Henry Law

The Henry's Law (after the English chemist William Henry ) describes the solubility of gases in a liquid.

The concentration of particles in the liquid phase (shown here in blue) depends on the partial pressure. One ...

Increasing the external pressure (shown here by pressing in a piston) leads to a higher partial pressure in the gas phase and consequently to a higher concentration.

definition

Henry's Law states that the partial pressure of a gas above a liquid is directly proportional to the concentration of the gas in the liquid. The proportionality is expressed by Henry's constant. The law is compatible with Le Châtelier's principle , because the system will react to an external increase in pressure by reducing the number of particles in the gas (reducing the pressure and thus avoiding the "constraint").

There are many ways to define Henry's law constant. These can be divided into two fundamental types: One possibility is to put the liquid phase in the numerator and the gas phase in the denominator. This gives the Henry solubility constant . Their value increases with solubility. Alternatively, the numerator and denominator can be swapped, which results in the Henry volatility constant. Their value increases with volatility, so it decreases with increasing solubility. There are several variants of the two fundamental types, as there are many ways of describing the composition of the phases, e.g. B. Mole concentration ( with index l for liquid), molality ( ) and mole fraction ( ) for the liquid phase. Molar concentration ( ) and partial pressure ( ) can be used for the gas phase . The exact variant is indicated in the Henry constant symbol by two superscript characters that refer to the numerator and denominator. For example, denotes the Henry solubility constant, which is defined as . ${\displaystyle H}$ ${\displaystyle K_{\rm {H}}}$ ${\displaystyle c_{\rm {l}}}$ ${\displaystyle b}$ ${\displaystyle x}$ ${\displaystyle c_{\rm {g}}}$ ${\displaystyle p}$ ${\displaystyle H^{cp}}$ ${\displaystyle c/p}$

Henry Solubility Constants ${\displaystyle H}$

Henry's constant of solubility ${\displaystyle H^{cp}}$

Atmospheric chemists usually define Henry's solubility constant as:

${\displaystyle H^{cp}={\frac {c_{\rm {l}}}{p}}\;}$.

Here is the concentration of a substance in the liquid phase and its partial pressure in the gas phase under equilibrium conditions. ${\displaystyle c_{\rm {l}}}$ ${\displaystyle p}$

The SI unit for is mol (m ³ · Pa) ⁻¹ . Often, however, the unit M · atm ^{−1 is} used, since it is usually expressed in M ​​(1 M = 1 mol · dm ⁻³ ) and in atm (1 atm = 101325 Pa). ${\displaystyle H^{cp}}$ ${\displaystyle c_{\rm {l}}}$ ${\displaystyle p}$

Henry's dimensionless solubility constant ${\displaystyle H^{cc}}$

Henry's solubility constant can also be defined as the dimensionless ratio between the liquid phase concentration and the gas phase concentration: ${\displaystyle c_{\rm {l}}}$ ${\displaystyle c_{\rm {g}}}$

${\displaystyle H^{cc}={\frac {c_{\rm {l}}}{c_{\rm {g}}}}.}$

For an ideal gas the conversion is:

${\displaystyle H^{cc}=H^{cp}\cdot RT}$,

with = gas constant and = temperature. is practically identical to the Ostwald coefficient (after Wilhelm Ostwald , symbol L , sometimes also λ ). ${\displaystyle R}$ ${\displaystyle T}$ ${\displaystyle H^{cc}}$

Henry's constant of solubility ${\displaystyle H^{xp}}$

Another Henry solubility constant is:

${\displaystyle H^{xp}={\frac {x}{p}}.}$

Here is the mole fraction in the liquid phase. For a dilute, aqueous solution the conversion between and is : ${\displaystyle x}$ ${\displaystyle x}$ ${\displaystyle c_{\rm {l}}}$

${\displaystyle c_{\rm {l}}\approx x{\frac {\varrho _{H_{2}O}}{M_{H_{2}O}}},}$

with = density of water and = molar mass of water. It follows: ${\displaystyle \varrho _{H_{2}O}}$ ${\displaystyle M_{H_{2}O}}$

${\displaystyle H^{xp}\approx {\frac {M_{H_{2}O}}{\varrho _{H_{2}O}}}\cdot H^{cp}.}$

The SI unit for is Pa ⁻¹ . However, atm ^{−1 is} often used. ${\displaystyle H^{xp}}$

Henry volatility constants ${\displaystyle K_{\rm {H}}}$

Henry's volatility constant ${\displaystyle K_{\rm {H}}^{pc}}$

The Henry volatility constant is often defined as the quotient of partial pressure and liquid phase concentration:

${\displaystyle K_{\rm {H}}^{pc}={\frac {p}{c_{\rm {l}}}}\,=\,{\frac {1}{H^{cp}}}.}$

The SI unit for is Pa · m ³ · mol ⁻¹ . ${\displaystyle K_{\rm {H}}^{pc}}$

Henry's volatility constant ${\displaystyle K_{\rm {H}}^{px}}$

Another Henry volatility constant is:

${\displaystyle K_{\rm {H}}^{px}={\frac {p}{x}}\,=\,{\frac {1}{H^{xp}}}.}$

The SI unit for is Pa. However, atm is often used. ${\displaystyle K_{\rm {H}}^{px}}$

Henry's dimensionless volatility constant ${\displaystyle K_{\rm {H}}^{cc}}$

The Henry volatility constant can also be defined as the dimensionless ratio between the gas phase concentration of a substance and its liquid phase concentration : ${\displaystyle c_{\rm {g}}}$ ${\displaystyle c_{\rm {l}}}$

${\displaystyle K_{\rm {H}}^{cc}={\frac {c_{\rm {g}}}{c_{\rm {l}}}}\,=\,{\frac {1}{H^{cc}}}.}$

In environmental chemistry , this constant is often referred to as the air-water partition coefficient . ${\displaystyle K_{AW}}$

Henry's constant values

Some selected Henry's constants are shown in the following table. A large collection of Henry's constants is available here:

Henry's constants for some gases in water ${\displaystyle T=298{,}15\,K}$

gas	${\displaystyle K_{\rm {H}}^{pc}={\frac {p}{c_{\mathrm {aq} }}}}$ in ${\displaystyle {\frac {\mathrm {L} \cdot \mathrm {atm} }{\mathrm {mol} }}}$	${\displaystyle H^{cp}={\frac {c_{\mathrm {aq} }}{p}}}$ in ${\displaystyle {\frac {\mathrm {mol} }{\mathrm {L} \cdot \mathrm {atm} }}}$	${\displaystyle K_{\rm {H}}^{px}={\frac {p}{x}}}$ in ${\displaystyle \mathrm {atm} }$	${\displaystyle H^{cc}={\frac {c_{\mathrm {aq} }}{c_{\mathrm {gas} }}}}$
O 2	770	1.3e-3	4th.3e4th	3.2e-2
H 2	1300	7th.8the-4th	7th.1e4th	1.9e-2
CO 2	29	3.4the-2	1.6the3	8th.3e-1
N 2	1600	6th.1e-4th	9.1e4th	1.5e-2
Hey	2700	3.7the-4th	1.5e5	9.1e-3
No	2200	4th.5e-4th	1.2e5	1.1e-2
Ar	710	1.4the-3	4th.0e4th	3.4the-2
CO	1100	9.5e-4th	5.8the4th	2.3e-2

Some examples (solubility in H ₂ O) for Henry's constants of organic substances are:

Alkylbenzenes ( butylbenzenes - benzene )	${\displaystyle H^{cp}}$ = 0.1… 1 mol / L bar
Chlorobenzenes ( hexachlorobenzene - monochlorobenzene )	${\displaystyle H^{cp}}$ = 0.1… 2 mol / L bar
Phthalic acid ester	${\displaystyle H^{cp}}$ = 1000 ... 2000 mol / L bar
Polycyclic Aromatic Hydrocarbons (PAH)	${\displaystyle H^{cp}}$ = 1… 5000 mol / L bar
aliphatic hydrocarbons (C18-C5)	${\displaystyle H^{cp}}$ = 0.0001 ... 0.1 mol / L bar
PCB	${\displaystyle H^{cp}(T)}$ = 1 ... 100 mol / L bar

Strictly speaking, Henry's constants are only valid for small partial pressures and for dilute solutions. In addition, the dissolved particle must not react with the solvent like carbon dioxide does with water, otherwise the equilibrium is disturbed.

Temperature dependence of Henry's constant

Henry's constant is not constant with changes in temperature, which is why it is sometimes referred to as the Henry coefficient. There are several approaches to expressing this dependency in formulas, a simple example is:

${\displaystyle H^{cp}=H^{cp,\Theta }\cdot \exp \left(C\cdot \left({\frac {1}{T}}-{\frac {1}{T_{\Theta }}}\right)\right)}$

The index stands for the standard temperature (298.15 K). The constant C can be interpreted as follows: ${\displaystyle \Theta }$

${\displaystyle C=-{\frac {\Delta _{\mathrm {solv} }H}{R}}={\frac {d\cdot \ln \left(H^{cp}\right)}{d(1/T)}}}$

where the enthalpy of solution and R is the gas constant . ${\displaystyle \Delta _{\mathrm {solv} }H}$

The following table lists some constants C ([ C ] = K) for the above formula:

gas	O 2	H 2	CO 2	N 2	Hey	No	Ar	CO
C in K	1700	500	2400	1300	230	490	1300	1300

It has been shown that the solubility of gases in water decreases with increasing temperature. This can be observed when water is heated in a saucepan, small gas bubbles form and rise long before the liquid boils.

Application in diving

The relatively simple Henry's Law explains decompression sickness in divers. The ambient pressure increases by around 1 bar per 10 meters of water depth. As the partial pressure increases, more nitrogen initially dissolves in the blood, which transports it to the periphery. There it diffuses preferentially into compartments with a high fat content. If you ascend too quickly or without the possibly necessary decompression breaks, the back diffusion of nitrogen (tissue → blood → lungs → water) is too slow so that it bubbles out. If this takes place in the tissue, one speaks of bends (joint pain), in the pulmonary circulation of chokes (breathing problems) or, when blisters form in arteries that supply the brain or spinal cord, of staggers (neurological symptoms).

See also

• Raoult's law
• Ostwald coefficient

Web links

• Video: Calculating the oxygen content of water according to HENRY's law . Jakob Günter Lauth (SciFox) 2013, made available by the Technical Information Library (TIB), doi : 10.5446 / 15712 .

Individual evidence

1. ^ William Henry : Experiments on the Quantity of Gases Absorbed by Water, at Different Temperatures, and under Different Pressures. In: Philosophical Transactions of the Royal Society of London , Volume 93, January 1, 1803, pp. 29-274, doi: 10.1098 / rstl.1803.0004 , ( full text ).
2. ^ Rolf Sander: Compilation of Henry's law constants (version 4.0) for water as solvent . In: Atmospheric Chemistry and Physics , Volume 15, 2015, pp. 4399-4981, doi: 10.5194 / acp-15-4399-2015 .