Henry’s Law and the Solubility of Gases in Liquids

Every breath you take depends on a simple fact: oxygen from the air dissolves in water. Without this, fish could not survive, and neither could any other aquatic organism. Yet oxygen dissolves only in small amounts, while a gas like hydrogen chloride ($HCl$) is enormously soluble in water. What controls how much of a gas goes into a liquid, and can we predict it? The answer lies in pressure, temperature, and a neat quantitative relationship discovered by William Henry.

How Pressure Controls Gas Solubility

Picture a sealed container. The bottom half holds a liquid with some gas already dissolved in it, and the upper half holds more of the same gas at a certain pressure $p$ and temperature $T$. At this point, the system is in dynamic equilibrium (the state where gas molecules enter and leave the liquid at exactly the same rate, so the amount of dissolved gas stays constant).

Now imagine you push a piston down onto the gas, compressing it into a smaller space. What changes?

• The number of gas molecules per unit volume above the liquid shoots up because the same amount of gas now occupies less room.
• More molecules hit the liquid surface every second, so more of them get captured into the solution.
• The dissolved gas concentration rises until a new equilibrium is set up at this higher pressure.

The result: higher pressure above the liquid means more gas dissolved in it.

Fig 1.1: Effect of pressure on the solubility of a gas. (a) At lower pressure, fewer gas molecules are dissolved. (b) At higher pressure, the gas is compressed and more molecules dissolve into the liquid.

Henry’s Law: The Quantitative Rule

William Henry was the first to put this pressure-solubility relationship into a precise mathematical form. His law, known as Henry’s law, states:

At constant temperature, the partial pressure of a gas in the vapour phase above a solution is directly proportional to the mole fraction of that gas dissolved in the solution.

If $x$ stands for the mole fraction (the fraction of total moles in the solution that belong to the dissolved gas) and $p$ is the partial pressure (the pressure contributed by that particular gas in a mixture of gases above the liquid), then Henry’s law is written as:

$p = K_\text{H} \, x \qquad \text{(1.11)}$

Here, $K_\text{H}$ is the Henry’s law constant (a proportionality factor whose value depends on which gas you are looking at and the temperature of the system). Its units are the same as pressure (bar, kbar, atm, or Pa).

John Dalton, working around the same time as Henry, arrived at the same conclusion independently: the amount of gas that dissolves in a liquid depends on the partial pressure of that gas above the solution.

What the Graph Looks Like

If you plot the partial pressure of a gas ($p$) on the y-axis against its mole fraction in the solution ($x$) on the x-axis, Henry’s law predicts a straight line passing through the origin. The slope of this line is the Henry’s law constant $K_\text{H}$.

Fig 1.2: Experimental results for the solubility of HCl gas in cyclohexane at 293 K. The straight-line plot confirms Henry’s law; the slope gives $K_\text{H}$.

The Henry’s Law Constant and What It Tells You

Different gases have very different $K_\text{H}$ values at the same temperature. The table below lists some representative values in water:

Table 1.2: Henry’s Law Constants for Selected Gases in Water

Gas	Temperature (K)	$K_\text{H}$ (kbar)
$He$	293	144.97
$H_2$	293	69.16
$N_2$	293	76.48
$N_2$	303	88.84
$O_2$	293	34.86
$O_2$	303	46.82
$Ar$	298	40.3
$CO_2$	298	1.67
Formaldehyde	298	$1.83 \times 10^{-5}$
$CH_4$	298	0.413
Vinyl chloride	298	0.611

Reading the table: higher $K_\text{H}$ means lower solubility

From Equation (1.11), rearranging gives:

$x = \frac{p}{K_\text{H}}$

At any given pressure $p$, a larger $K_\text{H}$ produces a smaller mole fraction $x$. In plain terms: a gas with a big Henry’s law constant is hard to dissolve. Helium ($K_\text{H}$ = 144.97 kbar) is far less soluble in water than carbon dioxide ($K_\text{H}$ = 1.67 kbar) under the same conditions.

$K_\text{H}$ depends on both the gas and the temperature

Notice that $N_2$ and $O_2$ each have two entries at different temperatures. For both gases, $K_\text{H}$ increases as temperature goes from 293 K to 303 K. Since a higher $K_\text{H}$ means lower solubility, this confirms that gas solubility drops when the temperature rises. The temperature effect is explored in more detail later in this topic.

Solved Example 1.4: How Much $N_2$ Dissolves in Water?

Problem: $N_2$ gas is bubbled through water at 293 K. The nitrogen exerts a partial pressure of 0.987 bar. Given that $K_\text{H}$ for $N_2$ at 293 K is 76.48 kbar, calculate the number of millimoles of $N_2$ that dissolve in 1 litre of water.

Solution:

Step 1: Find the mole fraction of dissolved $N_2$ using Henry’s law.

Rearrange $p = K_\text{H} \, x$ to isolate $x$:

$x(N_2) = \frac{p(N_2)}{K_\text{H}}$

Substitute the values (make sure both pressures are in the same unit; 76.48 kbar = 76,480 bar):

$x(N_2) = \frac{0.987 \text{ bar}}{76{,}480 \text{ bar}} = 1.29 \times 10^{-5}$

Step 2: Relate mole fraction to moles of $N_2$.

The mole fraction of $N_2$ in the solution is defined as:

$x(N_2) = \frac{n}{n + n_\text{water}}$

where $n$ is the number of moles of dissolved $N_2$, and $n_\text{water}$ is the number of moles of water.

One litre of water has a mass of approximately 1000 g. Since the molar mass of water is 18 g/mol:

$n_\text{water} = \frac{1000}{18} \approx 55.5 \text{ mol}$

Step 3: Simplify using the dilute solution approximation.

Since $n$ is going to be extremely small compared to 55.5 mol (we can see this because $x$ is of the order $10^{-5}$), we can safely approximate:

$x(N_2) \approx \frac{n}{55.5}$

Step 4: Solve for $n$.

$1.29 \times 10^{-5} = \frac{n}{55.5}$

$n = 1.29 \times 10^{-5} \times 55.5 = 7.16 \times 10^{-4} \text{ mol}$

Step 5: Convert to millimoles.

$n = 7.16 \times 10^{-4} \text{ mol} \times \frac{1000 \text{ mmol}}{1 \text{ mol}} = 0.716 \text{ mmol}$

So about 0.716 millimoles of $N_2$ dissolve per litre of water under these conditions. This tiny amount reflects the very high $K_\text{H}$ value (and therefore low solubility) of nitrogen.

Real-World Applications of Henry’s Law

Henry’s law is not just a textbook equation. It explains several everyday and life-critical phenomena.

Fizzy Drinks Stay Fizzy Under Pressure

Soft drinks and soda water get their fizz from dissolved $CO_2$. Manufacturers seal the bottle under high $CO_2$ pressure so that a large quantity of the gas stays dissolved (Henry’s law: higher pressure, more gas in solution). The moment you pop the cap, the pressure above the liquid drops to atmospheric levels, and $CO_2$ rapidly escapes as bubbles. That is why an open bottle of soda goes flat over time.

Scuba Diving and the Bends

When scuba divers breathe compressed air deep underwater, the total pressure on their bodies is much higher than at the surface. By Henry’s law, this elevated pressure forces more atmospheric gases, particularly $N_2$, to dissolve in their blood.

If a diver ascends too quickly, the surrounding pressure drops rapidly. The dissolved $N_2$ can no longer stay in solution and forms tiny bubbles inside the bloodstream. These bubbles block narrow blood vessels (capillaries), causing intense pain, joint stiffness, and potentially life-threatening complications. This condition is called bends (also known as decompression sickness).

To reduce this risk, as well as the toxic effects of high nitrogen concentrations in the blood, scuba tanks are filled with a modified air mixture diluted with helium. A typical composition is 11.7% helium, 56.2% nitrogen, and 32.1% oxygen. Because helium is much less soluble in blood than nitrogen, this lowers the total amount of gas that dissolves and makes decompression safer.

High Altitude and Anoxia

At high altitudes, the atmospheric pressure is lower, which means the partial pressure of oxygen is also lower than at sea level. According to Henry’s law, less oxygen dissolves in the blood of people at high altitudes.

This oxygen shortage in the blood and tissues leads to anoxia (a condition where the body does not receive enough oxygen). Symptoms include weakness, fatigue, dizziness, and difficulty thinking clearly. Mountain climbers are especially vulnerable to this and may require supplemental oxygen at very high elevations.

How Temperature Affects Gas Solubility

You may have noticed that a cold glass of soda stays fizzy longer than a warm one. This everyday observation has a solid scientific explanation.

When a gas dissolves in a liquid, the gas molecules move from the relatively free gas phase into the more ordered liquid phase. This process is similar to condensation (gas turning into liquid), and like condensation, it releases heat. In other words, the dissolution of a gas in a liquid is an exothermic (heat-releasing) process.

Since the dissolution equilibrium is a dynamic equilibrium, it follows Le Chatelier’s principle (when an external change is applied to a system at equilibrium, the system shifts to partially counteract that change). Applying this principle:

• Raising the temperature adds heat to the system.
• The system responds by shifting in the endothermic direction (the direction that absorbs heat), which is the reverse of dissolution.
• This means gas molecules leave the solution and return to the gas phase.
• The net result: gas solubility decreases as temperature increases.

This is exactly why:

• Aquatic species thrive in cold water. Colder water holds more dissolved oxygen, giving fish and other organisms a richer oxygen supply. In warm waters, the dissolved oxygen level drops, putting aquatic life under stress.
• A warm soda goes flat faster. The higher temperature drives $CO_2$ out of solution more readily.

The $K_\text{H}$ values in Table 1.2 confirm this pattern. For both $N_2$ and $O_2$, $K_\text{H}$ increases from 293 K to 303 K. Since higher $K_\text{H}$ means lower solubility, the data directly shows that warming the water makes these gases less soluble.