Henry\'s law - Citizendia

In chemistry, Henry's law is one of the gas laws, formulated by William Henry. Chemistry (from Egyptian kēme (chem meaning "earth") is the Science concerned with the composition structure and properties This articles outlines the historical development of the laws describing ideal gases For other men with the same name see Wiliam Henry (disambiguation. It states that:

At a constant temperature, the amount of a given gas dissolved in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid. In a mixture of Ideal gases each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume

1 Formula and Henry constant
- 1.1 Other forms of Henry's law
- 1.2 Temperature dependence of the Henry constant
2 Henry's law in geophysics
3 Henry's law versus Raoult's law
4 See also
5 References
6 External links

Formula and Henry constant

A formula for Henry's Law is:

$e^{p\,} = e^{kc\,} \,$

where:

$e\,$ is approximately 2. 7182818, the base of the natural logarithm (also called Euler's number)

$p\,$ is the partial pressure of the solute above the solution

$c\,$ is the concentration of the solute in the solution (in one of its many units)

$k\,$ is the Henry's Law constant, which has units such as L·atm/mol, atm/(mol fraction) or Pa·m³/mol. The natural logarithm, formerly known as the Hyperbolic logarithm is the Logarithm to the base e, where e is an irrational The Mathematical constant e is the unique Real number such that the function e x has the same value as the slope of the tangent line In a mixture of Ideal gases each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume In Chemistry, a solution is a Homogeneous Mixture composed of two or more substances In Chemistry, a solution is a Homogeneous Mixture composed of two or more substances In Chemistry, concentration is the measure of how much of a given substance there is mixed with another substance

Taking the natural logarithm of the formula, gives us the more commonly used formula:^[1]

$p = kc \,$

Some values for k include:

oxygen (O₂) : 769. The natural logarithm, formerly known as the Hyperbolic logarithm is the Logarithm to the base e, where e is an irrational Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the 2 L·atm/mol

carbon dioxide (CO₂) : 29. Carbon dioxide ( Chemical formula:) is a Chemical compound composed of two Oxygen Atoms covalently bonded to a single 4 L·atm/mol

hydrogen (H₂) : 1282. Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 1 L·atm/mol

when these gases are dissolved in water at 298 kelvin. Water is a common Chemical substance that is essential for the survival of all known forms of Life. The kelvin (symbol K) is a unit increment of Temperature and is one of the seven SI base units The Kelvin scale is a thermodynamic

Note that in the above, the unit of concentration was chosen to be molarity. In Chemistry, concentration is the measure of how much of a given substance there is mixed with another substance Hence the dimensional units: L is liters of solution, atm is the partial pressure of the gaseous solute above the solution (in atmospheres of absolute pressure), and mol is the moles of the gaseous solute in the solution. Also note that the Henry's Law constant, k, varies with the solvent and the temperature.

As discussed in the next section, there are other forms of Henry's Law each of which defines the constant k differently and requires different dimensional units. ^[2] The form of the equation presented above is consistent with the given example numerical values for oxygen, carbon dioxide and hydrogen and with their corresponding dimensional units.

Other forms of Henry's law

There are various other forms Henry's Law which are discussed in the technical literature. ^[3]^[4]^[2]

**Table 1: Some forms of Henry's law and constants (gases in water at 298 K), derived from ^[4]**
equation:	$k_{\mathrm{H,pc}} = \frac{p_{\mathrm{gas}}}{c_{\mathrm{aq}}}$	$k_{\mathrm{H,cp}} = \frac{c_{\mathrm{aq}}}{p_{\mathrm{gas}}}$	$k_{\mathrm{H,px}} = \frac{p_{\mathrm{gas}}}{x_{\mathrm{aq}}}$	$k_{\mathrm{H,cc}} = \frac{c_{\mathrm{aq}}}{c_{\mathrm{gas}}}$
dimension:	$\left[\frac{\mathrm{L}_{\mathrm{soln}} \cdot \mathrm{\mathrm{atm}}}{\mathrm{mol}_{\mathrm{gas}}}\right]$	$\left[\frac{\mathrm{mol}_{\mathrm{gas}}}{\mathrm{L}_{\mathrm{soln}} \cdot \mathrm{atm}}\right]$	$\left[\frac{\mathrm{atm} \cdot (\mathrm{mol}_{\mathrm{water}}+ \mathrm{mol}_{\mathrm{gas}})}{\mathrm{mol}_{\mathrm{gas}}}\right]$	$\left[ \text{dimensionless} \right]$
O₂	769. Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the 23	1. 3 E-3	4. 259 E4	3. 180 E-2
H₂	1282. Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 05	7. 8 E-4	7. 099 E4	1. 907 E-2
CO₂	29. Carbon dioxide ( Chemical formula:) is a Chemical compound composed of two Oxygen Atoms covalently bonded to a single 41	3. 4 E-2	0. 163 E4	0. 8317
N₂	1639. Nitrogen (ˈnaɪtɹəʤɪn is a Chemical element that has the symbol N and Atomic number 7 and Atomic weight 14 34	6. 1 E-4	9. 077 E4	1. 492 E-2
He	2702. Helium ( He) is a colorless odorless tasteless non-toxic Inert Monatomic Chemical 7	3. 7 E-4	14. 97 E4	9. 051 E-3
Ne	2222. Neon (ˈniːɒn is the Chemical element that has the symbol Ne and Atomic number 10 22	4. 5 E-4	12. 30 E4	1. 101 E-2
Ar	714. This article pertains to the chemical element For other uses see Argon (disambiguation. 28	1. 4 E-3	3. 955 E4	3. 425 E-2
CO	1052. Carbon monoxide, with the chemical formula CO is a colorless odorless tasteless yet highly toxic Gas. 63	9. 5 E-4	5. 828 E4	2. 324 E-2

where:

$c_{\mathrm{aq}}\,$ = moles of gas per liter of solution

$\mathrm{L}_{\mathrm{soln}}\,$ = liters of solution

$p_{\mathrm{gas}}\,$ = partial pressure of gas above the solution, in atmospheres of absolute pressure

$x_{\mathrm{aq}}\,$ = mole fraction of gas in solution = moles of gas per total moles ≈ moles of gas per mole of water

$\mathrm{atm}\,$ = atmospheres of absolute pressure. The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this The litre or liter (see spelling differences) is a unit of Volume. In a mixture of Ideal gases each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume The Standard atmosphere is an international reference pressure defined as 101325 Pa and formerly used as unit of Pressure (symbol atm Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface In Chemistry, the mole fraction of a component in a Mixture is the relative proportion of molecules belonging to the component to those in the mixture

As can be seen by comparing the equations in the above table, the Henry's Law constant $k H,pc$ is simply the inverse of the constant $k H,cp$ . Since all $k H$ may be referred to as the Henry's Law constant, readers of the technical literature must be quite careful to note which version of the Henry's Law equation is being used. ^[2]

It should also be noted the Henry's Law is a limiting law that only applies for dilute enough solutions. The range of concentrations in which it applies becomes narrower the more the system diverges from non-ideal behavior. Roughly speaking, that is the more chemically different the solute is from the solvent.

It also only applies for solutions where the solvent does not react chemically with the gas being dissolved. A chemical reaction is a process that always results in the interconversion of Chemical substances The substance or substances initially involved in a chemical reaction are called A common example of a gas that does react with the solvent is carbon dioxide, which rapidly forms hydrated carbon dioxide and then carbonic acid (H₂CO₃) with water. Carbon dioxide ( Chemical formula:) is a Chemical compound composed of two Oxygen Atoms covalently bonded to a single Carbonic acid (ancient name acid of air or aerial acid) has the formula H2CO3

Temperature dependence of the Henry constant

When the temperature of a system changes, the Henry constant will also change. ^[2] This is why some people prefer to name it Henry coefficient. There are multiple equations assessing the effect of temperature on the constant. A simple example is ^[4], which is a form of the van 't Hoff equation:

$k(T) = k(T_\Theta) \cdot e^{ \left[ -C \cdot \left( \frac{1}{T}-\frac{1}{T_\Theta}\right)\right]}\,$

where

k for a given temperature is the Henry's Law constant (as defined in the first section of this article), identical with k_H,pc defined in Table 1,

T is in Kelvin,

the index

Θ

(theta) refers to the standard temperature (298 K). The van 't Hoff equation (also known as the van 't Hoff isochore) in Chemical thermodynamics relates the change in temperature ( T) to the change in the Theta (uppercase Θ, lowercase θ or ϑ; Θήτα is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth

The above equation is an approximation only and should be used only when no better experimentally derived formula for a given gas exists.

The following table lists some values for constant C (dimension of kelvins) in the equation above:

**Table 2: Values of C**
Gas	O₂	H₂	CO₂	N₂	He	Ne	Ar	CO
C	1700	500	2400	1300	230	490	1300	1300

Because solubility of gases is decreasing with increasing temperature, the partial pressure a given gas concentration has in liquid must increase. Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 Carbon dioxide ( Chemical formula:) is a Chemical compound composed of two Oxygen Atoms covalently bonded to a single Nitrogen (ˈnaɪtɹəʤɪn is a Chemical element that has the symbol N and Atomic number 7 and Atomic weight 14 Helium ( He) is a colorless odorless tasteless non-toxic Inert Monatomic Chemical Neon (ˈniːɒn is the Chemical element that has the symbol Ne and Atomic number 10 This article pertains to the chemical element For other uses see Argon (disambiguation. Carbon monoxide, with the chemical formula CO is a colorless odorless tasteless yet highly toxic Gas. While heating water (saturated with nitrogen) from 25 °C to 95 °C the solubility will decrease to about 43% of its initial value. This can be verified when heating water in a pot. Small bubbles evolve and rise, long before the water reaches boiling temperature. Similarly, carbon dioxide from a carbonated drink escapes much faster when the drink is not cooled because of the increased partial pressure of CO₂ in higher temperatures. Partial pressure of CO₂ in seawater doubles with every 16 K increase in temperature. ^[5]

The constant C may be regarded as:

$C = \frac{\Delta_{solv}H}{R} = \frac{-d \ln\left(k(T)\right)}{d(1/T)}$

where

$\Delta_{solv}H \,$ is the enthalpy of solution

R

is the gas constant. The enthalpy of solution (or enthalpy of dissolution) is the Enthalpy change associated with the dissolution of a substance in a Solvent at constant pressure Relationship with the Boltzmann constant The Boltzmann constant kB (often abbreviated k) may be used in place of the gas constant by working

Henry's law in geophysics

In geophysics a version of Henry's law applies to the solubility of a noble gas in contact with silicate melt. Geophysics, a major discipline of Earth sciences, is the study of the Earth by quantitative physical methods especially by seismic, electromagnetic History Noble gas is translated from the German noun de ''Edelgas'' first used in 1898 by Hugo Erdmann to indicate their extremely low level of reactivity For the Artificial intelligence Androids of the 1990s Science fiction series Space Above and Beyond, see Silicate (AI One equation used is

$\rho_m/\rho_g=e^{-\beta(\mu_{{\rm ex},m}-\mu_{{\rm ex},g})}\,$

where:

subscript m = melt

subscript g = gas phase

ρ

= the number densities of the solute gas in the melt and gas phase

β = 1 / k B T

an inverse temperature scale

k B

= the Boltzmann constant

μ ex, m

and

μ ex, g

= the excess chemical potential of the solute in the two phases. Bridge from macroscopic to microscopic physics Boltzmann's constant k is a bridge between Macroscopic and microscopic physics In Thermodynamics and Chemistry, chemical potential, symbolized by μ, is a term introduced by the American engineer chemist and mathematical

Henry's law versus Raoult's law

Both Henry's law and Raoult's law state that the vapor pressure of a component, p, is proportional to its concentration. Established by François-Marie Raoult, Raoult's law states the Vapor pressure of an Ideal solution is dependent on the vapor pressure of each

Henry's law: $p = k \,x$

Raoult's law: $p = p^\star\,x$

where:

$\,x$ is the mole fraction of the component;

$\,k$ is the Henry constant; (Note that the numerical value and dimensions of this constant change when mole fractions are used rather than molarity, as seen in Table 1. )

$p^\star$ is the equilibrium vapor pressure of the pure component.

If the solution is ideal, both components follow Raoult's law over the entire composition range, but Henry noticed that at low concentrations of non-ideal solutions, the constant of proportionality is not p*. Therefore Henry's law uses an empirically-derived constant, k, based on an infinitely-dilute solution, i. e. x = 0, that is specific to the components in the mixture and the temperature.

In most systems, the laws can only be applied over very limited concentrations at the extreme ends of the mole-fraction range. Raoult's law, which uses the vapor pressure of the pure component, is best used for the major component (solvent) and in mixtures of similar components. Henry's law applies to the minor component (solute) in dilute solutions. In Chemistry, a solution is a Homogeneous Mixture composed of two or more substances

In ideal-dilute solutions, the minor component follows Henry's law, while the solvent obeys Raoult's law. This is proved by the Gibbs-Duhem equation. The Gibbs-Duhem equation in Thermodynamics describes the relationship between changes in Chemical potential for components in a thermodynamical system:

References

^ University of Delaware physical chemistry lecture
^ ^a ^b ^c ^d Francis L. Established by François-Marie Raoult, Raoult's law states the Vapor pressure of an Ideal solution is dependent on the vapor pressure of each In Chemistry and Physics, Dalton's law (also called Dalton's law of partial pressures) states that the total Pressure exerted by a In a mixture of Ideal gases each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume Smith and Allan H. Harvey (September 2007). "Avoid Common Pitfalls When Using Henry's Law". CEP (Chemical Engineering Progress). ISSN 0360-7275. An International Standard Serial Number ( ISSN) is a unique eight-digit number used to identify a print or electronic Periodical publication.
^ University of Arizona chemistry class notes
^ ^a ^b ^c An extensive list of Henry's law constants, and a conversion tool
^ Takahashi, T; Sutherland, SC; Sweeney, C; Poisson, A; Metzl, N; Tilbrook, B; Bates, N; Wanninkhof, R; Feely, RA; Sabine, C; Olafsson, J; Nojiri, Y "Global sea-air CO₂ flux based on climatological surface ocean pCO₂ and seasonal biological and temperature effects" Deep-Sea Research (Part II, Topical Studies in Oceanography) [Deep-Sea Research (II Top. Stud. Oceanogr. )] 49, 9-10, pp. 1601-1622, 2002

External links

www.henrys-law.org - Large compilation of Henry's law constants
New 'no air tanks' diving system, based on Henry's law - An article with flash presentation

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Contents

Formula and Henry constant

Other forms of Henry's law

Temperature dependence of the Henry constant

Henry's law in geophysics

Henry's law versus Raoult's law

See also

References

External links