Solubility of gases

Gases dissolve in liquids to different extents depending on the gas, the solvent, the temperature, and the pressure of gas sitting above the liquid surface. Henry's law captures the pressure dependence in one clean statement.

Henry's law. At a given temperature, the partial pressure $p$ of a gas above a dilute solution is directly proportional to the mole fraction $x$ of that gas dissolved in the solution:

where: $p$ is the partial pressure of the gas in the vapour phase above the liquid (usually in bar), $x$ is the mole fraction of the dissolved gas in the liquid phase (dimensionless), and $K_H$ is the Henry's law constant, which carries units of pressure and is specific to one gas dissolved in one solvent at one temperature.

Reading $K_H$. Because $K_H = p/x$, a larger $K_H$ means you need a larger pressure to force the same mole fraction into solution — so a large $K_H$ signals low solubility, not high. This inverse reading is the single most tested idea in the topic.

What changes gas solubility: Nature of the gas-solvent pair matters first: polar gases dissolve better in polar solvents ("like dissolves like"), so $K_H$ for one gas in water can be very different from $K_H$ for another gas in the same water. Temperature matters next, and in the opposite direction to solids: dissolving a gas in a liquid is generally exothermic, so by Le Chatelier's principle raising the temperature pushes the equilibrium back toward the gas phase and $K_H$ rises — solubility falls. This is why warm soda goes flat fast and why thermal pollution of a river lowers the dissolved oxygen fish depend on. Pressure matters through the law itself: raising the partial pressure of the gas above the liquid directly raises how much dissolves, in strict proportion. The figure below sketches the trend that follows from Henry's law and its temperature dependence: at fixed temperature, dissolved mole fraction rises in a straight line with pressure, and that line gets shallower (higher $K_H$, less solubility per unit pressure) as temperature increases.

Henry's law is a limiting law: it holds strictly only at low pressures and low dissolved concentrations, the same regime in which Raoult's law holds for the solvent. At high pressures, real gas-liquid systems deviate from the simple straight-line proportionality. The law also assumes the gas does not react chemically with the solvent. Gases like $NH_3$ or $HCl$, which ionise or react on dissolving in water, are not described by the plain form $p = K_H x$ without extra modification — Henry's law is a statement about physical dissolution equilibrium only.

Using $K_H(CO_2, 298\ \text{K}) = 3.33\times10^4\ \text{bar}$ found above, what partial pressure of $CO_2$ is needed to raise the dissolved mole fraction to $x = 3.6\times10^{-4}$ in the same water sample at 298 K, and how does this connect to bottling a soft drink?

Step 1. Identify what is known and what is asked. Temperature is fixed at $298\ \text{K}$, so the same $K_H = 3.33\times10^4\ \text{bar}$ found above applies. The target mole fraction is $x = 3.6\times10^{-4}$, three times the earlier value, and the unknown is the partial pressure $p$ needed to achieve it.

Step 2. Apply Henry's law directly, without rearranging, since $p$ is the unknown on the left-hand side already: $p = K_H\, x$.

Step 3. Substitute the numbers: $p = (3.33\times10^4\ \text{bar})\times(3.6\times10^{-4}) = 12.0\ \text{bar}$.

Step 4. Interpret the result physically. Tripling the target mole fraction required roughly tripling the pressure, exactly as the direct proportionality in Henry's law predicts. A partial pressure of about 12.0 bar of $CO_2$ is needed to dissolve it to $x = 3.6\times10^{-4}$ at 298 K — this is close to why soft-drink bottles are sealed under several bar of $CO_2$ pressure, well above atmospheric pressure, so that a useful amount of gas stays dissolved until the cap is opened and the pressure drops.

Everyday applications

Three situations use exactly this law. Soda water: bottled under high $CO_2$ pressure so solubility (and hence dissolved mole fraction) is high; opening the bottle drops $p$ to atmospheric, so $x$ at equilibrium falls and the excess gas escapes as fizz. Deep-sea diving: underwater pressure is high, so more $N_2$ from breathing air dissolves in a diver's blood than at the surface; ascending too quickly drops the pressure faster than the dissolved $N_2$ can safely leave through breathing, so it forms bubbles in the blood — decompression sickness, "the bends." Divers ascend slowly or breathe helium-diluted air to manage this. High altitude: lower atmospheric pressure means less $O_2$ dissolves in blood, which is why altitude sickness (anoxia) sets in at height.

• Writing Henry's law with molarity or molality instead of mole fraction — the ISC form is strictly $p = K_H x$ with $x$ as mole fraction.
• Assuming gas solubility rises with temperature the way most solid solubility does — for gases it is the reverse: higher temperature drives gas out of solution.
• Misreading $K_H$'s size: a larger $K_H$ means lower solubility, since $K_H = p/x$ and $x$ shrinks as $K_H$ grows for fixed $p$.
• Reusing one gas-solvent pair's $K_H$ for a different gas, a different solvent, or a different temperature — $K_H$ is valid only for the specific combination it was measured at, and only in the low-pressure, non-reacting regime.

Ask the tutor: Want to see how Henry's law's low-concentration limit connects to Raoult's law for the solvent in the same dilute solution? Ask the AI tutor for a side-by-side comparison.