Henry’s Law states that, at a constant temperature, the partial pressure of a gaseous species in equilibrium with its liquid form is directly proportional to its mole fraction in dilute solutions. Mathematically, Henry’s Law can be expressed as:
where:
is the partial pressure of the gas,
is the Henry’s Law constant (which varies with temperature),
is the mole fraction of the gas in the liquid.
The law was empirically derived in 1803 by William Henry, an English chemist. While Raoult’s law describes how the vapour pressure of a solvent is lowered when a non-volatile solute is added to an ideal solution, Henry’s law is primarily used to predict the solubility of a gas in real solutions, with important applications in environmental science, chemical engineering and biology. In other words, both the solute and solvent obey Raoult’s law in an ideal solution, while the solute follows Henry’s law in a real dilute solution (see diagram below). This is because, in a real dilute solution, each solute molecule is almost exclusively surrounded by solvent molecules, and its behaviour is determined by interactions with the solvent, not with other solute molecules. The proportionality constant reflects these solute-solvent interactions.
Despite being an empirical law, Henry’s law can be derived using basic thermodynamics principles. At equilibrium, the chemical potential of the gas in the gas phase must be equal to its chemical potential in the solution. Rearranging eq182, where is defined as 1 atm (the convention for the standard state of gases), gives
Since the exponential factor is a constant for a given temperature, eq188 is equivalent to eq187, with .
A solute-solvent system in which the mole fraction of the solvent is close to 1, and the two species have different intermolecular interactions, is called an ideal-dilute solution (see diagram above). In such a solution, the solvent obeys Raoult’s law (ideal) and the solute follows Henry’s law (dilute). The distinct behaviours exhibited by the solute and solvent in such solutions can be attributed to fundamental differences in their molecular environments.
In a dilute solution, solvent molecules are predominantly surrounded by other solvent molecules. As a result, their immediate molecular environment closely approximates that of the pure liquid solvent. This preservation of their native environment explains why the solvent’s vapour pressure continues to align with Raoult’s law, which describes the vapour pressure of an ideal pure component.
Conversely, solute molecules in a dilute solution are almost exclusively surrounded by solvent molecules. This marks a significant departure from their pure state, where they would typically be surrounded solely by other solute molecules. Due to this altered molecular environment, the solute’s behaviour, particularly its partial vapour pressure, deviates considerably from what might be expected from its pure form. This distinct behaviour is precisely what Henry’s law describes.
Therefore, the solvent behaves effectively as a slightly perturbed pure liquid, while the solute exhibits fundamentally different behaviour. Many naturally occuring systems are ideal-dilute solutions. For example, the small amount of dissolved oxygen in natural waters or blood follows Henry’s Law, while the water (solvent) makes up the majority and its vapour pressure is essentially determined by Raoult’s Law. In carbonated drinks, the dissolution of CO2 is well-described by Henry’s Law, while the water acts as the Raoultian solvent.