Ch. 2 | Solutions0/13

Henry's Law

Gas solubility in liquids, KH constants, and real-world consequences

Logical ReasoningLevel 3 · Analysis

A scuba diver breathes compressed air at 30 m depth where pressure is ~4 atm. Nitrogen dissolves into her blood and tissues at 4× the surface concentration. When she surfaces too quickly, she experiences severe joint pain, paralysis, and can die. What happens to the dissolved nitrogen when pressure suddenly drops — and why does surfacing slowly prevent this?

Real Life Hook

The fizz in your soda is compressed COX2\ce{CO2} dissolved under pressure. The bottle is sealed at ~2.5–4 atm of COX2\ce{CO2} pressure. The moment you open the cap, pressure drops to 1 atm — and Henry's law predicts exactly how much COX2\ce{CO2} will escape. Warm soda fizzes more violently because gas solubility decreases with temperature — the same amount of pressure drop releases more gas from a warm bottle. Soda manufacturers solve this by refrigerating product before sale. Every fizz is a demonstration of Henry's law.

Henry's Law Statement

Henry's Law: At constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.

p=KHxp = K_H \cdot x

where:

  • pp = partial pressure of the gas above the solution
  • xx = mole fraction of the dissolved gas in the solution
  • KHK_H = Henry's law constant (units: pressure, e.g. bar or Pa)

Important: KHK_H has a large value for gases that are less soluble (like NX2\ce{N2}, OX2\ce{O2}). A small KHK_H means the gas dissolves easily at low pressure (like COX2\ce{CO2}).

Henry's Law constants (KH) for common gases in water at 298 K

GasKH (kbar)Implication
OX2\ce{O2}46.82Moderately insoluble — enough for aquatic life
NX2\ce{N2}76.48Very insoluble — causes "the bends" at depth
COX2\ce{CO2}1.67Most soluble of common gases — makes carbonation possible
He\ce{He}144.97Extremely insoluble — used in diving gas mixes to avoid narcosis

Limitations of Henry's Law

Henry's law holds strictly only under these conditions:

  1. Low pressure — the gas must not interact strongly with the solvent
  2. Low concentration of dissolved gas
  3. The gas must not react with the solventHCl\ce{HCl} ionises in water (HCl+HX2OHX3OX++ClX\ce{HCl + H2O -> H3O+ + Cl-}), so it does not obey Henry's law. COX2\ce{CO2} partially reacts (COX2+HX2OHX2COX3\ce{CO2 + H2O -> H2CO3}) so it shows deviations at higher concentrations.
  4. The gas must not associate in solution
🖼 Image PendingDiagram showing Henry's Law: increasing gas pressure above liquid increases dissolved gas concentration

AI Generation Prompt

Henry's Law diagram. A sealed container divided horizontally: gas phase above, liquid phase below. Show three versions side by side at increasing pressures (0.5 atm, 1 atm, 2 atm). At 0.5 atm: few green dots (CO₂ molecules) in gas, very few dissolved in liquid. At 1 atm: twice as many green dots in gas, twice as many dissolved. At 2 atm: four times as many green dots in gas, four times dissolved. Arrows showing gas molecules entering liquid (dissolution). Label each panel with its pressure and corresponding mole fraction (x = 0.005, x = 0.01, x = 0.02). Show the linear p vs x graph below. Dark background, orange accent labels, clean technical illustration style.

📸 Henry's Law: doubling the partial pressure of CO₂ above a liquid doubles the dissolved CO₂ mole fraction
📖NCERT 2.5NCERT Intext

Problem

If the Henry's law constant for COX2\ce{CO2} in water is 1.67×1081.67 \times 10^8 Pa at 298 K, find the mole fraction of COX2\ce{CO2} dissolved in water when the COX2\ce{CO2} pressure above the solution is 2.5×1052.5 \times 10^5 Pa.

JEE / NEET Exam InsightJEE / NEET
Henry's law constant direction: Large KHK_H → gas less soluble. Small KHK_H → gas more soluble. Exams frequently ask you to compare solubilities from KH values without calculation.
Temperature effect: Gas solubility always decreases with temperature (opposite to most solids). Higher temperature → KHK_H increases → less gas dissolved at same pressure.
Applications always tested:
    Soda carbonation: high pCOX2p_{\ce{CO2}} in sealed bottle → dissolved COX2\ce{CO2}; opening reduces pp → fizzing
    Scuba diving: 'bends' caused by NX2\ce{N2} bubble formation on rapid decompression
    Fish mortality: warm water → less dissolved OX2\ce{O2} → suffocation
    Oxygen cylinders: mountaineers use at high altitude where pOX2p_{\ce{O2}} is low
Quick Check

Q1.Henry's law states that at constant temperature, the solubility of a gas in a liquid is: