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In physical chemistry, Henry's law is a gas law that states that the amount of dissolved gas in a liquid is directly proportional at equilibrium to its partial pressure 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 simple words, it states that the partial pressure of a gas in the vapour phase is directly proportional to the mole fraction of a gas in solution. An example where Henry's law is at play is the depth-dependent dissolution of oxygen and nitrogen in the blood of underwater divers that changes during decompression, going to
decompression sickness Decompression sickness (DCS; also called divers' disease, the bends, aerobullosis, and caisson disease) is a medical condition caused by dissolved gases emerging from Solution (chemistry), solution as bubbles inside the body tissues during D ...
. An everyday example is carbonated
soft drink A soft drink (see #Terminology, § Terminology for other names) is a class of non-alcoholic drink, usually (but not necessarily) Carbonated water, carbonated, and typically including added Sweetness, sweetener. Flavors used to be Natural flav ...
s, which contain dissolved carbon dioxide. Before opening, the gas above the drink in its container is almost pure
carbon dioxide Carbon dioxide is a chemical compound with the chemical formula . It is made up of molecules that each have one carbon atom covalent bond, covalently double bonded to two oxygen atoms. It is found in a gas state at room temperature and at norma ...
, at a pressure higher than
atmospheric pressure Atmospheric pressure, also known as air pressure or barometric pressure (after the barometer), is the pressure within the atmosphere of Earth. The standard atmosphere (symbol: atm) is a unit of pressure defined as , which is equivalent to 1,013. ...
. 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.


History

In his 1803 publication about the quantity of gases absorbed by water, William Henry described the results of his experiments:
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 at Princeton University, and was credited with building Princeton's history of scie ...
states that
John Dalton John Dalton (; 5 or 6 September 1766 – 27 July 1844) was an English chemist, physicist and meteorologist. He introduced the atomic theory into chemistry. He also researched Color blindness, colour blindness; as a result, the umbrella term ...
"supposed that the separation of gas particles one from another in the
vapor In physics, a vapor (American English) or vapour (Commonwealth English; American and British English spelling differences#-our, -or, see spelling differences) is a substance in the gas phase at a temperature lower than its critical temperature,R ...
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


In production of carbonated beverages

Under high pressure, solubility of increases. On opening a container of a carbonated beverage under pressure, pressure decreases to atmospheric, so that solubility decreases and the carbon dioxide forms bubbles that are released from the liquid.


In the service of cask-conditioned beer

It is often noted that beer served by gravity (that is, directly from a tap in the cask) is less heavily carbonated than the same beer served via a hand-pump (or beer-engine). This is because beer is pressurised on its way to the point of service by the action of the beer engine, causing carbon dioxide to dissolve in the beer. This then comes out of solution once the beer has left the pump, causing a higher level of perceptible 'condition' in the beer.


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

In
underwater diving Underwater diving, as a human activity, is the practice of descending below the water's surface to interact with the environment. It is also often referred to as diving (disambiguation), diving, an ambiguous term with several possible meani ...
, gas is breathed at the ambient pressure which increases with depth due to the hydrostatic pressure. Solubility of gases increases with greater depth (greater pressure) according to Henry's law, so the body tissues take on more gas over time in greater depths of water. 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 called divers' disease, the bends, aerobullosis, and caisson disease) is a medical condition caused by dissolved gases emerging from Solution (chemistry), solution as bubbles inside the body tissues during D ...
. To avoid this injury the diver must ascend slowly 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 H_. The value of H_ decreases with increased solubility.
IUPAC The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
describes 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 (c_), molality (b), and molar mixing ratio (x). For the gas phase, molar concentration (c_) and partial pressure (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 ''Hs''


Henry solubility defined via concentration (''H''s''cp'')

Atmospheric chemists often define the Henry solubility as H_\text^ = \frac, where 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 The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of units of measurement, system of measurement. It is the only system ...
for H_\text^ 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''s''cc''

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_\text^ = \frac. For an ideal gas, the conversion is H_\text^ = RTH_\text^, 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''s''xp'')

Another Henry's law solubility constant is H_\text^ = \frac, where 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 \rho_\ce is the density of water, and M_\ce is the molar mass of water. Thus H_\text^ \approx \frac H_\text^. The SI unit for H_\text^ is Pa−1, although atm−1 is still frequently used.


Henry solubility defined via molality (''H''s''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 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_\text^ = \frac, where 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_\text^ is mol/(kg·Pa). There is no simple way to calculate H_\text^ from H_\text^, 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 \rho 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 \rho \approx \rho_\ce. In this case the conversion reduces further to c_\text \approx b \rho_\ce, and thus H_\text^ \approx \frac.


The Bunsen coefficient ''α''

According to Sazonov and Shaw, the dimensionless Bunsen coefficient \alpha is defined as "the volume of saturating gas, ''V''1, reduced to ''T''° = 273.15 K, ''p''° = 1 bar, which is absorbed by unit volume ''V''2* 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_\text^ is simply H_\text^ = \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, and IUPAC considers it to be obsolete.


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_\text^ is H_\text^ = S \frac, where \rho 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 ''H''v


The Henry volatility defined via concentration (''H'')

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


The Henry volatility defined via aqueous-phase mixing ratio (''H'')

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


The dimensionless Henry volatility ''H''

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 :H_^ = \frac = \frac. In
chemical engineering Chemical engineering is an engineering field which deals with the study of the operation and design of chemical plants as well as methods of improving production. Chemical engineers develop economical commercial processes to convert raw materials ...
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 (2023). 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. This applies to the Henry's solubility ratio, H_s; for Henry's volatility ratio,H_v, the sign of the right-hand side must be reversed. 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 (around 20K of variations). 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_ can be defined as :H_ = \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_b(\text), where H_^ is the Henry's law constant in pure water, H_^ is the Henry's law constant in the salt solution, k_ 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 potential In thermodynamics, the chemical potential of a Chemical specie, species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potent ...
s. 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 infinite dilution 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 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 ''Hvpb'' all have different numerical values when molalities are used in place of concentrations.


Solvent mixtures

Henry's law solubility constant H_^ for a gas 2 in a mixture M of two solvents 1 and 3 depends on the individual constants for each solvent, H_^ and H_^ according to: : \ln H_^ = x_1 \ln H_^ + x_3 \ln H_^ + a_ x_1 x_3 Where x_1, x_3 are the molar ratios of each solvent in the mixture and a13 is the interaction parameter of the solvents from Wohl expansion of the excess chemical potential of the ternary mixtures. A similar relationship can be found for the volatility constant H_^, by remembering that H_^=1/H_^ and that, both being positive real numbers, \ln H_^=-\ln (1/H_^) = -\ln H_^ , thus: : \ln H_^ = x_1 \ln H_^ + x_3 \ln H_^ - a_ x_1 x_3 For a water-ethanol mixture, the interaction parameter a13 has values around 0.1 \pm 0.05 for ethanol concentrations (volume/volume) between 5% and 25%.


Miscellaneous


In geochemistry

In
geochemistry Geochemistry is the science that uses the tools and principles of chemistry to explain the mechanisms behind major geological systems such as the Earth's crust and its oceans. The realm of geochemistry extends beyond the Earth, encompassing the e ...
, a version of Henry's law applies to the solubility of a
noble gas The noble gases (historically the inert gases, sometimes referred to as aerogens) are the members of Group (periodic table), group 18 of the periodic table: helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), radon (Rn) and, in some ...
in contact with
silicate A silicate is any member of a family of polyatomic anions consisting of silicon and oxygen, usually with the general formula , where . The family includes orthosilicate (), metasilicate (), and pyrosilicate (, ). The name is also used ...
melt. One equation used is :\frac = \exp\left \beta\left(\mu^\text_\text - \mu^\text_\text\right)\right where :''C'' is the number concentration 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 potential In thermodynamics, the chemical potential of a Chemical specie, species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potent ...
s 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 = H_^ 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 ''Hvpx'' = ''p''*. This is true for pairs of closely related substances, such as
benzene Benzene is an Organic compound, organic chemical compound with the Chemical formula#Molecular formula, molecular formula C6H6. The benzene molecule is composed of six carbon atoms joined in a planar hexagonal Ring (chemistry), ring with one hyd ...
and
toluene Toluene (), also known as toluol (), is a substituted aromatic hydrocarbon with the chemical formula , often abbreviated as , where Ph stands for the phenyl group. It is a colorless, water Water is an inorganic compound with the c ...
, 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: \lim_\left( \frac \right) = p^*. :Henry's law: \lim_\left( \frac \right) = H_^. 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
{{authority control Physical chemistry Eponymous laws of physics Equilibrium chemistry Engineering thermodynamics Gas laws Underwater diving physics