Henry's law

From Wikipedia, the free encyclopedia

In chemistry, Henry's law is a gas law that states that the amount of dissolved gas is proportional to its partial pressure in the gas phase. The proportionality factor is called the Henry's law constant. It was formulated by the English chemist William Henry, who studied the topic in the early 19th century. In his publication about the quantity of gases absorbed by water,^[1] he 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."

An example where Henry's law is at play is in the depth-dependent dissolution of oxygen and nitrogen in the blood of underwater divers that changes during decompression, leading to decompression sickness. An everyday example is given by one's experience with 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 solution.

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").^[2] This results in the Henry's law solubility constant ${\displaystyle H}$. Its value increases with increased solubility. Alternatively, numerator and denominator can be switched ("gas/aq"), which results in the Henry's law volatility constant ${\displaystyle K_{\rm {H}}}$. The value of ${\displaystyle K_{\rm {H}}}$ decreases with increased solubility. There are 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 (${\displaystyle c_{\rm {a}}}$), molality (${\displaystyle b}$), and molar mixing ratio (${\displaystyle x}$). For the gas phase, molar concentration (${\displaystyle c_{\rm {g}}}$) and partial pressure (${\displaystyle p}$) are often used. It is not possible to use the gas-phase mixing ratio (${\displaystyle y}$) because at a given gas-phase mixing ratio, the aqueous-phase concentration ${\displaystyle c_{\rm {a}}}$ depends on the total pressure and thus the ratio ${\displaystyle y/c_{\rm {a}}}$ is not a constant.^[3] 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, ${\displaystyle H^{cp}}$ refers to the Henry solubility defined as ${\displaystyle c/p}$.

Henry's law solubility constants ${\displaystyle H}$

Henry solubility defined via concentration (${\displaystyle H^{cp}}$)

Atmospheric chemists often define the Henry solubility as

${\displaystyle H^{cp}=c_{\text{a}}/p}$.^[2]

Here ${\displaystyle c_{\text{a}}}$ is the concentration of a species in the aqueous phase, and ${\displaystyle p}$ is the partial pressure of that species in the gas phase under equilibrium conditions.^{[citation needed]}

The SI unit for ${\displaystyle H^{cp}}$ is mol/(m³ Pa); however, often the unit M/atm is used, since ${\displaystyle c_{\text{a}}}$ is usually expressed in M (1 M = 1 mol/dm³) and ${\displaystyle p}$ in atm (1 atm = 101325 Pa).^{[citation needed]}

The dimensionless Henry solubility ${\displaystyle H^{cc}}$

The Henry solubility can also be expressed as the dimensionless ratio between the aqueous-phase concentration ${\displaystyle c_{\text{a}}}$ of a species and its gas-phase concentration ${\displaystyle c_{\text{g}}}$:

${\displaystyle H^{cc}=c_{\text{a}}/c_{\text{g}}}$.^[2]

For an ideal gas, the conversion is:

${\displaystyle H^{cc}=H^{cp}\times RT}$ ,^[2]

where ${\displaystyle R}$ is the gas constant and ${\displaystyle T}$ is the temperature.

Sometimes, this dimensionless constant is called the "water-air partitioning coefficient" ${\displaystyle K_{\text{WA}}}$.^[4] It is closely related to the various, slightly different definitions of the "Ostwald coefficient" ${\displaystyle L}$, as discussed by Battino (1984).^[5]

Henry solubility defined via aqueous-phase mixing ratio (${\displaystyle H^{xp}}$)

Another Henry's law solubility constant is

${\displaystyle H^{xp}=x/p}$ .^[2]

Here ${\displaystyle x}$ is the molar mixing ratio in the aqueous phase. For a dilute aqueous solution the conversion between ${\displaystyle x}$ and ${\displaystyle c_{\text{a}}}$ is:

${\displaystyle c_{\text{a}}\approx x{\frac {\varrho _{\mathrm {H_{2}O} }}{M_{\mathrm {H_{2}O} }}}}$ ,^[2]

where ${\displaystyle \varrho _{\mathrm {H_{2}O} }}$ is the density of water and ${\displaystyle M_{\mathrm {H_{2}O} }}$ is the molar mass of water. Thus

${\displaystyle H^{xp}\approx {\frac {M_{\mathrm {H_{2}O} }}{\varrho _{\mathrm {H_{2}O} }}}\times H^{cp}}$ .^[2]

The SI unit for ${\displaystyle H^{xp}}$ is Pa⁻¹, although atm⁻¹ is still frequently used.^[2]

Henry solubility defined via molality (${\displaystyle H^{bp}}$)

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 ${\displaystyle T}$, since it refers to the mass of the solvent. In contrast, the concentration ${\displaystyle c}$ does change with ${\displaystyle T}$, 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

${\displaystyle H^{bp}=b/p.}$

Here ${\displaystyle b}$ is used as the symbol for molality (instead of ${\displaystyle m}$) to avoid confusion with the symbol ${\displaystyle m}$ for mass. The SI unit for ${\displaystyle H^{bp}}$ is mol/(kg Pa). There is no simple way to calculate ${\displaystyle H^{cp}}$ from ${\displaystyle H^{bp}}$, since the conversion between concentration ${\displaystyle c_{\text{a}}}$ and molality ${\displaystyle b}$ involves all solutes of a solution. For a solution with a total of ${\displaystyle n}$ solutes with indices ${\displaystyle i=1,\ldots ,n}$, the conversion is:

${\displaystyle c_{\text{a}}={\frac {b\varrho }{1+\sum _{i=1}^{n}b_{i}M_{i}}},}$

where ${\displaystyle \varrho }$ is the density of the solution, and ${\displaystyle M_{i}}$ are the molar masses. Here ${\displaystyle b}$ is identical to one of the ${\displaystyle b_{i}}$ in the denominator. If there is only one solute, the equation simplifies to

${\displaystyle c_{\text{a}}={\frac {b\varrho }{1+bM}}.}$

Henry's law is only valid for dilute solutions where ${\displaystyle bM\ll 1}$ and ${\displaystyle \varrho \approx \varrho _{\mathrm {H_{2}O} }}$. In this case the conversion reduces further to

${\displaystyle c_{\text{a}}\approx b\varrho _{\mathrm {H_{2}O} },}$

and thus

${\displaystyle H^{bp}\approx H^{cp}/\varrho _{\mathrm {H_{2}O} }.}$

The Bunsen coefficient ${\displaystyle \alpha }$

According to Sazonov and Shaw, the dimensionless Bunsen coefficient ${\displaystyle \alpha }$ 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."^[6] If the gas is ideal, the pressure cancels out, and the conversion to ${\displaystyle H^{cp}}$ is simply

${\displaystyle H^{cp}=\alpha \times {\frac {1}{RT^{\text{STP}}}}}$ ,

with ${\displaystyle T^{\text{STP}}}$ = 273.15 K. Note, that according to this definition, the conversion factor is not temperature-dependent.^{[citation needed]} Independent of the temperature that the Bunsen coefficient refers to, 273.15 K is always used for the conversion.^{[citation needed]} The Bunsen coefficient, which is named after Robert Bunsen, has been used mainly in the older literature.^{[citation needed]}

The Kuenen coefficient ${\displaystyle S}$

According to Sazonov and Shaw, the Kuenen coefficient ${\displaystyle S}$ 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."^[6] If the gas is ideal, the relation to ${\displaystyle H^{cp}}$ is

${\displaystyle H^{cp}=S\times {\frac {\varrho }{RT^{\text{STP}}}}}$ ,^{[citation needed][original research?]}

where ${\displaystyle \varrho }$ is the density of the solvent, and ${\displaystyle T^{\text{STP}}}$ = 273.15 K. The SI unit for ${\displaystyle S}$ is m³/kg.^[6] The Kuenen coefficient, which is named after Johannes Kuenen, has been used mainly in the older literature, and IUPAC considers it to be obsolete.^[7]

Henry's law volatility constants ${\displaystyle K_{\text{H}}}$

The Henry volatility defined via concentration (${\displaystyle K_{\text{H}}^{pc}}$)

A common way to define a Henry volatility is dividing the partial pressure by the aqueous-phase concentration:

${\displaystyle K_{\text{H}}^{pc}=p/c_{\text{a}}=1/H^{cp}.}$

The SI unit for ${\displaystyle K_{\text{H}}^{pc}}$ is Pa m³/mol.

The Henry volatility defined via aqueous-phase mixing ratio (${\displaystyle K_{\text{H}}^{px}}$)

Another Henry volatility is

${\displaystyle K_{\text{H}}^{px}=p/x=1/H^{xp}.}$

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

The dimensionless Henry volatility ${\displaystyle K_{\text{H}}^{cc}}$

The Henry volatility can also be expressed as the dimensionless ratio between the gas-phase concentration ${\displaystyle c_{\text{g}}}$ of a species and its aqueous-phase concentration ${\displaystyle c_{\text{a}}}$:

${\displaystyle K_{\text{H}}^{cc}=c_{\text{g}}/c_{\text{a}}=1/H^{cc}.}$

In chemical engineering and environmental chemistry, this dimensionless constant is often called the air–water partitioning coefficient ${\displaystyle K_{\text{AW}}}$.

Values of Henry's law constants

A large compilation of Henry's law constants has been published by Sander (2015).^[2] A few selected values are shown in the table below:

Henry's law constants (gases in water at 298.15 K)

equation:	${\displaystyle K_{\text{H}}^{pc}={\frac {p}{c_{\text{aq}}}}}$	${\displaystyle H^{cp}={\frac {c_{\text{aq}}}{p}}}$	${\displaystyle K_{\text{H}}^{px}={\frac {p}{x}}}$	${\displaystyle H^{cc}={\frac {c_{\text{aq}}}{c_{\text{gas}}}}}$
unit:	${\displaystyle {\frac {{\text{L}}\cdot {\text{atm}}}{\text{mol}}}}$	${\displaystyle {\frac {\text{mol}}{{\text{L}}\cdot {\text{atm}}}}}$	${\displaystyle {\text{atm}}}$	(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

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:

${\displaystyle {\frac {\mathrm {d} \ln H}{\mathrm {d} (1/T)}}={\frac {-\Delta _{\text{sol}}H}{R}},}$

where ${\displaystyle \Delta _{\text{sol}}H}$ is the enthalpy of dissolution. Note that the letter ${\displaystyle H}$ in the symbol ${\displaystyle \Delta _{\text{sol}}H}$ refers to enthalpy and is not related to the letter ${\displaystyle H}$ for Henry's law constants. Integrating the above equation and creating an expression based on ${\displaystyle H^{\circ }}$ at the reference temperature ${\displaystyle T^{\circ }}$ = 298.15 K yields:

${\displaystyle H(T)=H^{\circ }\times \exp \displaystyle \left[{\frac {-\Delta _{\text{sol}}H}{R}}\left({\frac {1}{T}}-{\frac {1}{T^{\circ }}}\right)\right].}$

The van 't Hoff equation in this form is only valid for a limited temperature range in which ${\displaystyle \Delta _{\text{sol}}H}$ does not change much with temperature.

The following table lists some temperature dependencies:

Values of ${\displaystyle -\Delta _{\text{sol}}H/R}$ (in K)

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.^[8]

Effective Henry's law constants H_eff

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

${\displaystyle H^{{\ce {cp}}}={\frac {c({\ce {H2CO}})}{p({\ce {H2CO}})}}.}$

In aqueous solution, methanal is almost completely hydrated:

${\displaystyle {\ce {{H2CO}+ {H2O}<=> {H2C(OH)2}}}}$

The total concentration of dissolved methanal is

${\displaystyle c_{{\ce {tot}}}=c({\ce {H2CO}})+c({\ce {H2C(OH)2}}).}$

Taking this equilibrium into account, an effective Henry's law constant ${\displaystyle H_{{\ce {eff}}}}$ can be defined as

${\displaystyle H_{{\ce {eff}}}={\frac {c_{{\ce {tot}}}}{p({\ce {H2CO}})}}={\frac {c({\ce {H2CO}})+c({\ce {H2C(OH)2}})}{p({\ce {H2CO}})}}.}$

For acids and bases, the effective Henry's law constant is not a useful quantity because it depends on the pH of the solution.^{[verification needed]} In order to obtain a pH-independent constant, the product of the intrinsic Henry's law constant ${\displaystyle H^{{\ce {cp}}}}$ and the acidity constant ${\displaystyle K_{{\ce {A}}}}$ is often used for strong acids like hydrochloric acid (HCl):

${\displaystyle H'=H^{{\ce {cp}}}\times K_{{\ce {A}}}={\frac {c({\ce {H+}})\times c({\ce {Cl^-}})}{p({\ce {HCl}})}}.}$

Although ${\displaystyle H'}$ is usually also called a Henry's law constant, it should be noted that it is a different quantity and it has different units than ${\displaystyle H^{{\ce {cp}}}}$.

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

${\displaystyle \log \left({\frac {H_{0}^{bp}}{H^{bp}}}\right)=k_{\text{s}}\times b({\text{salt}}),}$

where ${\displaystyle H_{0}^{bp}}$ is the Henry's law constant in pure water, ${\displaystyle H^{bp}}$ is the Henry's law constant in the salt solution, ${\displaystyle k_{\text{s}}}$ is the molality-based Sechenov constant, and ${\displaystyle b({\text{salt}})}$ 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 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:

${\displaystyle \mu =\mu _{c}^{\circ }+RT\ln {\frac {\gamma _{c}c}{c^{\circ }}}}$,

where ${\displaystyle \gamma _{c}={\frac {K_{{\text{H}},c}}{p^{*}}}}$ for a volatile solute; c° = 1 mol/L.

For non-ideal solutions, the activity coefficient γ_c 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:

${\displaystyle \sum _{i}n_{i}d\mu _{i}=0.}$

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.:

${\displaystyle \mu =\mu _{b}^{\circ }+RT\ln {\frac {\gamma _{b}b}{b^{\circ }}},}$

where ${\displaystyle \gamma _{b}={\frac {K_{{\text{H}},b}}{p^{*}}}}$ for a volatile solute; b° = 1 mol/kg.

The standard chemical potential μ_m°, the activity coefficient γ_m and the Henry's law constant K_H,b all have different numerical values when molalities are used in place of concentrations.

Solvent mixtures

Henry law constant H_{2, M} for a gas 2 in a mixture of solvents 1 and 3 is related to the constants for individual solvents H₂₁ and H₂₃:

${\displaystyle \ln H_{2M}=x_{1}\ln H_{21}+x_{2}\ln H_{23}-a_{13}x_{1}x_{3}}$

where a₁₃ is the interaction parameter of the solvents from Wohl expansion of the excess chemical potential of the ternary mixtures.

Miscellaneous

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

${\displaystyle C_{\text{melt}}/C_{\text{gas}}=\exp \left[-\beta (\mu _{\text{melt}}^{\text{E}}-\mu _{\text{gas}}^{\text{E}})\right],}$

where

C is the number concentrations of the solute gas in the melt and gas phases,

β = 1/k_BT, an inverse temperature parameter (k_B is the Boltzmann constant),

µ^E is the excess chemical potentials 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. 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.

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

${\displaystyle p=K_{\text{H}}x.}$

This can be compared with Raoult's law:

${\displaystyle p=p^{*}x,}$

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 K_H = 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: ${\displaystyle \lim _{x\to 1}\left({\frac {p}{x}}\right)=p^{*}.}$

Henry's law: ${\displaystyle \lim _{x\to 0}\left({\frac {p}{x}}\right)=K_{\text{H}}.}$

Raoult's law can also be related to non-gas solutes.

Symmetry in biology

From Wikipedia, the free encyclopedia

 

A selection of animals showing a range of possible body symmetries, including both asymmetry, radial and bilateral body plans

Symmetry in biology is the balanced distribution of duplicate body parts or shapes within the body of an organism. In nature and biology, symmetry is always approximate. For example, plant leaves – while considered symmetrical – rarely match up exactly when folded in half. Symmetry creates a class of patterns in nature, where the near-repetition of the pattern element is by reflection or rotation.

The body plans of most multicellular organisms exhibit some form of symmetry, whether radial, bilateral, or spherical. A small minority, notably among the sponges, exhibit no symmetry (i.e., are asymmetric). Symmetry was once important in animal taxonomy; the Radiata, animals with radial symmetry, formed one of the four branches of Georges Cuvier's classification of the animal kingdom.

Radial symmetry

These sea anemones have been painted to emphasize their radial symmetry. (Plate from Ernst Haeckel's Kunstformen der Natur).

Radially symmetric organisms resemble a pie where several cutting planes produce roughly identical pieces. Such an organism exhibits no left or right sides. They have a top and a bottom surface, or a front and a back.

Symmetry has been important historically in the taxonomy of animals; Georges Cuvier classified animals with radial symmetry in the taxon Radiata (Zoophytes),^[1][2] which is now generally accepted to be a polyphyletic assemblage of different phyla of the Animal kingdom.^[3] Most radially symmetric animals are symmetrical about an axis extending from the center of the oral surface, which contains the mouth, to the center of the opposite, aboral, end. Radial symmetry is especially suitable for sessile animals such as the sea anemone, floating animals such as jellyfish, and slow moving organisms such as starfish. Animals in the phyla Cnidaria and Echinodermata are radially symmetric,^[4] although many sea anemones and some corals have bilateral symmetry defined by a single structure, the siphonoglyph.^[5]

Lilium bulbiferum displays typical floral symmetry with repeated parts arranged around the axis of the flower.

Many flowers are radially symmetric or actinomorphic. Roughly identical flower parts – petals, sepals, and stamens – occur at regular intervals around the axis of the flower, which is often the female part, with the carpel, style and stigma.^[6]

Gastroenteritis viruses have radial symmetry, being icosahedral: A rotavirus, B adenovirus, C norovirus, D astrovirus.

Many viruses have radial symmetries, their coats being composed of a relatively small number of protein molecules arranged in a regular pattern to form polyhedrons, spheres, or ovoids. Most are icosahedrons.^[7]

Special forms of radial symmetry

Tetramerism is a variant of radial symmetry found in jellyfish, which have four canals in an otherwise radial body plan.

Apple cut horizontally, showing pentamerism

Pentamerism (also called pentaradial and pentagonal symmetry) means the organism is in five parts around a central axis, 72° apart. Among animals, only the echinoderms such as sea stars, sea urchins, and sea lilies are pentamerous as adults, with five arms arranged around the mouth. Being bilaterian animals, however, they initially develop with mirror symmetry as larvae, then gain pentaradial symmetry later.^[8]

Flowering plants show fivefold symmetry in many flowers and in various fruits. This is well seen in the arrangement of the five carpels (the botanical fruits containing the seeds) in an apple cut transversely.

Hexamerism is found in the corals and sea anemones (class Anthozoa) which are divided into two groups based on their symmetry. The most common corals in the subclass Hexacorallia have a hexameric body plan; their polyps have sixfold internal symmetry and the number of their tentacles is a multiple of six.

Octamerism is found in corals of the subclass Octocorallia. These have polyps with eight tentacles and octameric radial symmetry. The octopus, however, has bilateral symmetry, despite its eight arms.

Spherical symmetry

Volvox is a microscopic green freshwater alga with spherical symmetry. Young colonies can be seen inside the larger ones.

Spherical symmetry occurs in an organism if it is able to be cut into two identical halves through any cut that runs through the organism's center. Organisms which show approximate spherical symmetry include the freshwater green alga Volvox.^[4]

Bilateral symmetry

In bilateral symmetry (also called plane symmetry), only one plane, called the sagittal plane, divides an organism into roughly mirror image halves. Thus there is approximate reflection symmetry. Internal organs are however not necessarily symmetric.

The small emperor moth, Saturnia pavonia, displays a deimatic pattern with bilateral symmetry.

Animals that are bilaterally symmetric have mirror symmetry in the sagittal plane, which divides the body vertically into left and right halves, with one of each sense organ and limb group on either side. At least 99% of animals are bilaterally symmetric, including humans,^[9][10][11] where facial symmetry influences people's judgements of attractiveness.^[12]

When an organism normally moves in one direction, it inevitably has a front or head end. This end encounters the environment before the rest of the body as the organism moves along, so sensory organs such as eyes tend to be clustered there, and similarly it is the likely site for a mouth as food is encountered.^[11] A distinct head, with sense organs connected to a central nervous system, therefore (on this view) tends to develop (cephalization). Given a direction of travel which creates a front/back difference, and gravity which creates a dorsal/ventral difference, left and right are unavoidably distinguished, so a bilaterally symmetric body plan is widespread and found in most animal phyla.^[11][13] Bilateral symmetry also permits streamlining to reduce drag, and on a traditional view in zoology facilitates locomotion.^[11] However, in the Cnidaria, different symmetries exist, and bilateral symmetry is not necessarily aligned with the direction of locomotion, so another mechanism such as internal transport may be needed to explain the origin of bilateral symmetry in animals.^[11][14]

Starfish larvae are bilaterally symmetric, whereas the adults have fivefold symmetry.

The phylum Echinodermata, which includes starfish, sea urchins and sand dollars, is unique among animals in having bilateral symmetry at the larval stage, but pentamerism (fivefold symmetry) as adults.^[15]

Bilateral symmetry is not easily broken. In experiments using the fruit fly, Drosophila, in contrast to other traits (where laboratory selection experiments always yield a change), right- or left-sidedness in eye size, or eye facet number, wing-folding behavior (left over right) show a lack of response.^[16]

Females of some species select for symmetry, presumed by biologists to be a mark (technically a "cue") of fitness. Female barn swallows, a species where adults have long tail streamers, prefer to mate with males that have the most symmetrical tails.^[17]

Flower of bee orchid (Ophrys apifera) is bilaterally symmetrical (zygomorphic). The lip of the flower resembles the (bilaterally symmetric) abdomen of a female bee; pollination occurs when a male bee attempts to mate with it.

Flowers in some families of flowering plants, such as the orchid and pea families, and also most of the figwort family,^[18] are bilaterally symmetric (zygomorphic).^[19]

Biradial symmetry

Biradial symmetry is a combination of radial and bilateral symmetry, as in the ctenophores. Here, the body components are arranged with similar parts on either side of a central axis, and each of the four sides of the body is identical to the opposite side but different from the adjacent side. This may represent a stage in the evolution of bilateral symmetry "from a presumably radially symmetrical ancestor."^[14]

Asymmetry

Not all animals are symmetric. Many members of the phylum Porifera (sponges) have no symmetry, though some are radially symmetric.^[20]
It is normal for essentially symmetric animals to show some measure of asymmetry. Usually in humans the left brain is structured differently to the right; the heart is positioned towards the left; and the right hand functions better than the left hand.^[21] The scale-eating cichlid Perissodus microlepis develops left or right asymmetries in their mouths and jaws that allow them to be more effective when removing scales from the left or right flank of their prey.^[22]

The approximately 400 species of flatfish also lack symmetry as adults, though the larvae are bilaterally symmetrical. Adult flatfish rest on one side, and the eye that was on that side has migrated round to the other (top) side of the body.^[23]