Henry's Law (Solubility of Gas in Liquid)
Formulated by William Henry in 1803, Henry's Law is a gas law that describes the relationship between the pressure of a gas and its solubility in a particular liquid.
1. The Statement
"At a constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas present above the surface of the liquid or solution."
2. Mathematical Expression
The most common functional form used in chemistry relates partial pressure ($p$) to the mole fraction ($x$):
- $p$: Partial pressure of the gas in the vapor phase.
- $x$: Mole fraction of the gas in the solution (a measure of solubility).
- $K_H$: Henry's Law constant.
3. Significance of $K_H$
- $K_H$ depends on the nature of the gas and the solvent.
- Temperature Effect: $K_H$ increases as temperature increases. Since $x = p / K_H$, a higher $K_H$ means lower solubility. This is why aquatic animals are more comfortable in cold water (higher dissolved oxygen) than in warm water.
Why does solubility decrease?
The dissolution of most gases in water is an exothermic process:
$Gas + Solvent \rightleftharpoons Solution + \text{Heat}$
- Le Chatelier's Principle: When heat is added (temperature increases), the equilibrium shifts to the left (toward the gas phase) to absorb the excess energy, thus reducing solubility.
- Kinetic Energy: As temperature rises, gas molecules gain more kinetic energy, allowing them to overcome the intermolecular attractions of the solvent and escape into the atmosphere.
4. Practical Applications
- Soft Drinks: To increase the solubility of $CO_2$, bottles are sealed under high pressure. When opened, the pressure drops, and gas escapes as bubbles.
- Deep-Sea Diving: High pressure underwater causes more nitrogen to dissolve in a diver's blood. If they surface too quickly, the nitrogen forms bubbles, leading to a painful condition called "the bends" (decompression sickness).
- High Altitude (Anoxia): At high altitudes, the partial pressure of oxygen is low, leading to low blood-oxygen levels, which causes weakness and impaired thinking.
5. Limitations
- Pressure is not too high.
- Temperature is not too low.
- The gas does not react chemically with the solvent (e.g., $NH_3$ in water deviates because it forms $NH_4OH$).
- The gas does not dissociate or associate in the solvent.
6. Henry's Law Constants ($K_H$) for Selected Gases in Water
| Gas | Temperature (K) | $K_H$ (kbar) |
|---|---|---|
| Helium ($He$) | 293 | 144.97 |
| Hydrogen ($H_2$) | 293 | 69.16 |
| Nitrogen ($N_2$) | 293 | 76.48 |
| Nitrogen ($N_2$) | 303 | 88.84 |
| Oxygen ($O_2$) | 293 | 34.86 |
| Oxygen ($O_2$) | 303 | 46.82 |
*Observe that for the same gas (e.g., Nitrogen or Oxygen), as the temperature increases, the $K_H$ value increases, indicating a decrease in solubility.