Solubility and Henry's Law

CHEConcentration & Solubility

Henry's law governs how the solubility of a gas in a liquid depends on its partial pressure, and underlies real-world phenomena like the bends, breathlessness at altitude, and oxygen depletion in warm water. ISC asks both the conceptual explanations and the mole-fraction numerical.

Henry's law

p = K_H \, x_{gas}

p

partial pressure of the gas,

K_H

Henry's constant,

x_{gas}

mole fraction of dissolved gas

Solubility from partial pressure

x_{gas} = \dfrac{p}{K_H}

larger

K_H

means lower solubility

Henry's law: the partial pressure of a gas over a solution is proportional to its mole fraction in solution, $p = K_H \, x_{gas}$ — higher $K_H$ means lower solubility.
At constant temperature, solubility of a gas rises with its partial pressure: $x_{gas} = \dfrac{p}{K_H}$ .
Gas solubility decreases as temperature rises (dissolution is exothermic), so warm water holds less dissolved $O_2$ — aquatic life suffers more in warm water.
Decompression sickness (the bends): high pressure underwater dissolves more $N_2$ in blood; on rapid ascent the $N_2$ comes out as bubbles. Divers' tanks use air diluted with helium to lower the $N_2$ partial pressure and prevent it.
High altitude: low partial pressure of $O_2$ lowers its solubility in blood, causing breathlessness and anoxia (mountain sickness).
Larger $K_H$ value implies the gas is less soluble; $K_H$ itself increases with temperature.
Soda bottles are sealed under high $CO_2$ pressure (high solubility); on opening, pressure drops and dissolved $CO_2$ fizzes out — a direct demonstration of Henry's law.
Henry's law applies only to gases that do not react with or ionise in the solvent and to dilute solutions at moderate pressure; gases like $NH_3$ and $CO_2$ that react with water deviate.
$K_H$ is gas- and solvent-specific: among common gases at $293\,\text{K}$ , $K_H$ increases (solubility falls) in the order roughly $CO_2 < O_2 < N_2 < He$ .
Raoult's law for the solvent is the limiting case of Henry's law where the proportionality constant $K_H$ equals the pure-component vapour pressure $p^\circ$ .
Practical uses: carbonated drinks bottled under pressure, sealing soda water, and supplying divers with helium-diluted breathing mixtures all exploit the pressure dependence of solubility.

Where the marks go

Reading a large $K_H$ as high solubility — it is the opposite; $K_H$ is inversely related to solubility.
Saying gas solubility increases with temperature; dissolution of a gas is exothermic, so warming drives gas out of solution.
Applying Henry's law to gases that react with the solvent (e.g. $NH_3$ , $HCl$ in water) where the simple proportionality fails.
Confusing the bends (caused by dissolved $N_2$ coming out on ascent) with altitude breathlessness (caused by low $O_2$ partial pressure).
Forgetting that $K_H$ itself rises with temperature, so the same partial pressure dissolves less gas in warmer water.

How the board asks it

Define / statehenry's law statement and $K_H$ significance
State Henry's law and write its mathematical expression $p = K_H \, x_{gas}$ , explaining the significance of the Henry's law constant $K_H$ .
Numerical $x_{gas} = p/K_H$
The partial pressure of $CO_2$ over a soft drink is $2.5\,\text{atm}$ at $298\,\text{K}$ . If $K_H$ for $CO_2$ in water is $1.67 \times 10^{8}\,\text{Pa}$ , calculate the mole fraction of $CO_2$ dissolved in the drink.
Give reasonstemperature dependence of gas solubility
Account for the following: aquatic species are more comfortable in cold water than in warm water.
Distinguish $K_H$ is inversely related to solubility
At $293\,\text{K}$ the $K_H$ values for $N_2$ and $CO_2$ are $76.48\,\text{kbar}$ and $1.67\,\text{kbar}$ respectively. Which gas has the higher solubility in water, and why?
Give reasonslimitations and deviations from henry's law
Give reasons: gases like $NH_3$ and $CO_2$ do not strictly obey Henry's law in water.

Practise this topic

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Written for Sublevo. Question text quoted anywhere in these notes is the Council’s and carries its year and paper; the board’s own diagrams are not reproduced.