Spin isomers of hydrogen
Encyclopedia
Molecular hydrogen occurs in two isomeric forms, one with its two proton spins aligned parallel (orthohydrogen), the other with its two proton spins aligned antiparallel (parahydrogen). At room temperature
and thermal equilibrium
, hydrogen consists of 25% parahydrogen and 75% orthohydrogen.
molecule
(H2) consists of two hydrogen atom
s linked by a covalent bond
. If we neglect the small proportion of deuterium
and tritium
which may be present, each hydrogen atom
consists of one proton
and one electron
. The proton has an associated magnetic moment
, which is associated with the proton's spin. In the H2 molecule, the spins of the two hydrogen nuclei (protons) couple to form a triplet state
(I = 1, α1α2, (α1β2 + β1α2)/(21/2), or β1β2 for which MI = 1, 0, −1 respectively — this is orthohydrogen) or to form a singlet state (I = 0, (α1β2 – β1α2)/(21/2) MI = 0 — this is parahydrogen). The ratio between the ortho and para forms is about 3:1 at standard temperature and pressure - a reflection of the spin degeneracy ratio, but if thermal equilibrium
between the two forms is established, the para form dominates at low temperatures (approx. 99.8% at 20 K). Other molecules and functional groups containing two hydrogen atoms, such as water and methylene
, also have ortho and para forms (e.g. orthowater and parawater), although their ratios differ from that of the dihydrogen molecule.
approximation, the energies and degeneracies of the rotational states are given by
.
The rotational partition function
is conventionally written as
.
However, as long as these two spin isomers are not in equilibrium, it is more useful to write separate partition functions for each,
.
The factor of 3 in the partition function for orthohydrogen accounts for the spin degeneracy associated with the +1 spin state. When equilibrium between the spin isomers is possible, then a general partition function incorporating this degeneracy difference can be written as
The molar rotational energies and heat capacities are derived for any of these cases from
Because of the antisymmetry-imposed restriction on possible rotational states, orthohydrogen has residual rotational energy at low temperature wherein nearly all the molecules are in the J = 1 state (molecules in the symmetric spin-triplet state cannot fall into the lowest, symmetric rotational state) and possesses nuclear-spin entropy
due to the triplet state's threefold degeneracy. The residual energy is significant because the rotational energy levels are relatively widely spaced in H2; the gap between the first two levels when expressed in temperature units is twice the rotational temperature for H2,
.
This is the T = 0 intercept seen in the molar energy of orthohydrogen. This residual energy, 1091 J/mol, is somewhat larger than the enthalpy of vaporization of normal hydrogen, 904 J/mol at the boiling point, Tb = 20.369 K (this refers to the "normal", room-temperature, 3:1 ortho:para mixture).http://webbook.nist.gov/chemistry/fluid/ Notably, the boiling points of parahydrogen and normal (3:1) hydrogen are nearly equal; for parahydrogen ∆Hvap = 898 J/mol at Tb = 20.277 K. It follows that nearly all the residual rotational energy of orthohydrogen is retained in the liquid state. Orthohydrogen is consequently unstable at low temperatures and spontaneously converts into parahydrogen, but the process is slow in the absence of a magnetic catalyst to facilitate interconversion of the singlet and triplet spin states. At room temperature, hydrogen contains 75% orthohydrogen, a proportion which the liquefaction process preserves if carried out in the absence of a catalyst like ferric oxide, activated carbon
, platinized asbestos, rare earth metals, uranium compounds,
chromic oxide, or some nickel compounds to accelerate the conversion of the liquid hydrogen
into parahydrogen, or supply additional refrigeration equipment to absorb the heat that the orthohydrogen fraction will release as it spontaneously converts into parahydrogen. If orthohydrogen is not removed from liquid hydrogen, the heat released during its decay can boil off as much as 50% of the original liquid.
The first synthesis of pure parahydrogen was achieved by Paul Harteck
and Karl Friedrich Bonhoeffer
in 1929.
Modern isolation of pure parahydrogen has been achieved utilizing rapid in-vacuum deposition of millimeters thick solid parahydrogen (pH2) samples which are notable for their excellent optical qualities.
Further research regarding parahydrogen thinfilm quantum state polarization matrices for computation seems a likely future prospect for these material sets.
When an excess of parahydrogen is used during hydrogenation
reactions, the resultant product exhibits hyperpolarized
signals in proton NMR
spectra. This effect is called Parahydrogen Inducded Polarisation (PHIP) and has utilized to study the mechanism of hydrogenation reactions.
Room temperature
-Comfort levels:The American Society of Heating, Refrigerating and Air-Conditioning Engineers has listings for suggested temperatures and air flow rates in different types of buildings and different environmental circumstances. For example, a single office in a building has an occupancy ratio per...
and thermal equilibrium
Thermal equilibrium
Thermal equilibrium is a theoretical physical concept, used especially in theoretical texts, that means that all temperatures of interest are unchanging in time and uniform in space...
, hydrogen consists of 25% parahydrogen and 75% orthohydrogen.
Nuclear spin states of H2
Each hydrogenHydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...
molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
(H2) consists of two hydrogen atom
Hydrogen atom
A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively-charged proton and a single negatively-charged electron bound to the nucleus by the Coulomb force...
s linked by a covalent bond
Covalent bond
A covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms. The stable balance of attractive and repulsive forces between atoms when they share electrons is known as covalent bonding....
. If we neglect the small proportion of deuterium
Deuterium
Deuterium, also called heavy hydrogen, is one of two stable isotopes of hydrogen. It has a natural abundance in Earth's oceans of about one atom in of hydrogen . Deuterium accounts for approximately 0.0156% of all naturally occurring hydrogen in Earth's oceans, while the most common isotope ...
and tritium
Tritium
Tritium is a radioactive isotope of hydrogen. The nucleus of tritium contains one proton and two neutrons, whereas the nucleus of protium contains one proton and no neutrons...
which may be present, each hydrogen atom
Hydrogen atom
A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively-charged proton and a single negatively-charged electron bound to the nucleus by the Coulomb force...
consists of one proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
and one electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
. The proton has an associated magnetic moment
Magnetic moment
The magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it...
, which is associated with the proton's spin. In the H2 molecule, the spins of the two hydrogen nuclei (protons) couple to form a triplet state
Triplet state
A spin triplet is a set of three quantum states of a system, each with total spin S = 1 . The system could consist of a single elementary massive spin 1 particle such as a W or Z boson, or be some multiparticle state with total spin angular momentum of one.In physics, spin is the angular momentum...
(I = 1, α1α2, (α1β2 + β1α2)/(21/2), or β1β2 for which MI = 1, 0, −1 respectively — this is orthohydrogen) or to form a singlet state (I = 0, (α1β2 – β1α2)/(21/2) MI = 0 — this is parahydrogen). The ratio between the ortho and para forms is about 3:1 at standard temperature and pressure - a reflection of the spin degeneracy ratio, but if thermal equilibrium
Thermal equilibrium
Thermal equilibrium is a theoretical physical concept, used especially in theoretical texts, that means that all temperatures of interest are unchanging in time and uniform in space...
between the two forms is established, the para form dominates at low temperatures (approx. 99.8% at 20 K). Other molecules and functional groups containing two hydrogen atoms, such as water and methylene
Methylene
Methylene is a chemical species in which a carbon atom is bonded to two hydrogen atoms. Three different possibilities present themselves:* the -CH2- substituent group: e.g., dichloromethane ....
, also have ortho and para forms (e.g. orthowater and parawater), although their ratios differ from that of the dihydrogen molecule.
Thermal properties
The permutational antisymmetry of the H2 wavefunction (protons are fermions) imposes restrictions on the possible rotational states the two forms of H2 can adopt. Orthohydrogen, with symmetric nuclear spin functions, can only have rotational wavefunctions that are antisymmetric with respect to permutation of the two protons. Conversely, parahydrogen with an antisymmetric nuclear spin function, can only have rotational wavefunctions that are symmetric with respect to permutation of the two protons. Applying the rigid rotorRigid rotor
The rigid rotor is a mechanical model that is used to explain rotating systems.An arbitrary rigid rotor is a 3-dimensional rigid object, such as a top. To orient such an object in space three angles are required. A special rigid rotor is the linear rotor which isa 2-dimensional object, requiring...
approximation, the energies and degeneracies of the rotational states are given by
.The rotational partition function
Partition function (statistical mechanics)
Partition functions describe the statistical properties of a system in thermodynamic equilibrium. It is a function of temperature and other parameters, such as the volume enclosing a gas...
is conventionally written as
.However, as long as these two spin isomers are not in equilibrium, it is more useful to write separate partition functions for each,
.The factor of 3 in the partition function for orthohydrogen accounts for the spin degeneracy associated with the +1 spin state. When equilibrium between the spin isomers is possible, then a general partition function incorporating this degeneracy difference can be written as
The molar rotational energies and heat capacities are derived for any of these cases from
Because of the antisymmetry-imposed restriction on possible rotational states, orthohydrogen has residual rotational energy at low temperature wherein nearly all the molecules are in the J = 1 state (molecules in the symmetric spin-triplet state cannot fall into the lowest, symmetric rotational state) and possesses nuclear-spin entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
due to the triplet state's threefold degeneracy. The residual energy is significant because the rotational energy levels are relatively widely spaced in H2; the gap between the first two levels when expressed in temperature units is twice the rotational temperature for H2,
.This is the T = 0 intercept seen in the molar energy of orthohydrogen. This residual energy, 1091 J/mol, is somewhat larger than the enthalpy of vaporization of normal hydrogen, 904 J/mol at the boiling point, Tb = 20.369 K (this refers to the "normal", room-temperature, 3:1 ortho:para mixture).http://webbook.nist.gov/chemistry/fluid/ Notably, the boiling points of parahydrogen and normal (3:1) hydrogen are nearly equal; for parahydrogen ∆Hvap = 898 J/mol at Tb = 20.277 K. It follows that nearly all the residual rotational energy of orthohydrogen is retained in the liquid state. Orthohydrogen is consequently unstable at low temperatures and spontaneously converts into parahydrogen, but the process is slow in the absence of a magnetic catalyst to facilitate interconversion of the singlet and triplet spin states. At room temperature, hydrogen contains 75% orthohydrogen, a proportion which the liquefaction process preserves if carried out in the absence of a catalyst like ferric oxide, activated carbon
Activated carbon
Activated carbon, also called activated charcoal, activated coal or carbo activatus, is a form of carbon that has been processed to make it extremely porous and thus to have a very large surface area available for adsorption or chemical reactions.The word activated in the name is sometimes replaced...
, platinized asbestos, rare earth metals, uranium compounds,
chromic oxide, or some nickel compounds to accelerate the conversion of the liquid hydrogen
Liquid hydrogen
Liquid hydrogen is the liquid state of the element hydrogen. Hydrogen is found naturally in the molecular H2 form.To exist as a liquid, H2 must be pressurized above and cooled below hydrogen's Critical point. However, for hydrogen to be in a full liquid state without boiling off, it needs to be...
into parahydrogen, or supply additional refrigeration equipment to absorb the heat that the orthohydrogen fraction will release as it spontaneously converts into parahydrogen. If orthohydrogen is not removed from liquid hydrogen, the heat released during its decay can boil off as much as 50% of the original liquid.
The first synthesis of pure parahydrogen was achieved by Paul Harteck
Paul Harteck
Paul Karl Maria Harteck was a German physical chemist. He was arrested by the allied British and American Armed Forces and incarcerated at Farm Hall for six months in 1945 under Operation Epsilon.-Education:Harteck studied chemistry at the University of Vienna and the Humboldt University of Berlin...
and Karl Friedrich Bonhoeffer
Karl Friedrich Bonhoeffer
-Life:Born in Breslau, he was an older brother of martyred theologian Dietrich Bonhoeffer.Bonhoeffer studied from 1918 in Tübingen and Berlin, finishing his PhD in 1922 in Berlin with Walther Nernst. From 1923 to 1930 he was an assistant with Fritz Haber at Kaiser Wilhelm Institute for Physical...
in 1929.
Modern isolation of pure parahydrogen has been achieved utilizing rapid in-vacuum deposition of millimeters thick solid parahydrogen (pH2) samples which are notable for their excellent optical qualities.
Further research regarding parahydrogen thinfilm quantum state polarization matrices for computation seems a likely future prospect for these material sets.
When an excess of parahydrogen is used during hydrogenation
Hydrogenation
Hydrogenation, to treat with hydrogen, also a form of chemical reduction, is a chemical reaction between molecular hydrogen and another compound or element, usually in the presence of a catalyst. The process is commonly employed to reduce or saturate organic compounds. Hydrogenation typically...
reactions, the resultant product exhibits hyperpolarized
Hyperpolarization (physics)
Hyperpolarization is the nuclear spin polarization of a material far beyond thermal equilibrium conditions. It is commonly applied to gases such as 129Xe and 3He which are then used, for instance, in hyperpolarized magnetic resonance imaging of the lungs....
signals in proton NMR
Nuclear magnetic resonance
Nuclear magnetic resonance is a physical phenomenon in which magnetic nuclei in a magnetic field absorb and re-emit electromagnetic radiation...
spectra. This effect is called Parahydrogen Inducded Polarisation (PHIP) and has utilized to study the mechanism of hydrogenation reactions.