Solubility of solids and gases; Henry's law
A solid dissolves best in a solvent like itself; temperature matters, pressure does not. A gas's solubility rises with pressure (Henry's law) and falls as temperature rises.
Solubility of a solid in a liquid
Solubility is the largest amount of a substance that dissolves in a given amount of solvent at a given temperature. Like dissolves like: polar or ionic solutes such as sugar and common salt dissolve in polar water, while non-polar naphthalene and anthracene dissolve in non-polar benzene. When a solid is added to a solvent, it dissolves and some of it also crystallises back. When the two rates become equal, a dynamic equilibrium is reached and the solution is saturated.
What changes the solubility of a solid
| Factor | Effect | Reason |
|---|---|---|
| Temperature, when dissolving absorbs heat (ΔsolH > 0) | Solubility increases on heating | Le Chatelier's principle: heat favours the endothermic change |
| Temperature, when dissolving gives out heat (ΔsolH < 0) | Solubility decreases on heating | Heat favours the reverse change, crystallisation |
| Pressure | No significant effect | Solids and liquids are almost incompressible |
Solubility of a gas in a liquid
Gases such as O₂, N₂ and CO₂ dissolve in water only a little. Solubility increases with pressure: at higher pressure, more gas molecules strike the liquid surface and enter it until a new equilibrium is reached. Henry's law puts this in numbers: at constant temperature, the solubility of a gas is proportional to its partial pressure, or p = K_H x. Solubility decreases as temperature rises, because dissolving a gas gives out heat, so heating drives the gas out. That is why fish are more comfortable in cold water than in warm water.
Henry's law in daily life
- Soda water and soft drinks are sealed under a high pressure of CO₂ to raise its solubility. When the bottle is opened, the pressure falls and CO₂ fizzes out.
- Scuba divers breathe air at high pressure deep under water, so more N₂ dissolves in their blood. If they rise too fast, the N₂ forms bubbles that block capillaries: the painful condition called the bends. Their air tanks are diluted with helium (about 11.7% helium, 56.2% nitrogen and 32.1% oxygen), which is much less soluble in blood.
- At high altitudes the partial pressure of oxygen is low, so less O₂ dissolves in blood. Climbers become weak and cannot think clearly: this is anoxia.
Some K_H values in water (higher K_H means lower solubility)
| Gas | Temperature (K) | K_H (kbar) |
|---|---|---|
| Helium | 293 | 144.97 |
| Nitrogen | 293 | 76.48 |
| Nitrogen | 303 | 88.84 |
| Oxygen | 293 | 34.86 |
| Oxygen | 303 | 46.82 |
| Carbon dioxide | 298 | 1.67 |
Worked example: CO₂ in a soda bottle
K_H for CO₂ in water at 298 K is 1.67 kbar. A soda bottle is sealed with CO₂ at a partial pressure of 3.34 bar. Find (a) the mole fraction of CO₂ in the water and (b) the mass of CO₂ dissolved in 1 kg of water.
- Given: p = 3.34 bar; K_H = 1.67 kbar = 1670 bar.
- (a) Henry's law: x = p ÷ K_H = 3.34 bar ÷ 1670 bar = 2.0 × 10⁻³.
- (b) Moles of water in 1000 g = 1000 ÷ 18 = 55.6 mol.
- x = n(CO₂) ÷ [n(CO₂) + n(water)]. Because n(CO₂) is very small, x ≈ n(CO₂) ÷ n(water).
- n(CO₂) = 2.0 × 10⁻³ × 55.6 = 0.111 mol.
- Mass of CO₂ = 0.111 mol × 44 g mol⁻¹ = 4.9 g.
(a) x(CO₂) = 2.0 × 10⁻³; (b) about 4.9 g of CO₂ per kilogram of water
The hiss when the marble of a goli soda is pushed down is Henry's law at work: the pressure drops and CO₂ escapes. Fish in a village pond gulp air at the surface on hot summer afternoons, because warm water holds less oxygen.
2 marks: “State Henry's law. Why are bottles of soda water sealed under high pressure?” At constant temperature, the partial pressure of a gas above a solution is proportional to its mole fraction in the solution: p = K_H x. High pressure raises the solubility of CO₂, so more of it stays dissolved.
1 marks: “At 293 K, K_H for O₂ is 34.86 kbar and for N₂ is 76.48 kbar. Which gas is more soluble in water?” O₂, because a lower K_H means a higher solubility at the same partial pressure.
3 marks: “Give reasons: (i) aquatic animals are more comfortable in cold water, (ii) climbers feel weak at high altitudes, (iii) divers' air tanks are diluted with helium.” (i) More O₂ dissolves in cold water, since gas solubility falls as temperature rises. (ii) Low partial pressure of O₂ means less O₂ in blood (anoxia). (iii) Helium is much less soluble in blood than N₂, which avoids the bends.
Gases: Pressure up, solubility up; Temperature up, solubility down. A high K_H means the gas Hates to dissolve.