Henry's Law (Gas Solubility)

William Henry found in 1803 that a gas dissolves in proportion to its partial pressure above the liquid, and the constant of proportionality is the one number a whole field of environmental engineering rests on. Oxygen at 25 °C has $H^{cp} = 1.3\times 10^{-5}$ mol/(m³·Pa). Air puts 21% of an atmosphere of oxygen over a lake, which is 21278 Pa, so the water holds $1.3\times 10^{-5}\times 21278 = 0.277$ mol/m³, or about 8.9 mg/L once you multiply by 32 g/mol. That is the dissolved oxygen reading a probe gives in air-saturated water, and the number every aeration system is designed against.

The units are a minefield, and it is worth being blunt about it. There are at least five conventions in circulation: solubility forms with concentration over pressure, volatility forms with pressure over concentration, dimensionless air-water partition coefficients, and versions using mole fraction instead of concentration. They are reciprocals and rescalings of one another, so getting one wrong produces an answer off by many orders of magnitude. This page uses the solubility form $H^{cp}$ in mol/(m³·Pa), which is the convention Sander's compilation tabulates.

Two things the equation does not say out loud. Solubility falls sharply with temperature, roughly halving between 0 and 30 °C for oxygen, which is why summer fish kills happen in warm shallow water exactly when the fish need oxygen most. And Henry's law is a dilute-solution law: it describes the solute, while Raoult's law describes the solvent, and the two are the opposite limits of the same curve. Push the concentration up towards saturation and the linear relation quietly stops being true.