In chemistry, Henry's law is one of the gas laws formulated by the English chemist William Henry, who studied the topic in the early 19th century. In his publication about the quantity of gases absorbed by water, he described the results of his experiments:
Contents
- Fundamental types and variants of Henrys law constants
- Henry solubility defined via concentration H c p displaystyle Hcp
- The dimensionless Henry solubility H c c displaystyle Hcc
- Henry solubility defined via aqueous phase mixing ratio H x p displaystyle Hxp
- Henry solubility defined via molality H b p displaystyle Hbp
- The Bunsen coefficient displaystyle alpha
- The Kuenen coefficient S displaystyle S
- The Henry volatility defined via concentration K H p c displaystyle K extHpc
- The Henry volatility defined via aqueous phase mixing ratio K H p x displaystyle K extHpx
- The dimensionless Henry volatility K H c c displaystyle K extHcc
- Values of Henrys law constants
- Temperature dependence
- Effective Henrys law constants H e f f displaystyle H m eff
- Dependence on ionic strength Sechenov equation
- Non ideal solutions
- Solvent mixtures
- In geochemistry
- Comparison to Raoults law
- References
In other words, the amount of dissolved gas is proportional to its partial pressure in the gas phase. The proportionality factor is called the Henry's law constant.
An example where Henry's law is at play is in the depth-dependent dissolution of oxygen and nitrogen in the blood of underwater divers that changes during decompression, leading to decompression sickness. An everyday example is given by one's experience with carbonated soft drinks, which contain dissolved carbon dioxide. Before opening, the gas above the drink in its container is almost pure carbon dioxide, at a pressure higher than atmospheric pressure. After the bottle is opened, this gas escapes, moving the partial pressure of carbon dioxide above the liquid to be much lower, resulting in degassing as the dissolved carbon dioxide comes out of solution.
Fundamental types and variants of Henry's law constants
There are many ways to define the proportionality constant of Henry's law, which can be subdivided into two fundamental types: One possibility is to put the aqueous phase into the numerator and the gas phase into the denominator ("aq/gas"). This results in the Henry's law solubility constant
Henry solubility defined via concentration ( H c p {displaystyle H^{cp}} )
Atmospheric chemists often define the Henry solubility as
Here
The SI unit for
The dimensionless Henry solubility H c c {displaystyle H^{cc}}
The Henry solubility can also be expressed as the dimensionless ratio between the aqueous-phase concentration
For an ideal gas, the conversion is:
where
Sometimes, this dimensionless constant is called the "water-air partitioning coefficient"
Henry solubility defined via aqueous-phase mixing ratio ( H x p {displaystyle H^{xp}} )
Another Henry's law solubility constant is
Here
where
The SI unit for
Henry solubility defined via molality ( H b p {displaystyle H^{bp}} )
It can be advantageous to describe the aqueous phase in terms of molality instead of concentration. The molality of a solution does not change with
Here
where
Henry's law is only valid for dilute solutions where
and thus
The Bunsen coefficient α {displaystyle alpha }
According to Sazonov and Shaw, the dimensionless Bunsen coefficient
with
The Kuenen coefficient S {displaystyle S}
According to Sazonov and Shaw, the Kuenen coefficient
where
The Henry volatility defined via concentration ( K H p c {displaystyle K_{ ext{H}}^{pc}} )
A common way to define a Henry volatility is dividing the partial pressure by the aqueous-phase concentration:
The SI unit for
The Henry volatility defined via aqueous-phase mixing ratio ( K H p x {displaystyle K_{ ext{H}}^{px}} )
Another Henry volatility is
The SI unit for
The dimensionless Henry volatility K H c c {displaystyle K_{ ext{H}}^{cc}}
The Henry volatility can also be expressed as the dimensionless ratio between the gas-phase concentration
In chemical engineering and environmental chemistry, this dimensionless constant is often called the air–water partitioning coefficient
Values of Henry's law constants
A large compilation of Henry's law constants has been published by Sander (2015). A few selected values are shown in the table below:
Temperature dependence
When the temperature of a system changes, the Henry constant also changes. The temperature dependence of equilibrium constants can generally be described with the van 't Hoff equation, which also applies to Henry's law constants:
where
The van 't Hoff equation in this form is only valid for a limited temperature range in which
The following table lists some temperature dependencies:
Solubility of permanent gases usually decreases with increasing temperature at around room temperature. However, for aqueous solutions, the Henry's law solubility constant for many species goes through a minimum. For most permanent gases, the minimum is below 120 °C. Often, the smaller the gas molecule (and the lower the gas solubility in water), the lower the temperature of the maximum of the Henry's law constant. Thus, the maximum is at about 30 °C for helium, 92 to 93 °C for argon, nitrogen and oxygen, and 114 °C for xenon.
Effective Henry's law constants H e f f {displaystyle H_{ m {eff}}}
The Henry's law constants mentioned so far do not consider any chemical equilibria in the aqueous phase. This type is called the "intrinsic" (or "physical") Henry's law constant. For example, the intrinsic Henry's law solubility constant of methanal can be defined as
In aqueous solution, methanal is almost completely hydrated:
The total concentration of dissolved methanal is
Taking this equilibrium into account, an effective Henry's law constant
For acids and bases, the effective Henry's law constant is not a useful quantity because it depends on the pH of the solution. In order to obtain a pH-independent constant, the product of the intrinsic Henry's law constant
Although
Dependence on ionic strength (Sechenov equation)
Values of Henry's law constants for aqueous solutions depend on the composition of the solution, i.e., on its ionic strength and on dissolved organics. In general, the solubility of a gas decreases with increasing salinity ("salting out"). However, a "salting in" effect has also been observed, for example for the effective Henry's law constant of glyoxal. The effect can be described with the Sechenov equation, named after the Russian physiologist Ivan Sechenov (sometimes the German transliteration "Setschenow" of the Cyrillic name Се́ченов is used). There are many alternative ways to define the Sechenov equation, depending on how the aqueous-phase composition is described (based on concentration, molality, or molar fraction) and which variant of the Henry's law constant is used. Describing the solution in terms of molality is preferred because molality is invariant to temperature and to the addition of dry salt to the solution. Thus, the Sechenov equation can be written as
where
Non-ideal solutions
Henry's law has been shown to apply to a wide range of solutes in the limit of "infinite dilution" (x → 0), including non-volatile substances such as sucrose. In these cases, it is necessary to state the law in terms of chemical potentials. For a solute in an ideal dilute solution, the chemical potential depends only on the concentration. For non-ideal solutions, the activity coefficients of the components must be taken into account:
where
For non-ideal solutions, the activity coefficient γc depends on the concentration and must be determined at the concentration of interest. The activity coefficient can also be obtained for non-volatile solutes, where the vapor pressure of the pure substance is negligible, by using the Gibbs-Duhem relation:
By measuring the change in vapor pressure (and hence chemical potential) of the solvent, the chemical potential of the solute can be deduced.
The standard state for a dilute solution is also defined in terms of infinite-dilution behavior. Although the standard concentration c° is taken to be 1 mol/l by convention, the standard state is a hypothetical solution of 1 mol/l in which the solute has its limiting infinite-dilution properties. This has the effect that all non-ideal behavior is described by the activity coefficient: the activity coefficient at 1 mol/l is not necessarily unity (and is frequently quite different from unity).
All the relations above can also be expressed in terms of molalities b rather than concentrations, e.g.:
where
The standard chemical potential μm°, the activity coefficient γm and the Henry's law constant KH,b all have different numerical values when molalities are used in place of concentrations.
Solvent mixtures
Henry law constant H2, M for a gas 2 in a mixture of solvents 1 and 3 is related to the constants for individual solvents H21 and H23:
where a13 is the interaction parameter of the solvents from Wohl expansion of the excess chemical potential of the ternary mixtures.
In geochemistry
In geochemistry, a version of Henry's law applies to the solubility of a noble gas in contact with silicate melt. One equation used is
where
C is the number concentrations of the solute gas in the melt and gas phases, β = 1/kBT, an inverse temperature parameter (kB is the Boltzmann constant), µE is the excess chemical potentials of the solute gas in the two phases.Comparison to Raoult's law
Henry's law is a limiting law that only applies for "sufficiently dilute" solutions. The range of concentrations in which it applies becomes narrower the more the system diverges from ideal behavior. Roughly speaking, that is the more chemically "different" the solute is from the solvent.
For a dilute solution, the concentration of the solute is approximately proportional to its mole fraction x, and Henry's law can be written as
This can be compared with Raoult's law:
where p* is the vapor pressure of the pure component.
At first sight, Raoult's law appears to be a special case of Henry's law, where KH = p*. This is true for pairs of closely related substances, such as benzene and toluene, which obey Raoult's law over the entire composition range: such mixtures are called "ideal mixtures".
The general case is that both laws are limit laws, and they apply at opposite ends of the composition range. The vapor pressure of the component in large excess, such as the solvent for a dilute solution, is proportional to its mole fraction, and the constant of proportionality is the vapor pressure of the pure substance (Raoult's law). The vapor pressure of the solute is also proportional to the solute's mole fraction, but the constant of proportionality is different and must be determined experimentally (Henry's law). In mathematical terms:
Raoult's law:Raoult's law can also be related to non-gas solutes.