Henry's Law

How Henry's law works

Pour plain water and let it sit. Atmospheric oxygen dissolves into the surface, nitrogen slightly less, argon and CO₂ in trace amounts. After a few hours the dissolved concentrations stop changing. That equilibrium follows a simple proportionality:

c_gas = K_H · p_gas

c_gas is molar concentration of dissolved gas, p_gas is its partial pressure above the liquid, K_H is Henry's constant — depending on the gas, solvent, and temperature. Double the partial pressure and the dissolved concentration doubles. Microscopically, gas molecules enter the liquid by surface collision and leave by Brownian escape; at equilibrium the rates match.

Henry's constants for common gases in water at 25°C

Gas	KH (mol/(L·atm))	Solubility at 1 atm	Notes
Helium	3.7 × 10⁻⁴	0.0015 g/L	Least soluble noble gas
Nitrogen	6.4 × 10⁻⁴	0.018 g/L	Diver's bends gas
Oxygen	1.3 × 10⁻³	0.042 g/L (~9 mg/L at 0.21 atm)	Aquatic life depends on this
Methane	1.4 × 10⁻³	0.022 g/L	Marsh gas in lakes
Carbon dioxide	3.4 × 10⁻²	1.5 g/L (physical only)	26× more soluble than O₂
Hydrogen sulphide	0.10	3.4 g/L	Reactive in water
Sulphur dioxide	1.2	77 g/L	Hydrolyses to sulphurous acid
Ammonia	~58	~990 g/L	Reactive; not purely physical

The four-decade range reflects whether the gas merely dissolves physically (low K_H for O₂, N₂) or also reacts with water (high K_H for SO₂, NH₃, HCl, all forming acids or bases on dissolution). Henry's law in its strict form applies only to physical dissolution; reactive cases need extra terms for the consuming equilibria.

Worked example: a Coca-Cola bottle

A sealed 500-mL bottle of Coca-Cola has CO₂ packed in at ~3 atm partial pressure. At room temperature K_H(CO₂) = 0.034 mol/(L·atm), so dissolved CO₂ = 0.034 × 3.0 = 0.102 mol/L = 2.24 g of CO₂ in the bottle — about 1.1 L of CO₂ gas at STP packed into half a litre of liquid. Open the bottle and p_CO₂ above the liquid drops to atmospheric (only 0.0004 atm). The new equilibrium concentration is just 0.6 mg/L.

The bottle was holding 5,000× more CO₂ than equilibrium with open atmosphere allows. The mismatch drives the fizz: bubbles nucleate on bottle walls, surfactant micelles, and sugar crystals or scratches. The first burst releases seconds' worth of supersaturated gas; the rest creeps out over 24–48 hours, leaving the soda flat at ~0.6 mg/L. A Mentos in cola erupts because the rough surface and gum-arabic coating provide huge nucleation area, turning slow off-gassing into a violent geyser within a second.

Decompression sickness: Henry's law in your veins

Air at sea level is 78% N₂ at 0.78 atm partial pressure. Dissolved N₂ in blood equilibrates to ~14 mg/L. Descend to 30 m: total pressure is 4 atm (1 atmospheric + 3 from water), p_N₂ rises to 3.12 atm, and dissolved N₂ quadruples to ~56 mg/L per Henry's law.

If the diver ascends slowly, the lungs offload N₂ as p_N₂ falls and tissues equilibrate downward. Ascend too fast and the partial pressure drops faster than tissues can off-gas. Blood becomes supersaturated with N₂, which nucleates as bubbles in joints (the classic bends), spinal cord (paralysis), or pulmonary capillaries (the "chokes," fatal within minutes).

Recreational dive tables limit ascent to 9 m/min and add decompression stops on long deep dives. Trimix divers swap some N₂ for helium — He's lower K_H means less gas dissolves and helium off-gases faster.

Why warm rivers kill fish

Henry's constant decreases with rising temperature for almost all gases. O₂ saturation at 0.21 atm partial pressure: 14.6 mg/L at 0°C, 11.3 mg/L at 10°C, 9.1 mg/L at 20°C, 7.5 mg/L at 30°C. Power-plant cooling-water discharge raises river temperature 2–10°C in plumes downstream of outflow — Henry's law dictates that warmer water dissolves less O₂, and combined with the higher metabolic O₂ demand of fish in warmer water, "thermal pollution" suffocates aquatic life. Environmental regulations cap discharge temperature at +5°C above ambient for this exact reason. The same physics drives lake stratification in summer: warm surface water holds less dissolved O₂ than cold deep water, but biological consumption in the depths exceeds resupply, producing anoxic bottom layers that kill anything below the thermocline.

Henry's law vs Raoult's law

	Henry's law	Raoult's law
Equation	p = KH · X	p = X · P°
Applies to	Dilute solute (X → 0)	Concentrated solvent (X → 1)
Slope of vapor curve	Empirical Henry constant	Pure-component vapor pressure
Measures	Gas solubility, sparingly soluble species	Vapor pressure of major component
Coincide when	KH = P° (ideal solution)	Same condition
Practical examples	CO₂ in soda, O₂ in lakes, N₂ in divers	Vapor over salt water, distillation, antifreeze

The two laws describe opposite ends of the same vapor pressure vs composition curve. For an ideal solution they collapse to a single straight line; for a real solution Henry's law fits the dilute end and Raoult's the concentrated end.

When Henry's law breaks: reactive gases

Plain Henry's law applies to physical dissolution only. When the dissolved gas reacts with solvent or other species, total uptake vastly exceeds Henry's prediction. CO₂ in seawater (pH ~8.1) cascades through CO₂(aq) ⇌ H₂CO₃ ⇌ HCO₃⁻ + H⁺ ⇌ CO₃²⁻ + H⁺; carbonate equilibria capture additional CO₂ as bicarbonate, raising effective uptake ~50×. This is why oceans absorb ~25% of human CO₂ emissions. NH₃ becomes NH₄⁺ at low pH; SO₂ hydrolyses to bisulphite (acid-rain chemistry); HCl ionizes essentially completely. Hemoglobin's sigmoidal O₂ binding carries ~200 mg O₂/L of blood — without it physical Henry's law would limit blood to ~3 mg/L and large animals could not exist.

Variants and refinements

• Multiple unit forms: Henry's constant comes as K_H = c/p (mol/(L·atm), used here), as p/c (the reciprocal volatility form), as p/X (mole-fraction form aligned with Raoult), or as a dimensionless gas-phase / liquid-phase ratio. Always check the form before plugging in.
• Setschenow equation (salting out): Adding salts decreases gas solubility because dissolved ions tie up water molecules. Brewers exploit the effect; seawater holds ~20% less O₂ than fresh water at the same temperature.
• Temperature dependence: ln(K_H) varies nearly linearly with 1/T (a van 't Hoff-style relation). Slope yields the enthalpy of solution; ΔH_sol < 0 for most gases, which is why higher T means lower solubility.
• Pressure corrections: Above ~10 atm the linear relation drifts; activity-based formulations using fugacity replace partial pressure for accurate work in gas-storage and CO₂-sequestration design.

Pitfalls and common mistakes

• Wrong form of K_H. Tabulated Henry's constants exist in at least four conventions with reciprocal units. Factor-of-1000 errors from picking the wrong form are common.
• Using total pressure instead of partial pressure. A 4 atm scuba tank of air gives p_O₂ = 0.84 atm, not 4 atm. Henry's law uses each gas's own partial pressure.
• Ignoring temperature. K_H tables are typically at 25°C. At 5°C the value for O₂ and CO₂ is ~50% larger. Always temperature-correct for environmental work.
• Applying Henry to reactive gases. NH₃, HCl, SO₂, HF dissolve far more than physical Henry predicts. Use combined chemical-physical equilibrium models.
• Forgetting salting-out. Seawater holds ~20% less dissolved O₂ than fresh water at the same T, per the Setschenow equation.
• Confusing supersaturation with equilibrium. Carbonated soda is far above Henry equilibrium; it obeys nucleation kinetics until relaxing to the Henry concentration over hours.