Henry's Law (Gas Solubility)

Henry's constant is expressed in at least four different ways depending on the concentration unit chosen for the liquid phase: (1) H^P = P_i/x_i in pressure units — this calculator uses this form; (2) H^c = P_i/c_i in pressure·volume/mol; (3) H^cp = c_i/P_i in mol/(volume·pressure); (4) H^cc = c_i/c_gas dimensionless. The numerical values differ by factors of molar volume and solvent molarity — for water at 25 °C, H^P (atm) ≈ 55.5 × H^c (atm·L/mol). Always check the units carefully when comparing values from different references, and use the form that matches your concentration units.

Henry's Law is a limiting law valid for dilute solutions where the solute-solvent interactions dominate over solute-solute interactions. It breaks down when: (1) the gas is highly soluble (x_i > 0.01–0.05), as with ammonia or HCl in water; (2) the gas reacts chemically with the solvent — CO₂ + H₂O → H₂CO₃ → H⁺ + HCO₃⁻ — in which case a chemical equilibrium model is required; (3) the solvent is a mixture and preferential solvation effects matter; (4) the pressure is high enough that gas-phase non-ideality becomes significant (fugacity ≠ partial pressure); (5) temperature is near the critical temperature of the gas. In these cases, more sophisticated models (e.g., activity coefficient models, equations of state) are required.

Henry's Law is central to environmental fate and transport modeling. It determines how volatile organic compounds (VOCs) partition between water and air, which controls whether they evaporate from contaminated groundwater, accumulate in surface water, or are removed by air stripping towers. It is used in the design of activated sludge wastewater treatment plants to ensure adequate oxygen transfer, in the modeling of radon and other gases in drinking water, and in assessing the fate of pesticides and industrial chemicals in the environment. The dimensionless Henry's constant H^cc = c_air/c_water is used directly in environmental models and is often tabulated rather than the pressure-based form.

A carbonated beverage is bottled under high CO₂ pressure, which dissolves CO₂ into the liquid according to Henry's Law. When you open the bottle, the pressure drops to atmospheric, and the equilibrium shifts — CO₂ starts escaping. At higher temperatures, H for CO₂ in water increases, so the equilibrium solubility at atmospheric pressure decreases. A warm soda therefore has a lower equilibrium CO₂ concentration and loses its carbonation faster. Additionally, higher temperature increases the diffusion rate of CO₂ through the liquid and speeds up the kinetics of gas escape, further accelerating the loss. This is why keeping soda cold and sealed preserves carbonation.

Raoult's Law applies to the solvent in an ideal solution: P_solvent = x_solvent · P^sat_solvent, where P^sat is the pure-component vapor pressure. Henry's Law applies to the solute in dilute solution: P_solute = H · x_solute, where H is the Henry's constant. Both are limiting laws for ideal behavior, but in different composition ranges: Raoult's Law applies as x_solvent → 1 (dilute in solute), and Henry's Law applies as x_solute → 0 (dilute in solvent). Together they describe the two ends of the vapor-liquid equilibrium curve for a binary mixture.

When a scuba diver breathes compressed air at depth, the increased partial pressure of nitrogen dissolves more N₂ into the bloodstream and tissues, according to Henry's Law. The longer and deeper the dive, the more nitrogen is absorbed. When the diver ascends, the external pressure drops rapidly. If the ascent is too fast, tissues become supersaturated in nitrogen — the equilibrium solubility has decreased faster than the nitrogen can be removed by circulation. The excess nitrogen forms bubbles in tissues and blood, causing decompression sickness ("the bends"). The treatment (slow ascent, safety stops, hyperbaric chamber) works by managing the rate at which ambient pressure is reduced so that nitrogen is eliminated gradually without forming bubbles.