Solubility and Henry's Law

Solubility is the maximum amount of a solute that dissolves in a given amount of solvent at a specified temperature and pressure. It depends on the nature of solute and solvent ("like dissolves like"), temperature and, for gases, pressure.

Solubility of solids in liquids

• Polar solutes dissolve in polar solvents; non-polar in non-polar.
• For most solids, solubility increases with temperature if dissolution is endothermic (e.g. KNO₃); it decreases if exothermic (e.g. cerium sulfate).
• Pressure has almost no effect on solids and liquids.

Solubility of gases in liquids — Henry's Law

Henry's law: the solubility (mole fraction) of a gas in a liquid is directly proportional to the partial pressure of the gas over the solution.

• p = Kʜ x, where p is partial pressure, x is mole fraction of the gas, and Kʜ is Henry's constant.
• Higher Kʜ means LOWER solubility of the gas.
• Kʜ increases with temperature, so gases are less soluble in warm liquids.

Applications

• Soda water and soft drinks are bottled under high CO₂ pressure.
• Deep-sea divers face 'bends' (nitrogen bubbles) — tanks use diluted air (helium-oxygen).
• At high altitudes low oxygen partial pressure causes anoxia (climber's weakness).

Exam Tricks & Tips

• 🎯 Larger Kʜ = smaller solubility — this inverse relation is a favourite 1-mark trap.
• 🎯 Kʜ increases with temperature, so aquatic life suffers as warm water holds less dissolved O₂.
• 🎯 Henry's law is a special case of Raoult's law for the volatile (gaseous) component.
• 🎯 Effect of pressure applies only to gases — solids/liquids solubility is nearly pressure independent.
• 🎯 Learn the three applications (soda water, divers' bends, high-altitude anoxia) — commonly asked.
• ❌ Common mistake: thinking a high Henry's constant means high solubility. It is the opposite — p = Kʜx, so for a given pressure a large Kʜ gives a small x (low solubility).

Board exam focus

A numerical using p = Kʜx to find dissolved gas amount, and a reasoning question on why cold soda is more fizzy or why divers use helium.

Cover the answer, recall, then check. 10 cards on solubility and Henry's law.

Q1. Define solubility.
A1. The maximum amount of solute that dissolves in a given amount of solvent at a specified temperature and pressure.

Q2. State Henry's law.
A2. The partial pressure of a gas over a solution is proportional to its mole fraction in solution: p = Kʜx.

Q3. What does a large value of Henry's constant Kʜ indicate?
A3. Lower solubility of the gas (since x = p/Kʜ, a larger Kʜ gives a smaller mole fraction).

Q4. How does Kʜ change with temperature?
A4. It increases with temperature, so gas solubility decreases as the liquid warms.

Q5. Why are cold drinks bottled under high pressure?
A5. High CO₂ partial pressure increases its solubility (Henry's law), keeping the drink fizzy.

Q6. Why do deep-sea divers get the 'bends'?
A6. High pressure dissolves more N₂ in blood; rapid ascent releases N₂ bubbles that block capillaries.

Q7. Why do climbers feel weak at high altitude?
A7. Low oxygen partial pressure lowers O₂ solubility in blood (anoxia), causing weakness.

Q8. Does pressure affect the solubility of solids in liquids?
A8. No — solids and liquids are nearly incompressible, so pressure has negligible effect.

Q9. For a solid whose dissolution is exothermic, how does solubility change with temperature?
A9. Solubility decreases as temperature rises (by Le Chatelier's principle).

Q10. Henry's law is a special case of which broader law?
A10. Raoult's law — applied to the gaseous (volatile) component of the solution.

Why a warm cola goes flat

Open a warm soft drink and it fizzes furiously, then goes flat fast; a chilled one holds its fizz. The gas is CO₂ dissolved under pressure, and its escape is governed by two ideas: solubility and Henry's Law.

Core idea: Solubility is the maximum amount of solute that dissolves in a given amount of solvent at a fixed temperature and pressure. For a gas dissolving in a liquid, that solubility is directly proportional to the partial pressure of the gas above the liquid.

Deep explanation

Beginner: solubility of solids in liquids

Every solute has a characteristic solubility that follows the rule "like dissolves like" — polar solutes (NaCl, sugar) dissolve in polar solvents (water), non-polar solutes (naphthalene) in non-polar solvents (benzene). Most solids become more soluble as temperature rises if dissolution is endothermic (ΔH_sol > 0), and less soluble if exothermic (as with Ce₂(SO₄)₃).

Intermediate: gases and Henry's Law

For a gas dissolved in a liquid, Henry's Law states:

p = K_H · x

where p is the partial pressure of the gas above the solution, x is its mole fraction in solution, and K_H is Henry's constant. A higher K_H means lower solubility (for the same pressure, less gas dissolves). K_H is characteristic of a gas–solvent pair and increases with temperature.

Advanced: the temperature effect and why gases behave "backwards"

Dissolution of a gas is exothermic (the gas loses kinetic energy as it enters solution), so by Le Chatelier's principle, raising temperature drives gas out of solution — solubility falls. That is why a warm cola fizzes out and why aquatic life suffers in thermally polluted (warmer) water: dissolved O₂ drops. K_H therefore rises with temperature. Because solubility ∝ p and inversely with K_H, deep-sea divers face two problems: at high pressure more N₂ dissolves in blood, and on rapid ascent it comes out as bubbles (the "bends"). Divers use helium–oxygen mixes because helium's high K_H (low solubility) reduces this risk.

Limitations: Henry's Law holds only if the gas does not react with, dissociate in, or associate within the solvent. HCl and NH₃ in water, or CO₂ forming carbonic acid, deviate strongly.

Worked example

The partial pressure of CO₂ over a soft drink is 2.5 atm at 298 K. If K_H for CO₂ in water is 1.67 × 10³ bar (per unit mole fraction), find the mole fraction of CO₂ dissolved. (Take 2.5 atm ≈ 2.53 bar.)

x = p / K_H = 2.53 / (1.67 × 10³) = 1.52 × 10⁻³.

So only about 0.15 mole percent of the liquid is dissolved CO₂ — tiny, yet enough to make the drink fizzy.

Real-world / exam application

Henry's Law explains scuba diving (nitrogen narcosis and the bends), high-altitude anoxia (low O₂ partial pressure means less O₂ in blood, causing "anoxia"), sealing soft-drink bottles under high CO₂ pressure, and the choice of helium in diver breathing gas. Exams often give K_H and pressure and ask for mole fraction, molality, or amount dissolved.

Exam tricks & shortcuts

• Large K_H ⇒ low solubility. Between gases, the one with the higher K_H is less soluble.
• Convert pressure to the same unit as K_H before dividing.
• Mnemonic — "Higher K_H, Harder to dissolve."

Key formulas

• Henry's law: p = K_H·x (partial pressure of a gas ∝ its mole fraction in solution).
• K_H = Henry's constant; higher K_H → lower solubility.
• Effect of temperature: gas solubility decreases as T increases (dissolution is exothermic).
• Effect of pressure: gas solubility increases with partial pressure.

Henry's law explains why fizzy drinks release gas when opened (pressure drops) and why aquatic life suffers in warm water.

Worked Example

Problem: The Henry's law constant for oxygen dissolved in water is K_H = 3.5 × 10⁴ bar at a given temperature. If the partial pressure of oxygen above the water is 0.5 bar, find the mole fraction of oxygen dissolved in the water.

Solution:
Step 1 — State Henry's law: the partial pressure of a gas above a solution is proportional to its mole fraction in the solution:
p = K_H × x.

Step 2 — Rearrange to solve for the mole fraction x:
x = p / K_H.

Step 3 — Substitute p = 0.5 bar and K_H = 3.5 × 10⁴ bar:
x = 0.5 / (3.5 × 10⁴).

Step 4 — Evaluate:
x = 1.43 × 10⁻⁵.

Step 5 — Interpretation: the very small mole fraction shows oxygen is only slightly soluble; solubility rises with partial pressure (why soda is bottled under high CO₂ pressure and fizzes when opened).

Answer: The mole fraction of dissolved oxygen is about 1.43 × 10⁻⁵.