial pressure in atm and kH is the Henry’s law constant, which depends on the gas, the solvent and the temperature. In terms of particles, a higher pressure means more gas molecules striking the surface of the liquid per second, so more of them enter the liquid until the rate of leaving matches the rate of entering again.

The law applies to each gas in a mixture separately, so the partial pressure of each gas and not the total pressure determines how much of it dissolves.

Henry’s law constants for common gases

Approximate Henry’s law constants in water at 25 °C
Gas kH (mol/(L·atm))
Helium3.7 × 10−4
Nitrogen6.1 × 10−4
Hydrogen7.8 × 10−4
Oxygen1.3 × 10−3
Carbon dioxide3.4 × 10−2

Carbon dioxide is about 26 times more soluble than oxygen, in part because it interacts more strongly with water and partly reacts with it to form carbonic acid. Gases that react with water in this way, such as ammonia and hydrogen chloride, dissolve so well that Henry’s law no longer describes them accurately.

How do you use Henry’s law?

Example 1: oxygen in water

Air contains 21 % oxygen. Find the concentration of oxygen in water at 25 °C in equilibrium with air at 1.00 atm.

  1. P(O2) = 0.21 × 1.00 atm = 0.21 atm.
  2. C = 1.3 × 10−3 × 0.21 = 2.7 × 10−4 mol/L.
  3. In mass units: 2.7 × 10−4 mol/L × 32.0 g/mol = 8.7 × 10−3 g/L, or about 8.7 mg/L.
P(O2) = 0.21 × 1.00 atm = 0.21 atm C = 1.3 × 10−3 × 0.21 = 2.7 × 10−4 mol/L 2.7 × 10−4 mol/L × 32.0 g/mol = 8.7 × 10−3 g/L

This value is close to the 8 mg/L or so of dissolved oxygen found in natural waters at this temperature.

Example 2: a bottle of soda

A soft drink is bottled under 4.0 atm of CO2 at 25 °C. What is the concentration of dissolved CO2, and what is the concentration after opening, when the partial pressure of CO2 in air is 4.0 × 10−4 atm?

  1. In the sealed bottle: C = 3.4 × 10−2 × 4.0 = 0.14 mol/L.
  2. In the open bottle at equilibrium: C = 3.4 × 10−2 × 4.0 × 10−4 = 1.4 × 10−5 mol/L.
C = 3.4 × 10−2 × 4.0 = 0.14 mol/L C = 3.4 × 10−2 × 4.0 × 10−4 = 1.4 × 10−5 mol/L

The drink is therefore far from equilibrium after it is opened, so the excess CO2 escapes as bubbles. The process is slow enough for you to drink the soda, which then goes flat over hours.

Example 3: using two data points

A gas dissolves to 0.025 mol/L at 1.5 atm. What is the solubility at 4.5 atm at the same temperature? The pressure is tripled, so C = 0.025 × 3 = 0.075 mol/L.

0.025 / 1.5 = C / 4.5 C = 0.025 × 3 = 0.075 mol/L
Dissolved gas concentration against pressure, straight lines through the origin 0 1 2 3 4 5 0 0.05 0.10 0.15 Pressure of CO2 (atm) Dissolved gas (mol/L) 0.14 mol/L at 4.0 atm CO2 O2 (dashed)
Henry’s law at 25 °C, C = kHP, using the constants in the table. Both lines are straight, so doubling the pressure doubles the dissolved gas. The CO2 line (kH = 3.4 × 10−2 mol/(L·atm)) is far steeper than the O2 line (dashed, 1.3 × 10−3). At 4.0 atm of CO2, 0.14 mol/L dissolves.

How does temperature affect gas solubility?

The solubility of most gases in water decreases as the temperature rises. Dissolving a gas is generally exothermic, and the equilibrium shifts towards the gas phase on heating. Hence the constant kH is only valid for the temperature at which it was measured. For oxygen, the solubility in water at 1 atm of O2 falls from about 2.2 mmol/L at 0 °C to about 1.3 mmol/L at 25 °C. Thermal pollution, such as warm water from power stations, can lower the oxygen level of rivers enough to harm fish.

Why does Henry’s law matter to divers?

At a depth of 30 m, the absolute pressure is about 4 atm. The partial pressure of nitrogen in air at that depth is 0.78 × 4 = 3.1 atm, so the concentration of nitrogen dissolved in the blood and tissues is four times higher than at the surface: roughly 1.9 × 10−3 mol/L in water, against 4.8 × 10−4 mol/L at the surface. If a diver ascends too fast, the nitrogen leaves the solution as bubbles in the same way as CO2 escapes from a soda. This causes decompression sickness, known as “the bends”. For this reason, divers ascend slowly and make stops, and deep divers use mixtures with helium instead of nitrogen.

P(N2) = 0.78 × 4 = 3.1 atm

Who was William Henry?

William Henry (1774–1836) was an English chemist from Manchester who published his findings on the absorption of gases by water in 1803. His work was a part of the early study of gases by chemists such as Dalton, who was a friend and colleague of his and who used Henry’s results in his own studies. Henry’s physician background also led him to work on the medical uses of gases.

When does Henry’s law not work?

The law is accurate for dilute solutions and for gases that do not react with the solvent. It fails at very high pressures, where gas behavior is not ideal, and for gases that react with water or ionize in it. In such cases the total dissolved amount includes the reacted forms, for example HCO3− and CO32− in the case of CO2.

Which mistakes are common?