Henry’s Law provides a quantitative way to understand the solubility of a gas in a liquid, establishing a clear relationship between the pressure of a gas above a liquid and how much of that gas dissolves into it. Formulated by the English chemist William Henry in 1803, the law describes the equilibrium state where the rate of gas molecules entering the liquid equals the rate of molecules escaping back into the gas phase. This principle is foundational to fields ranging from environmental science to human physiology, influencing everything from carbonated beverages to deep-sea diving safety.
The Mathematical Relationship
Henry’s Law demonstrates a direct proportionality between the pressure of a gas and its concentration within a liquid solvent. The mathematical expression is often written as \(C = k_H P\). Here, \(C\) represents the concentration of the dissolved gas, typically measured in moles per liter (M) or as a mole fraction. \(P\) is the partial pressure of the gas above the liquid surface, measured in atmospheres or bars.
The constant of proportionality, \(k_H\), is known as the Henry’s Law Constant. Its value is unique to a specific gas, a specific solvent, and a specific temperature. This constant translates the gas pressure into a solubility value, fundamentally linking the gaseous phase to the liquid phase. The equation confirms that a higher partial pressure of a gas results in a greater amount of that gas being dissolved, provided the temperature remains constant.
Factors Controlling Gas Solubility
The Henry’s Law Constant, \(k_H\), changes depending on the specific conditions of the system. The primary external factor influencing this value is temperature, as increasing the temperature generally decreases the solubility of a gas in a liquid. For most gases, the value of \(k_H\) increases as temperature rises, reflecting the reduced ability of the solvent to hold gas molecules. This explains why a warm glass of soda goes flat faster than a cold one, since dissolved carbon dioxide escapes more easily from the heated liquid.
The inherent nature of the gas and the solvent also determines the constant’s value. Gases with larger or heavier molecules tend to have lower solubility compared to smaller molecules. The polarity and molecular interactions between the gas and the solvent play a large role; a gas that forms weak intermolecular attractions with the solvent will be more soluble. Therefore, \(k_H\) is an empirical measurement that must be determined for every unique gas-solvent combination at a specified temperature.
Everyday Applications
Carbonated Beverages
Manufacturers dissolve carbon dioxide (\(\text{CO}_2\)) into the liquid under high pressure within a sealed container, drastically increasing the \(\text{CO}_2\) concentration in the soda. When the bottle is opened, the pressure above the liquid rapidly drops to atmospheric pressure, instantly decreasing the solubility of \(\text{CO}_2\). This sudden drop in pressure forces the excess dissolved gas out of the solution, creating the familiar bubbles and fizz.
Scuba Diving and Decompression Sickness
Henry’s Law is crucial for understanding decompression sickness, commonly known as “the bends,” in scuba diving. As a diver descends, the ambient pressure increases, causing more nitrogen gas from the breathing air to dissolve into the diver’s blood and tissues. If the diver ascends too rapidly, the external pressure falls too quickly, and the nitrogen gas comes out of solution as bubbles within the body. A slow, controlled ascent allows the dissolved nitrogen to escape gradually through the lungs, maintaining equilibrium with the decreasing external pressure.
Aquatic Life and Physiology
The health of aquatic life is connected to this law, particularly concerning dissolved oxygen. Fish rely on oxygen dissolved in the water, and because oxygen solubility decreases as water temperature rises, aquatic environments are stressed by warming water. Colder water can hold more dissolved oxygen, which is why fish often fare better in cooler conditions. Furthermore, the exchange of oxygen and carbon dioxide in human lungs operates based on partial pressure differences, with gases moving between the air in the alveoli and the blood according to Henry’s Law.
Limitations of the Law
Henry’s Law is an ideal gas approximation and only holds true for solutions that are sufficiently dilute, meaning the concentration of the dissolved gas is low. The linear relationship breaks down under extremely high pressures, such as those encountered in deep-sea environments, because the gas molecules begin to interact significantly. For the law to apply, the system must also be in a state of physical equilibrium, allowing the dissolving and escaping rates to balance.
The law also fails when the gas chemically reacts with the solvent, rather than simply dissolving as a distinct molecule. For instance, ammonia (\(\text{NH}_3\)) reacts with water to form ammonium and hydroxide ions, resulting in a solubility far higher than the law predicts for a non-reactive gas. Although carbon dioxide forms carbonic acid in water, Henry’s Law still provides a reasonable approximation under normal atmospheric conditions, treating it as an exception.