In physical chemistry, Henry's law is a gas law that states that the amount of dissolved gas in a liquid is directly proportional 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, we can say that the partial pressure of a gas in 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. An everyday example is 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 the solution.
In his 1803 publication about the quantity of gases absorbed by water, [1] William Henry described the results of his experiments:
… water takes up, of gas condensed by one, two, or more additional atmospheres, a quantity which, ordinarily compressed, would be equal to twice, thrice, &c. the volume absorbed under the common pressure of the atmosphere.
Charles Coulston Gillispie states that John Dalton "supposed that the separation of gas particles one from another in the vapor 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." [2]
[[File:Hartwall Jaffa Greippi & Appelsiini.jpg|thumb|upright|Hartwall Jaffa Under high pressure, solubility of CO
2 increases. On opening the bottle to atmospheric pressure, solubility decreases and the gas bubbles are released from the liquid.
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 pressured on its way to the point of service by the action of the beer engine, which causes 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.
Concentration of O
2 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. 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. 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.
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 . Its value increases with increased solubility. Alternatively, numerator and denominator can be switched ("gas/aq"), which results in the Henry's law volatility constant . The value of decreases with increased solubility. IUPAC describes several variants of both fundamental types. [3] 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 (), molality (), and molar mixing ratio (). For the gas phase, molar concentration () and partial pressure () are often used. It is not possible to use the gas-phase mixing ratio () because at a given gas-phase mixing ratio, the aqueous-phase concentration depends on the total pressure and thus the ratio is not a constant. [4] 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, refers to the Henry solubility defined as .
Atmospheric chemists often define the Henry solubility as
Here is the concentration of a species in the aqueous phase, and is the partial pressure of that species in the gas phase under equilibrium conditions.
The SI unit for is mol/(m3·Pa); however, often the unit M/atm is used, since is usually expressed in M (1 M = 1 mol/dm3) and in atm (1 atm = 101325 Pa).
The Henry solubility can also be expressed as the dimensionless ratio between the aqueous-phase concentration of a species and its gas-phase concentration :
For an ideal gas, the conversion is:
where is the gas constant, and is the temperature.
Sometimes, this dimensionless constant is called the water–air partitioning coefficient. [5] It is closely related to the various, slightly different definitions of the Ostwald coefficient, as discussed by Battino (1984). [6]
Another Henry's law solubility constant is:
Here is the molar mixing ratio in the aqueous phase. For a dilute aqueous solution the conversion between and is:
where is the density of water and is the molar mass of water. Thus
The SI unit for is Pa−1, although atm−1 is still frequently used.
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 , since it refers to the mass of the solvent. In contrast, the concentration does change with , 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
Here is used as the symbol for molality (instead of ) to avoid confusion with the symbol for mass. The SI unit for is mol/(kg·Pa). There is no simple way to calculate from , since the conversion between concentration and molality involves all solutes of a solution. For a solution with a total of solutes with indices , the conversion is:
where is the density of the solution, and are the molar masses. Here is identical to one of the in the denominator. If there is only one solute, the equation simplifies to
Henry's law is only valid for dilute solutions where and . In this case the conversion reduces further to
and thus
According to Sazonov and Shaw, [7] the dimensionless Bunsen coefficient 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 is simply
with = 273.15 K. Note, that according to this definition, the conversion factor is not temperature-dependent. Independent of the temperature that the Bunsen coefficient refers to, 273.15 K 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. [3]
According to Sazonov and Shaw, [7] the Kuenen coefficient 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 is
where is the density of the solvent, and = 273.15 K. The SI unit for is m3/kg. [7] The Kuenen coefficient, which is named after Johannes Kuenen, has been used mainly in the older literature, and IUPAC considers it to be obsolete. [3]
A common way to define a Henry volatility is dividing the partial pressure by the aqueous-phase concentration:
The SI unit for is Pa·m3/mol.
Another Henry volatility is
The SI unit for is Pa. However, atm is still frequently used.
The Henry volatility can also be expressed as the dimensionless ratio between the gas-phase concentration of a species and its aqueous-phase concentration :
In chemical engineering and environmental chemistry, this dimensionless constant is often called the air–water partitioning coefficient. [8] [9]
A large compilation of Henry's law constants has been published by Sander (2023). [10] A few selected values are shown in the table below:
Gas | ||||
---|---|---|---|---|
(dimensionless) | ||||
O2 | 770 | 1.3×10−3 | 4.3×104 | 3.2×10−2 |
H2 | 1300 | 7.8×10−4 | 7.1×104 | 1.9×10−2 |
CO2 | 29 | 3.4×10−2 | 1.6×103 | 8.3×10−1 |
N2 | 1600 | 6.1×10−4 | 9.1×104 | 1.5×10−2 |
He | 2700 | 3.7×10−4 | 1.5×105 | 9.1×10−3 |
Ne | 2200 | 4.5×10−4 | 1.2×105 | 1.1×10−2 |
Ar | 710 | 1.4×10−3 | 4.0×104 | 3.4×10−2 |
CO | 1100 | 9.5×10−4 | 5.8×104 | 2.3×10−2 |
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 is the enthalpy of dissolution. Note that the letter in the symbol refers to enthalpy and is not related to the letter for Henry's law constants. This applies to the Henry's solubility ratio, ; for Henry's volatility ratio,, the sign of the right-hand side must be reversed.
Integrating the above equation and creating an expression based on at the reference temperature = 298.15 K yields:
The van 't Hoff equation in this form is only valid for a limited temperature range in which does not change much with temperature (around 20K of variations).
The following table lists some temperature dependencies:
O2 | H2 | CO2 | N2 | He | Ne | Ar | CO |
1700 | 500 | 2400 | 1300 | 230 | 490 | 1300 | 1300 |
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. [12]
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
In aqueous solution, formaldehyde is almost completely hydrated:
The total concentration of dissolved formaldehyde is
Taking this equilibrium into account, an effective Henry's law constant can be defined as
For acids and bases, the effective Henry's law constant is not a useful quantity because it depends on the pH of the solution. [10] In order to obtain a pH-independent constant, the product of the intrinsic Henry's law constant and the acidity constant is often used for strong acids like hydrochloric acid (HCl):
Although is usually also called a Henry's law constant, it is a different quantity and it has different units than .
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 is the Henry's law constant in pure water, is the Henry's law constant in the salt solution, is the molality-based Sechenov constant, and is the molality of the salt.
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 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:
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 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.
Henry's law solubility constant for a gas 2 in a mixture M of two solvents 1 and 3 depends on the individual constants for each solvent, and according [13] to:
Where , 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 , by remembering that and that, both being positive real numbers, , thus:
For a water-ethanol mixture, the interaction parameter a13 has values around for ethanol concentrations (volume/volume) between 5% and 25%. [14]
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
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. [15] 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
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 Hvpx = 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 can also be related to non-gas solutes.
Osmotic pressure is the minimum pressure which needs to be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane. It is also defined as the measure of the tendency of a solution to take in its pure solvent by osmosis. Potential osmotic pressure is the maximum osmotic pressure that could develop in a solution if it were separated from its pure solvent by a semipermeable membrane.
Raoult's law ( law) is a relation of physical chemistry, with implications in thermodynamics. Proposed by French chemist François-Marie Raoult in 1887, it states that the partial pressure of each component of an ideal mixture of liquids is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture. In consequence, the relative lowering of vapor pressure of a dilute solution of nonvolatile solute is equal to the mole fraction of solute in the solution.
In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas as if it alone occupied the entire volume of the original mixture at the same temperature. The total pressure of an ideal gas mixture is the sum of the partial pressures of the gases in the mixture.
In chemistry, solubility is the ability of a substance, the solute, to form a solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form such a solution.
Solubility equilibrium is a type of dynamic equilibrium that exists when a chemical compound in the solid state is in chemical equilibrium with a solution of that compound. The solid may dissolve unchanged, with dissociation, or with chemical reaction with another constituent of the solution, such as acid or alkali. Each solubility equilibrium is characterized by a temperature-dependent solubility product which functions like an equilibrium constant. Solubility equilibria are important in pharmaceutical, environmental and many other scenarios.
In chemical thermodynamics, activity is a measure of the "effective concentration" of a species in a mixture, in the sense that the species' chemical potential depends on the activity of a real solution in the same way that it would depend on concentration for an ideal solution. The term "activity" in this sense was coined by the American chemist Gilbert N. Lewis in 1907.
In chemistry, colligative properties are those properties of solutions that depend on the ratio of the number of solute particles to the number of solvent particles in a solution, and not on the nature of the chemical species present. The number ratio can be related to the various units for concentration of a solution such as molarity, molality, normality (chemistry), etc. The assumption that solution properties are independent of nature of solute particles is exact only for ideal solutions, which are solutions that exhibit thermodynamic properties analogous to those of an ideal gas, and is approximate for dilute real solutions. In other words, colligative properties are a set of solution properties that can be reasonably approximated by the assumption that the solution is ideal.
In electrochemistry, the standard hydrogen electrode, is a redox electrode which forms the basis of the thermodynamic scale of oxidation-reduction potentials. Its absolute electrode potential is estimated to be 4.44 ± 0.02 V at 25 °C, but to form a basis for comparison with all other electrochemical reactions, hydrogen's standard electrode potential is declared to be zero volts at any temperature. Potentials of all other electrodes are compared with that of the standard hydrogen electrode at the same temperature.
In thermochemistry, the enthalpy of solution is the enthalpy change associated with the dissolution of a substance in a solvent at constant pressure resulting in infinite dilution.
In chemistry, an ideal solution or ideal mixture is a solution that exhibits thermodynamic properties analogous to those of a mixture of ideal gases. The enthalpy of mixing is zero as is the volume change on mixing by definition; the closer to zero the enthalpy of mixing is, the more "ideal" the behavior of the solution becomes. The vapor pressures of the solvent and solute obey Raoult's law and Henry's law, respectively, and the activity coefficient is equal to one for each component.
In the physical sciences, a partition coefficient (P) or distribution coefficient (D) is the ratio of concentrations of a compound in a mixture of two immiscible solvents at equilibrium. This ratio is therefore a comparison of the solubilities of the solute in these two liquids. The partition coefficient generally refers to the concentration ratio of un-ionized species of compound, whereas the distribution coefficient refers to the concentration ratio of all species of the compound.
The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency towards further change. For a given set of reaction conditions, the equilibrium constant is independent of the initial analytical concentrations of the reactant and product species in the mixture. Thus, given the initial composition of a system, known equilibrium constant values can be used to determine the composition of the system at equilibrium. However, reaction parameters like temperature, solvent, and ionic strength may all influence the value of the equilibrium constant.
In chemical thermodynamics, the fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of chemical equilibrium. It is equal to the pressure of an ideal gas which has the same temperature and molar Gibbs free energy as the real gas.
In thermodynamics, an activity coefficient is a factor used to account for deviation of a mixture of chemical substances from ideal behaviour. In an ideal mixture, the microscopic interactions between each pair of chemical species are the same and, as a result, properties of the mixtures can be expressed directly in terms of simple concentrations or partial pressures of the substances present e.g. Raoult's law. Deviations from ideality are accommodated by modifying the concentration by an activity coefficient. Analogously, expressions involving gases can be adjusted for non-ideality by scaling partial pressures by a fugacity coefficient.
Dissociation in chemistry is a general process in which molecules (or ionic compounds such as salts, or complexes) separate or split into other things such as atoms, ions, or radicals, usually in a reversible manner. For instance, when an acid dissolves in water, a covalent bond between an electronegative atom and a hydrogen atom is broken by heterolytic fission, which gives a proton (H+) and a negative ion. Dissociation is the opposite of association or recombination.
Flory–Huggins solution theory is a lattice model of the thermodynamics of polymer solutions which takes account of the great dissimilarity in molecular sizes in adapting the usual expression for the entropy of mixing. The result is an equation for the Gibbs free energy change for mixing a polymer with a solvent. Although it makes simplifying assumptions, it generates useful results for interpreting experiments.
The Langmuir adsorption model explains adsorption by assuming an adsorbate behaves as an ideal gas at isothermal conditions. According to the model, adsorption and desorption are reversible processes. This model even explains the effect of pressure; i.e., at these conditions the adsorbate's partial pressure is related to its volume V adsorbed onto a solid adsorbent. The adsorbent, as indicated in the figure, is assumed to be an ideal solid surface composed of a series of distinct sites capable of binding the adsorbate. The adsorbate binding is treated as a chemical reaction between the adsorbate gaseous molecule and an empty sorption site S. This reaction yields an adsorbed species with an associated equilibrium constant :
An osmotic coefficient is a quantity which characterises the deviation of a solvent from ideal behaviour, referenced to Raoult's law. It can be also applied to solutes. Its definition depends on the ways of expressing chemical composition of mixtures.
In thermodynamics, the enthalpy of fusion of a substance, also known as (latent) heat of fusion, is the change in its enthalpy resulting from providing energy, typically heat, to a specific quantity of the substance to change its state from a solid to a liquid, at constant pressure.
Equilibrium chemistry is concerned with systems in chemical equilibrium. The unifying principle is that the free energy of a system at equilibrium is the minimum possible, so that the slope of the free energy with respect to the reaction coordinate is zero. This principle, applied to mixtures at equilibrium provides a definition of an equilibrium constant. Applications include acid–base, host–guest, metal–complex, solubility, partition, chromatography and redox equilibria.