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In physical
chemistry Chemistry is the scientific discipline involved with Chemical element, elements and chemical compound, compounds composed of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during a Ch ...
, Henry's law is a
gas law The gas laws were developed at the end of the 18th century, when scientists began to realize that relationships between pressure, volume and temperature of a sample of gas could be obtained which would hold to approximation for all gases. Boyle' ...
that states that the amount of dissolved gas in a liquid is proportional to its
partial pressure In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas if it alone occupied the entire volume of the original mixture at the same temperature. The total pressure of an ideal gas m ...
above the liquid. The proportionality factor is called Henry's law constant. It was 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: 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 Decompression sickness (DCS; also known as divers' disease, the bends, aerobullosis, or caisson disease) describes a condition arising from dissolved gases coming out of solution into bubbles inside the body on depressurisation. DCS most common ...
. An everyday example is given by one's experience with carbonated
soft drink A soft drink (see § Terminology for other names) is a drink that usually contains carbonated water (although some vitamin waters and lemonades are not carbonated), a sweetener, and a natural and/or artificial flavoring. The sweetener m ...
s, which contain dissolved carbon dioxide. Before opening, the gas above the drink in its container is almost pure
carbon dioxide Carbon dioxide (chemical formula ) is a colorless gas with a density about 53% higher than that of dry air. Carbon dioxide molecules consist of a carbon atom covalent bond, covalently double bonded to two oxygen atoms. It occurs naturally in At ...

carbon dioxide
, at a pressure higher than
atmospheric pressure Atmospheric pressure, also known as barometric pressure (after the barometer), is the pressure within the atmosphere of Earth File:Atmosphere gas proportions.svg, Composition of Earth's atmosphere by volume, excluding water vapor. Lower pie ...
. 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 the solution.


Background

Charles Coulston Gillispie Charles Coulston Gillispie (; August 6, 1918 – October 6, 2015) was an American historian of science. He was the Dayton-Stockton Professor of History of Science, Emeritus at Princeton University. He was succeeded by Arno J. Mayer. Life The son of ...
states that
John Dalton John Dalton (; 6 September 1766 – 27 July 1844) was an English chemist, physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, ...
"supposed that the separation of gas particles one from another in the
vapor In physics, a vapor (American English American English (AmE, AE, AmEng, USEng, en-US), sometimes called United States English or U.S. English, is the set of varieties of the English language native to the United States. Currently, America ...
phase bears the ratio of a small whole number to their interatomic distance in solution. Henry's law follows as a consequence if this ratio is a constant for each gas at a given temperature."


Applications of Henry's law

; In production of carbonated beverages: Under high pressure, solubility of increases. On opening the bottle to atmospheric pressure, solubility decreases and the gas bubbles are released from the liquid. ; For climbers or people living at high altitude: Concentration of in the blood and tissues is so low that they feel weak and are unable to think properly, a condition called hypoxia. ; In underwater diving: Gas is breathed at the ambient pressure which increases with depth due to the
hydrostatic pressure Fluid statics or hydrostatics is the branch of fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical object ...
. Solubility of gases increase at depth in accordance with Henry's law, so the body tissues take on more gas over time until saturated for the depth. When ascending the diver is decompressed and the solubility of the gases dissolved in the tissues decreases accordingly. If the supersaturation is too great, bubbles may form and grow, and the presence of these bubbles can cause blockages in capillaries, or distortion in the more solid tissues which can cause damage known as
decompression sickness Decompression sickness (DCS; also known as divers' disease, the bends, aerobullosis, or caisson disease) describes a condition arising from dissolved gases coming out of solution into bubbles inside the body on depressurisation. DCS most common ...
. To avoid this injury the diver must ascend slow enough that the excess dissolved gas is carried away by the blood and released into the lung gas.


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 gaseous phase into the denominator ("aq/gas"). This results in the Henry's law solubility constant H. Its value increases with increased solubility. Alternatively, numerator and denominator can be switched ("gas/aq"), which results in the Henry's law volatility constant K_. The value of K_ decreases with increased solubility. There are several variants of both fundamental types. This results from the multiplicity of quantities that can be chosen to describe the composition of the two phases. Typical choices for the aqueous phase are
molar concentration Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solution, solute in a solution, in terms of amount of substance per unit volume ...
(c_),
molality Molality is a measure of number of moles of solute present in 1 kg of solvent. This contrasts with the definition of molarity Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the conce ...
(b), and molar mixing ratio (x). For the gas phase, molar concentration (c_) and
partial pressure In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas if it alone occupied the entire volume of the original mixture at the same temperature. The total pressure of an ideal gas m ...
(p) are often used. It is not possible to use the gas-phase mixing ratio (y) because at a given gas-phase mixing ratio, the aqueous-phase concentration c_ depends on the total pressure and thus the ratio y/c_ is not a constant. To specify the exact variant of the Henry's law constant, two superscripts are used. They refer to the numerator and the denominator of the definition. For example, H^ refers to the Henry solubility defined as c/p.


Henry's law solubility constants H


Henry solubility defined via concentration (H^)

Atmospheric chemists often define the Henry solubility as :H^ = \frac. Here c_\text is the concentration of a species in the aqueous phase, and p is the partial pressure of that species in the gas phase under equilibrium conditions. The SI unit for H^ is mol/(m3·Pa); however, often the unit M/atm is used, since c_\text is usually expressed in M (1M = 1 mol/dm3) and p in atm (1atm = 101325Pa).


The dimensionless Henry solubility H^

The Henry solubility can also be expressed as the dimensionless ratio between the aqueous-phase concentration c_\text of a species and its gas-phase concentration c_\text: :H^ = \frac. For an ideal gas, the conversion is :H^ = RTH^, where R is the gas constant, and T is the temperature. Sometimes, this dimensionless constant is called the ''water–air partitioning coefficient'' K_\text. It is closely related to the various, slightly different definitions of the ''Ostwald coefficient'' L, as discussed by Battino (1984).


Henry solubility defined via aqueous-phase mixing ratio (H^)

Another Henry's law solubility constant is :H^ = \frac . Here x is the molar mixing ratio in the aqueous phase. For a dilute aqueous solution the conversion between x and c_\text is: :c_\text \approx x \frac, where \varrho_\mathrm is the density of water and M_\mathrm is the molar mass of water. Thus :H^ \approx \frac H^. The SI unit for H^ is Pa−1, although atm−1 is still frequently used.


Henry solubility defined via molality (H^)

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 T, since it refers to the ''mass'' of the solvent. In contrast, the concentration c does change with T, since the density of a solution and thus its volume are temperature-dependent. Defining the aqueous-phase composition via molality has the advantage that any temperature dependence of the Henry's law constant is a true solubility phenomenon and not introduced indirectly via a density change of the solution. Using molality, the Henry solubility can be defined as :H^ = \frac. Here b is used as the symbol for molality (instead of m) to avoid confusion with the symbol m for mass. The SI unit for H^ is mol/(kg·Pa). There is no simple way to calculate H^ from H^, since the conversion between concentration c_\text and molality b involves ''all'' solutes of a solution. For a solution with a total of n solutes with indices i = 1, \ldots, n, the conversion is: :c_\text = \frac, where \varrho is the density of the solution, and M_i are the molar masses. Here b is identical to one of the b_i in the denominator. If there is only one solute, the equation simplifies to :c_\text = \frac. Henry's law is only valid for dilute solutions where bM \ll 1 and \varrho \approx \varrho_\mathrm. In this case the conversion reduces further to :c_\text \approx b \varrho_\mathrm, and thus :H^ \approx \frac.


The Bunsen coefficient \alpha

According to Sazonov and Shaw, the dimensionless Bunsen coefficient \alpha is defined as "the volume of saturating gas, V1, reduced to T° = 273.15 K, p° = 1 bar, which is absorbed by unit volume V2* of pure solvent at the temperature of measurement and partial pressure of 1 bar." If the gas is ideal, the pressure cancels out, and the conversion to H^ is simply :H^ = \alpha\frac, with T^\text = 273.15K. Note, that according to this definition, the conversion factor is ''not'' temperature-dependent. Independent of the temperature that the Bunsen coefficient refers to, 273.15K is always used for the conversion. The Bunsen coefficient, which is named after Robert Bunsen, has been used mainly in the older literature.


The Kuenen coefficient S

According to Sazonov and Shaw, the Kuenen coefficient S is defined as "the volume of saturating gas V(g), reduced to T° = 273.15 K, p° = bar, which is dissolved by unit mass of pure solvent at the temperature of measurement and partial pressure 1 bar." If the gas is ideal, the relation to H^ is :H^ = S\frac, where \varrho is the density of the solvent, and T^\text = 273.15 K. The SI unit for S is m3/kg. The Kuenen coefficient, which is named after Johannes Kuenen, has been used mainly in the older literature, and IUPAC considers it to be obsolete.


Henry's law volatility constants K_\text


The Henry volatility defined via concentration (K_\text^)

A common way to define a Henry volatility is dividing the partial pressure by the aqueous-phase concentration: :K_\text^ = \frac = \frac. The SI unit for K_\text^ is Pa·m3/mol.


The Henry volatility defined via aqueous-phase mixing ratio (K_\text^)

Another Henry volatility is :K_\text^ = \frac = \frac. The SI unit for K_\text^ is Pa. However, atm is still frequently used.


The dimensionless Henry volatility K_\text^

The Henry volatility can also be expressed as the dimensionless ratio between the gas-phase concentration c_\text of a species and its aqueous-phase concentration c_\text: :K_\text^ = \frac = \frac. In chemical engineering and environmental chemistry, this dimensionless constant is often called the ''air–water partitioning coefficient'' K_\text.


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: :\frac = \frac, where \Delta_\textH is the enthalpy of dissolution. Note that the letter H in the symbol \Delta_\textH refers to enthalpy and is not related to the letter H for Henry's law constants. Integrating the above equation and creating an expression based on H^\circ at the reference temperature T^\circ = 298.15 K yields: :H(T) = H^\circ\exp\left[\frac\left(\frac - \frac\right)\right]. The van 't Hoff equation in this form is only valid for a limited temperature range in which \Delta_\textH does not change much with temperature. 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

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 formaldehyde can be defined as :H^\ce = \frac. In aqueous solution, formaldehyde is almost completely hydrated: :H2CO + H2O <=> H2C(OH)2 The total concentration of dissolved formaldehyde is :c_\ce = c\left(\ce\right) + c\left(\ce\right). Taking this equilibrium into account, an effective Henry's law constant H_\ce can be defined as :H_\ce = \frac = \frac. 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 H^\ce and the acidity constant K_\ce is often used for strong acids like hydrochloric acid (HCl): :H' = H^\ce K_\ce = \frac. Although H' is usually also called a Henry's law constant, it is a different quantity and it has different units than H^\ce.


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 :\log\left(\frac\right) = k_\textb(\text), where H^_0 is the Henry's law constant in pure water, H^ is the Henry's law constant in the salt solution, k_\text is the molality-based Sechenov constant, and b(\text) is the molality of the salt.


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: :\mu = \mu_c^\circ + RT\ln\frac, where \gamma_c = \frac for a volatile solute; ''c''° = 1 mol/L. 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: :\sum_i n_i d\mu_i = 0. 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 molality, molalities ''b'' rather than concentrations, e.g.: :\mu = \mu_b^\circ + RT\ln\frac, where \gamma_b = \frac for a volatile solute; ''b''° = 1 mol/kg. The standard chemical potential ''μm''°, the activity coefficient ''γm'' and the Henry's law constant ''K''H,''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: :\ln H_ = x_1 \ln H_ + x_3 \ln H_ - a_ x_1 x_3 where a13 is the interaction parameter of the solvents from Wohl expansion of the excess chemical potential of the ternary mixtures.


Miscellaneous


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 :\frac = \exp\left[-\beta\left(\mu^\text_\text - \mu^\text_\text\right)\right], where :''C'' is the number concentrations of the solute gas in the melt and gas phases, :''β'' = 1/''k''B''T'', an inverse temperature parameter (''k''B is the Boltzmann constant), :''µ''E 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, while Raoult's law is generally valid when the liquid phase is almost pure or for mixtures of similar substances. The range of concentrations in which Henry's law 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 :p = K_\text x. This can be compared with Raoult's law: :p = p^* x, 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 ''K''H = ''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 of a function, 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: \lim_\left( \frac \right) = p^*. :Henry's law: \lim_\left( \frac \right) = K_\text. Raoult's law can also be related to non-gas solutes.


See also

* * * * * *


References


External links


EPA On-line Tools for Site Assessment Calculation – Henry's law conversion
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