In physics, Henry's law is one of the gas laws formulated by William Henry in 1803.
It states: "At a constant temperature, the amount of
a given gas that dissolves in a given type and volume of liquid is directly proportional
to the partial pressure of that gas in equilibrium with that liquid."
An equivalent way of stating the law is that the solubility of a gas in a liquid is directly
proportional to the partial pressure of the gas above the liquid.
An everyday example of Henry's law is given by carbonated soft drinks. Before the bottle
or can of carbonated drink is opened, the gas above the drink is almost pure carbon
dioxide at a pressure slightly higher than atmospheric pressure. The drink itself contains
dissolved carbon dioxide. When the bottle or can is opened, this gas escapes, giving
the characteristic hiss. Because the partial pressure of carbon dioxide above the liquid
is now much lower, some of the dissolved carbon dioxide comes out of solution as bubbles.
If a glass of the drink is left in the open, the concentration of carbon dioxide in solution
will come into equilibrium with the carbon dioxide in the air, and the drink will go
"flat". A slightly more exotic example of Henry's
law is in the decompression and decompression sickness of underwater divers.
Formula and the Henry's law constant Henry's law can be put into mathematical terms
as
where p is the partial pressure of the gaseous solute above the solution, c is the concentration
of the dissolved gas and kH is a constant with the dimensions of pressure divided by
concentration. The constant, known as the Henry's law constant, depends on the solute,
the solvent and the temperature. Some values for kH for gases dissolved in
water at 298 K include: oxygen : 769.2 L·atm/mol
carbon dioxide : 29.41 L·atm/mol hydrogen : 1282.1 L·atm/mol
There are various other forms of Henry's Law which define the constant kH differently and
require different dimensional units. In particular, the "concentration" of the solute in solution
may also be expressed as a mole fraction or as a molarity.
Other forms of Henry's law The various other forms of Henry's law are
discussed in the technical literature. As can be seen by comparing the equations
in the above table, the Henry's law constant kH,pc is simply the inverse of the constant
kH,cp. Since all kH may be referred to as Henry's law constants, readers of the technical
literature must be quite careful to note which version of the equation is being used.
It should also be noted, the Henry's law is a limiting law that only applies for 'sufficiently
dilute' solutions. The range of concentrations in which it 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. Typically, Henry's law is only applicable to gas solute
mole fractions less than 0.03. It also only applies simply for solutions
where the solvent does not react chemically with the gas being dissolved. A common example
of a gas that does react with the solvent is carbon dioxide, which forms carbonic acid
to a certain degree with water. Temperature dependence of the Henry constant
When the temperature of a system changes, the Henry constant will also change. This
is why some people prefer to name it Henry coefficient. Multiple equations assess the
effect of temperature on the constant. These forms of the van 't Hoff equation are examples:
where kH for a given temperature is Henry's constant.
Note that the sign of C depends on whether kH,pc or kH,cp is used.
T is any given temperature, in K T o refers to the standard temperature.
This equation is only an approximation, and should be used only when no better, experimentally
derived formula is known for a given gas. The following table lists some values for
constant C in the equation above: Because solubility of permanent gases usually
decreases with increasing temperature at around room temperature, the partial pressure a given
gas concentration has in liquid must increase. While heating water from 25 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 the required partial pressure of CO2 to achieve the same solubility increases
in higher temperatures. Partial pressure of CO2 in the gas phase in equilibrium with seawater
doubles with every 16 K increase in temperature. The constant C may be regarded as:
where ΔsolvH is the enthalpy of solution
R is the gas constant. The solubility of gases does not always decrease
with increasing temperature. For aqueous solutions, the Henry's law constant usually goes through
a maximum. For most permanent gases, the minimum is below 120 °C. Often, the smaller the gas
molecule, the lower the temperature of the maximum of the Henry's law constant. Thus,
the maximum is about 30 °C for helium, 92 to 93 °C for argon, nitrogen and oxygen,
and 114 °C for xenon. Influence of electrolytes
The influence of electrolytes on the solubility of gases is sometimes given by Sechenov equation
which accounts for the "salting out" or "salting in" effect. The Sechenov equation can be written
as:
where: *z1 is the solubility of gas 1 in pure solvent
z1 is the solubility of gas 1 in an electrolyte solution
y expresses the salt composition 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
where: C = the number concentrations of the solute
gas in the melt and gas phases β = 1/kBT, an inverse temperature scale:
kB = the Boltzmann constant µE = the excess chemical potentials of the
solute gas in the two phases. Comparison to Raoult's law
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 kH =
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. 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. In mathematical terms:
Raoult's law: Henry's law:
Raoult's law can also be related to non-gas solutes.
Standard chemical potential Henry's law has been shown to apply to a wide
range of solutes in the limit of "infinite dilution", including non-volatile substances
such as sucrose or even sodium chloride. 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 on the concentration: , where for a volatile solute; co = 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:
By measuring the change in vapor pressure 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
co 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.
All the relations above can also be expressed in terms of molalities b rather than concentrations,
e.g.: , where for a volatile solute; bo = 1 mol/kg.
The standard chemical potential μmo, the activity coefficient γm and the Henry's law
constant kH,b all have different numerical values when molalities are used in place of
concentrations. See also
Bunsen solubility coefficient Dalton's law
Partial pressure Pervaporation
Sieverts' law Henry adsorption constant
References
Further reading Battino, Rubin; Clever, H. Lawrence. "The
Solubility of Gases in Liquids". Chemical Reviews 66: 395–463. doi:10.1021/cr60242a003.
Clever, H. Lawrence. "Setchenov salt-effect parameter". Journal of Chemical & Engineering
Data 28: 340–343. doi:10.1021/je00033a018. Borgstedt, Hans Ulrich. "IUPAC-NIST Solubility
Data Series. 75. Nonmetals in Liquid Alkali Metals". Journal of Physical and Chemical
Reference Data 30: 835–1158. Bibcode:2001JPCRD..30..835B. doi:10.1063/1.1391426.
Crovetto, Rosa; Fernández‐Prini, R.; Japas, Maria Laura. "Solubilities of inert gases
and methane in H2O and in D2O in the temperature range of 300 to 600 K". J. Chem. Phys. 76:
1077. Bibcode:1982JChPh..76.1077C. doi:10.1063/1.443074. External links
Ethanol solubility in EPDM, Solubility of chemicals in polymers using Henry's law