Henry's Law for Dissolved Gases

Introduction

The amount of a gas dissolved in a liquid can depend on that gas's pressure above the liquid. In a simple dilute equilibrium model, raising the gas partial pressure raises its dissolved amount. This is Henry's law. The relationship helps explain why carbonated drinks lose dissolved CO₂ after opening, but calculations require careful attention to which mathematical convention defines the Henry constant.

Core explanation

One common convention writes pgas = KH xgas, where xgas is the gas's equilibrium mole fraction in the liquid and KH has pressure units. With this convention, xgas = pgas/KH. At a fixed temperature and for a fixed gas–solvent pair, doubling the gas partial pressure doubles the predicted dissolved mole fraction in the range where the law applies. A larger KH in this convention means less gas dissolves at a given pressure. Another convention writes dissolved concentration cgas = kH pgas; its constant has different units and the opposite numerical interpretation. Never interchange constants from the two conventions without converting them.

The pressure is the partial pressure of the named gas, not necessarily total pressure above a liquid. If air has total pressure 1 atm, oxygen's partial pressure is only a fraction of that total. Using 1 atm as oxygen's p in Henry's law would exaggerate a prediction. Likewise if a container holds CO₂ plus an inert gas, adding inert gas at unchanged CO₂ partial pressure does not simply double dissolved CO₂ in the ideal Henry model.

Henry's law is a limiting relation for dilute solutions of gases that do not significantly react with the solvent in the simple model. Some gases can chemically react or ionise after dissolving. CO₂ in water, for example, can participate in acid–base equilibria, so total dissolved inorganic carbon is not always equal to a single molecular CO₂(aq) amount. A classroom carbonation explanation can still use pressure dependence qualitatively, but precise chemistry needs species and equilibrium data.

Temperature affects the Henry constant, so its numerical value must match the temperature used. Many familiar gases become less soluble in water when warmed, but that observation is not a universal algebraic consequence of p = KH x by itself; KH changes with temperature according to the particular gas and solvent. Pressure and temperature effects should be discussed separately. A bottle warmed before opening may fizz differently for more than one reason, including changed gas pressure and solubility.

At a sealed-bottle equilibrium, elevated CO₂ partial pressure helps keep more CO₂ dissolved. Opening lowers the gas pressure above the liquid. The previous dissolved amount now exceeds the new equilibrium amount, and CO₂ can leave as bubbles or diffuse into the air. Bubble formation also depends on nucleation sites and motion; Henry's law gives an equilibrium tendency, not the detailed rate or bubble size.

The model's concentration must be defined. A question may give liquid mole fraction x, molarity c or mass per volume; constants for one basis cannot be inserted into another equation unchanged. If the problem says p = KH x and gives KH in atm, use liquid x. If it says c = kH p with kH in mol L⁻¹ atm⁻¹, use dissolved molarity. Dimensional analysis is an efficient guard against convention errors.

Step-by-step reasoning

1. Identify the named gas, liquid solvent and specified temperature. 2. Read the exact Henry-law equation and units supplied by the problem. 3. Use the gas's partial pressure above liquid, not unexamined total pressure. 4. Solve for the matching dissolved mole fraction or concentration. 5. State limits when gas reacts, solutions are concentrated or temperature changes.

Visual explanation

Draw a sealed bottle with many CO₂ dots above and within liquid, labelled “high pCO₂, more dissolved.” Next draw the opened bottle with fewer gas dots in the headspace and an upward arrow from liquid labelled “CO₂ leaves until new equilibrium.” Underneath put two separate formula boxes: p = KH x and c = kH p, with different constant units to prevent accidental mixing.

Real-world analogy

Imagine people entering a hall through a doorway more often when the crowd outside pushes harder; at equilibrium the hall holds more people. Reducing the outside crowd pressure permits net exit. Gas dissolution responds to gas partial pressure in an analogous way, though individual molecules cross the interface because of molecular collisions and chemical potential, not social crowding.

Real-world example

A sealed carbonated drink keeps CO₂ at elevated partial pressure above its liquid. When the cap is removed, the external CO₂ partial pressure drops and the drink becomes supersaturated relative to the new condition. Gas then escapes. The rate of visible fizz is influenced by rough surfaces and agitation, while Henry's law sets the direction of equilibrium change.

Why?

Why does adding a nonreactive gas that raises total pressure not necessarily increase dissolved CO₂ in the basic model? Henry's relation uses CO₂'s own partial pressure. If that partial pressure remains unchanged, its equilibrium dissolved amount remains approximately unchanged under the stated ideal assumptions.

Common misconception

“Every Henry constant gets larger when a gas is more soluble.” In p = KH x, more solubility means larger x at fixed p and hence a smaller KH. In c = kH p, more solubility means a larger kH. Always read the defining equation.

Worked example

At a fixed temperature, a gas–solvent pair follows p = KH x with KH = 200 atm. If the gas partial pressure is 2.0 atm, the predicted dissolved mole fraction is x = 2.0/200 = 0.010. At 1.0 atm under the same conditions, x = 0.0050. Halving p halves x in this model. If a different textbook gives a numerical kH for c = kH p, it cannot replace 200 atm because the units and concentration basis differ.

Quick check

1. In p = KH x, what happens to liquid x if gas partial pressure doubles at fixed temperature? Answer: It doubles within the dilute range where the Henry-law model applies.

Exam focus

Write the supplied convention, units and gas partial pressure before calculating. Explain opening a carbonated drink by a lower equilibrium dissolved CO₂ amount, and distinguish the equilibrium prediction from fizzing rate.

Advanced insight

For reactive gases, equilibrium dissolution can be coupled to chemical conversion. The freely dissolved molecular gas may obey a Henry relation while its reaction products add to total analytical concentration. Acid–base state, pH and ionic strength then influence how much total gas-derived material appears in solution, beyond the one-species Henry equation.

Summary

Henry's law links a gas's partial pressure to its dilute equilibrium amount in liquid at fixed temperature. The common p = KH x convention and c = kH p convention use different constants. Pressure release can drive gas out of solution, while reaction, temperature and kinetics set practical limits.

Practice questions

1. Under p = KH x, KH = 500 kPa and p = 5 kPa. Find x. Answer: x = 5/500 = 0.010. 2. Which pressure enters Henry's law for oxygen in air: total air pressure or oxygen partial pressure? Answer: Oxygen partial pressure. 3. Why can p = KH x be inadequate for calculating total dissolved carbon from CO₂ in water? Answer: Dissolved CO₂ can react in acid–base equilibria, producing additional carbon-containing species.