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| [[Image:Spinisomersofmolecularhydrogen.gif|thumb|right|Spin isomers of molecular hydrogen]]
| | Hi there. Allow me begin by introducing the writer, her name is Myrtle Cleary. South Dakota is where I've usually been living. My day job is a meter reader. His wife doesn't like it the way he does but what he truly likes performing is to do aerobics and he's been doing it for fairly a while.<br><br>Also visit my weblog ... [http://www.videoworld.com/blog/211112 http://www.videoworld.com/] |
| 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).<ref>P. Atkins and J. de Paula, Atkins' Physical Chemistry, 8th edition (W.H.Freeman 2006), p.452</ref> At [[room temperature]] and [[thermal equilibrium]], hydrogen consists of approximately 75% orthohydrogen and 25% parahydrogen.
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| == Nuclear spin states of H<sub>2</sub> ==
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| Each [[hydrogen]] [[molecule]] (H<sub>2</sub>) 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]]. Each proton has an associated [[magnetic moment]], which is associated with the proton's spin of 1/2. In the H<sub>2</sub> molecule, the spins of the two hydrogen nuclei (protons) couple to form a [[triplet state]] known as '''orthohydrogen''', and a [[singlet state]] known as '''parahydrogen'''.
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| The triplet orthohydrogen state has total nuclear spin I = 1 so that the component along a defined axis can have the three values M<sub>I</sub> = 1, 0, or −1. The corresponding nuclear spin wavefunctions are <math> |\uparrow \uparrow \rangle, 1/ \sqrt{2}(|\uparrow \downarrow \rangle +|\downarrow \uparrow \rangle) </math> and <math> |\downarrow \downarrow \rangle </math> (in standard [[Bra ket notation|bra-ket]] notation). Each orthohydrogen energy level then has a (nuclear) spin [[Degenerate energy levels|degeneracy]] of three, meaning that it corresponds to three states of the same energy, although this degeneracy can be broken by a magnetic field.
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| The singlet parahydrogen state has nuclear spin quantum numbers I = 0 and M<sub>I</sub> = 0, with wavefunction <math> 1/\sqrt{2}(|\uparrow \downarrow \rangle - |\downarrow \uparrow \rangle) </math>. Since there is only one possibility, each parahydrogen level has a spin degeneracy of one and is said to be nondegenerate.
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| The ratio between the ortho and para forms is about 3:1 at [[standard temperature and pressure]] – a reflection of the ratio of spin degeneracies. However if [[thermal equilibrium]] between the two forms is established, the para form dominates at low temperatures (approx. 99.8% at 20 K<ref>Rock, Peter A. "Chemical Thermodynamics", MacMillan 1969, p.478</ref>). Other molecules and functional groups containing two hydrogen atoms, such as [[water (molecule)|water]] and [[methylene group|methylene]], also have ortho and para forms (e.g. orthowater and parawater), although their ratios differ from that of the dihydrogen molecule.
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| == Thermal properties ==
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| Since protons have spin 1/2, they are [[fermion]]s and the permutational antisymmetry of the total H<sub>2</sub> wavefunction imposes restrictions on the possible rotational states the two forms of H<sub>2</sub> 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 rotor]] approximation, the energies and degeneracies of the rotational states are given by<ref>F. T. Wall (1974). ''Chemical Thermodynamics, 3rd Edition.'' W. H. Freeman and Company.</ref>
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| <math>\begin{align}
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| & E_{J}=\frac{J(J+1)\hbar ^{2}}{2I};\text{ }g_{J}=2J+1 \\
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| \end{align}</math>.
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| The rotational [[partition function (statistical mechanics)|partition function]] is conventionally written as
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| <math>Z_{\text{rot}}=\sum\limits_{J=0}^{\infty }{g_{J}e^{-{E_{J}}/{k_{B}T}\;}}</math>.
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| However, as long as these two spin isomers are not in equilibrium, it is more useful to write separate partition functions for each,
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| <math>Z_{\text{para}}=\sum\limits_{\text{even }J}{(2J+1)e^{{-J(J+1)\hbar ^{2}}/{2Ik_{B}T}\;}}\text{ ; }Z_{\text{ortho}}=3\sum\limits_{\text{odd }J}{(2J+1)e^{{-J(J+1)\hbar ^{2}}/{2Ik_{B}T}\;}}</math>.
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| 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
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| <math>\begin{align}
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| & Z_{\text{equil}}=\sum\limits_{J=0}^{\infty }{(2-(-1)^{J})(2J+1)e^{{-J(J+1)\hbar ^{2}}/{2Ik_{B}T}\;}} \\
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| \end{align}</math>
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| The molar rotational energies and heat capacities are derived for any of these cases from
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| <math>\begin{align}
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| & U_{\text{rot}}=RT^{2}\left( \frac{\partial \ln Z_{\text{rot}}}{\partial T} \right)\text{ ; }C_{v,\text{ rot}}=\left( \frac{\partial U_{\text{rot}}}{\partial T} \right) \\
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| \end{align}</math>
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| Plots shown here are molar rotational energies and heat capacities for ortho- and parahydrogen, and the "normal" ortho/para (3:1) and equilibrium mixtures:
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| <gallery>
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| Image:ortho-para_H2_energies.jpg|Molar Rotational Energies.
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| Image:ortho-para_H2_Cvs.jpg|Molar Heat Capacities.
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| </gallery>
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| 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 H<sub>2</sub>; the gap between the first two levels when expressed in temperature units is twice the characteristic [[rotational temperature]] for H<sub>2</sub>,
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| <math>\frac{E_{J=1}-E_{J=0}}{k_{B}}=2\theta _{rot}=\frac{\hbar ^{2}}{k_{B}I}=174.98\text{ K}</math>.
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| This is the T = 0 intercept seen in the molar energy of orthohydrogen. Since "normal" room-temperature hydrogen is a 3:1 ortho:para mixture, its molar residual rotational energy at low temperature is (3/4) x 2Rθ<sub>rot</sub> = 1091 J/mol, which is somewhat larger than the [[enthalpy of vaporization]] of normal hydrogen, 904 J/mol at the boiling point, T<sub>b</sub> = 20.369 K.[http://webbook.nist.gov/chemistry/fluid/] Notably, the boiling points of parahydrogen and normal (3:1) hydrogen are nearly equal; for parahydrogen ∆H<sub>vap</sub> = 898 J/mol at T<sub>b</sub> = 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,
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| [[chromic oxide]], or some nickel compounds<ref>[http://www.mae.ufl.edu/NasaHydrogenResearch/h2webcourse/L11-liquefaction2.pdf Ortho-Para conversion. Pag. 13]</ref> 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.<ref>[http://www.mae.ufl.edu/NasaHydrogenResearch/h2webcourse/L11-liquefaction2.pdf ]{{dead link|date=August 2012}}</ref>
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| The first synthesis of pure parahydrogen was achieved by [[Paul Harteck]] and [[Karl Friedrich Bonhoeffer]] in 1929.
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| 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.<ref>[http://www.stormingmedia.us/72/7208/A720893.html Rapid Vapor Deposition of Millimeters Thick Optically Transparent Solid Parahydrogen Samples for Matrix Isolation Spectroscopy]</ref>
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| Further research regarding parahydrogen thinfilm quantum state polarization matrices for computation seems a likely future prospect for these material sets.
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| == Use in [[NMR]]==
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| When an excess of parahydrogen is used during [[hydrogenation]] reactions (instead of the normal mixture of orthohydrogen to parahydrogen of 3:1), the resultant product exhibits [[Hyperpolarization (physics)|hyperpolarized]] signals in proton [[Nuclear magnetic resonance|NMR]] spectra. This effect is called PHIP ("Parahydrogen Induced Polarisation") or PASADENA ("Parahydrogen and Synthesis allow dramatically enhanced nuclear alignment" – named this way as the first recognition of the effect was done by Bowers and Weitekamp of [[Caltech]] in [[Pasadena, California|Pasadena]]<ref>C. R. Bowers and D. P. Weitekamp, Phys. Rev. Lett. 57, 2645 (1986)</ref>) and has been utilized to study the mechanism of hydrogenation reactions. See references <ref>http://www.oxford-instruments.com/products/low-temperature/applications-library/high-field-magnet/Documents/Boosting-the-Sensitivity-of-NMR-Spectroscopy-using-Parahydrogen.pdf</ref>
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| <ref>{{cite web|url=http://www.york.ac.uk/res/sbd/parahydrogen/para_nmr.html |title=University of York, Department of Chemistry, SBD Research Group |publisher=York.ac.uk |date= |accessdate=2012-08-22}}</ref>
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| .<ref>{{cite web|url=http://www.sciencemag.org/content/323/5922/1708.abstract |title=Reversible Interactions with para-Hydrogen Enhance NMR Sensitivity by Polarization Transfer |publisher=Sciencemag.org |date=2009-03-27 |accessdate=2012-08-22}}</ref>
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| ==References==
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| {{reflist}}
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| ==Other literature ==
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| #{{cite journal
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| | author = Tikhonov V. I., Volkov A. A.
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| | title = Separation of water into its ortho and para isomers
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| | journal = Science
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| | volume = 296
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| | issue = 5577
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| | page = 2363
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| | year = 2002| doi = 10.1126/science.1069513
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| | pmid = 12089435
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| }}
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| #{{cite journal
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| | author = [[Karl Friedrich Bonhoeffer|Bonhoeffer KF]], [[Paul Harteck|Harteck P]]
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| | title = Para- and ortho hydrogen
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| | journal = Zeitschrift für Physikalische Chemie B
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| | volume = 4
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| | issue = 1–2
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| | pages = 113–141
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| | year = 1929}}
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| #{{cite book
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| | title = Orthohydrogen, parahydrogen and heavy hydrogen,
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| | author = A. Farkas
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| | publisher = The Cambridge series of physical chemistry
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| | year = 1935}}
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| #{{cite journal
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| | title = Rapid Vapor Deposition of Millimeters Thick Optically Transparent Solid Parahydrogen Samples for Matrix Isolation Spectroscopy
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| | author = Mario E. Fajardo; Simon Tam
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| | publisher = AIR FORCE RESEARCH LAB EDWARDS AFB CA PROPULSION DIRECTORATE WEST
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| | year = 1997}}
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| [[Category:Hydrogen physics]]
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| [[Category:Hydrogen technologies]]
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| [[Category:Hydrogen]]
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Hi there. Allow me begin by introducing the writer, her name is Myrtle Cleary. South Dakota is where I've usually been living. My day job is a meter reader. His wife doesn't like it the way he does but what he truly likes performing is to do aerobics and he's been doing it for fairly a while.
Also visit my weblog ... http://www.videoworld.com/