Henry's Law

William Henry studied how the solubility of a gaseous solute in a particular solvent depends on pressure. His finding, now called Henry's law: "at low concentrations, the partial pressure of the gas in the vapour phase (i.e. the vapour pressure of the dissolved solute) is directly proportional to the mole fraction of the gaseous solute in the solution."

Mathematically:

Here $p_{solute}$ is the partial pressure of the gas above the solution (commonly called its vapour pressure), $x_{solute\ in\ solution}$ is the mole fraction of the dissolved gas, and $K_H$ (Henry's law constant) is an empirical proportionality constant with the dimensions of pressure. $K_H$ depends on both the identity of the gas and the identity of the solvent -- it is not a universal constant.

Equation 9.2 has the form of a straight line through the origin, $y=mx$: plotting the gas's partial pressure ($y$) against its mole fraction in solution ($x$) gives a straight line whose slope is $K_H$ (Figure 9.3, HCl dissolved in cyclohexane at 293 K). A larger $K_H$ means the gas is comparatively less soluble at a given pressure (a small mole fraction already produces a large partial pressure), while a smaller $K_H$ means the gas is more soluble.

Practical applications:

• Carbonated beverages. Manufacturers dissolve CO$_2$ in these drinks by bubbling it through under high pressure, then sealing the container to maintain that pressure. Opening the container drops the CO$_2$ partial pressure suddenly to the atmospheric level; by Henry's law, the equilibrium mole fraction of dissolved CO$_2$ at this lower pressure is much smaller, so CO$_2$ rapidly leaves solution as bubbles -- effervescence, which is even more vigorous if the drink is warm (since solubility also falls with temperature, section 9.4.1).

• Deep-sea divers and "the bends". Divers breathe compressed air, which is mostly nitrogen and oxygen. At the surface these gases are not very soluble in blood and body fluids, but at depth the ambient pressure is far higher than at the surface, so by Henry's law more nitrogen dissolves into the diver's blood and tissues. If the diver ascends too quickly, the pressure drops rapidly and the dissolved nitrogen comes out of solution abruptly, forming bubbles in the bloodstream -- restricting blood flow, disrupting nerve signal transmission, and potentially bursting or blocking capillaries. This dangerous, painful condition is called "the bends." To reduce the risk, professional divers use air diluted with helium (about 11.7% helium, 56.2% nitrogen, 32.1% oxygen) instead of ordinary compressed air, because helium is less soluble in blood than nitrogen (so fewer bubbles form on ascent) and its very small atoms can pass harmlessly through cell walls. The extra dissolved oxygen is simply consumed in normal metabolism and does not contribute to the bends.

Worked example (Example Problem 2). 0.24 g of a gas dissolves in 1 L of water at 1.5 atm pressure. What mass dissolves at 6.0 atm, same temperature? …