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| Equilibrium isotope [[fractionation]] is the partial separation of [[isotopes]] between two or more substances in [[chemical equilibrium]]. '''Equilibrium fractionation''' is strongest at low temperatures, and (along with [[kinetic isotope effect]]s) forms the basis of the most widely used isotopic [[paleothermometer]]s (or [[proxy (climate)|climate proxies]]): [[deuterium|D/H]] and [[oxygen isotope ratio cycle|<sup>18</sup>O/<sup>16</sup>O]] records from [[ice cores]], and <sup>18</sup>O/<sup>16</sup>O records from calcium carbonate. It is thus important for the construction of [[geologic temperature record]]s.<ref name='Urey_1947'>{{cite journal | author=H. C. Urey | year=1947 | journal=J. Chem. Soc. | title=The Thermodynamic Properties of Isotopic Substances | pages=562–581 | doi=10.1039/JR9470000562 }}</ref> Isotopic fractionations attributed to equilibrium processes have been observed in many elements, from hydrogen ([[deuterium|D/H]]) to uranium ([[Isotopes of uranium|<sup>238</sup>U/<sup>235</sup>U]]). In general, the light elements (especially [[hydrogen]], [[boron]], [[carbon]], [[nitrogen]], [[oxygen]] and [[sulfur]]) are most susceptible to fractionation, and their isotopes tend to be separated to a greater degree than heavier elements.
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| Most equilibrium fractionations are thought to result from the reduction in vibrational energy (especially [[zero-point energy]]) when a more massive isotope is substituted for a less massive one. This leads to higher concentrations of the massive isotopes in substances where the vibrational energy is most sensitive to isotope substitution, i.e., those with the highest bond force constants.
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| In a reaction involving the exchange of two isotopes, <sup>l</sup>X and <sup>h</sup>X, of element "X" in [[molecule]]s AX and BX,
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| :<math>A^lX + B^hX \rightleftharpoons A^hX + B^lX</math>
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| each reactant molecule is identical to a product except for the distribution of isotopes (i.e., they are [[isotopologue]]s). The amount of isotopic fractionation in an exchange reaction can be expressed as a fractionation factor:
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| :<math>\alpha = \frac{(^hX/^lX)_{AX}}{(^hX/^lX)_{BX}}</math>
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| <math>\alpha = 1</math> indicates that the isotopes are distributed evenly between AX and BX, with no isotopic fractionation. <math>\alpha > 1</math> indicates that <sup>h</sup>X is concentrated in substance AX, and <math>\alpha < 1 </math> indicates <sup>h</sup>X is concentrated in substance BX. <math>\alpha</math> is closely related to the [[equilibrium constant]] (K<sub>eq</sub>):
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| :<math>\alpha = (K_{eq} \cdot \Pi \sigma_{Products}/ \Pi \sigma_{Reactants})^{1/n}</math>
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| where <math>\Pi\sigma_{Products}</math> is the product of the rotational symmetry numbers of the products (right side of the exchange reaction), <math>\Pi\sigma_{Reactants}</math> is the product of the rotational symmetry numbers of the reactants (left side of the exchange reaction), and <math>n</math> is the number of atoms exchanged.
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| An example of equilibrium isotope fractionation is the concentration of heavy isotopes of [[oxygen]] in liquid [[water]], relative to [[water vapor]],
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| :<math>H_2^{16}O_{(l)} + H_2^{18}O_{(g)} \rightleftharpoons H_2^{18}O_{(l)} + H_2^{16}O_{(g)}</math>
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| At 20 °C, the equilibrium fractionation factor for this reaction is
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| :<math>\alpha = \frac{(^{18}O/^{16}O)_{Liquid}}{(^{18}O/^{16}O)_{Vapor}} = 1.0098 </math>
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| Equilibrium fractionation is a type of mass-dependent isotope fractionation, while [[mass-independent fractionation]] is usually assumed to be a non-equilibrium process.
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| For non-equilibrium reactions, isotopic effects are better described by the GEBIK and GEBIF equations for [[transient kinetic isotope fractionation]], which generalize non-steady isotopic effects in any chemical and biochemical reactions.<ref>Maggi F. and W. J. Riley, (2010), Mathematical treatment of isotopologue and isotopomer speciation and fractionation in biochemical kinetics, Geochim. Cosmochim. Acta, {{doi|10.1016/j.gca.2009.12.021}}</ref>
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| ==See also==
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| [[Stable isotope]]<br />
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| [[Standard electrode potential]]<br/>
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| [[Isotope geochemistry]]<br />
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| [[Kinetic isotope effect]]<br />
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| [[Isotope analysis]]<br />
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| [[Isotope electrochemistry]]<br />
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| [[D18O|δ<sup>18</sup>O]]<br />
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| [[Kinetic fractionation]]<br />
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| [[Mass-independent fractionation]] <br />
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| [[Transient kinetic isotope fractionation|Transient kinetic isotope effect]]<br />
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| [[Transient kinetic isotope fractionation|Isotopic ratio]]<br />
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| [[Transient kinetic isotope fractionation|Isotopic composition]]<br />
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| [[Transient kinetic isotope fractionation|Fractionation factor]]<br />
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| [[Transient kinetic isotope fractionation|Isotopic enrichment]]
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| == References ==
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| <references/>
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| Chacko T., Cole D.R., and Horita J. (2001) Equilibrium oxygen, hydrogen and carbon isotope fractionation factors applicable to geologic systems. Reviews in Mineralogy and Geochemistry, v. 43, p. 1-81.
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| Horita J. and Wesolowski D.J. (1994) Liquid-vapor fractionation of oxygen and hydrogen isotopes of water from the freezing to the critical temperature. Geochimica et Cosmochimica Acta, v. 58, p. 3425-2437.
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| ==External links==
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| AlphaDelta: Stable Isotope fractionation calculator - http://www2.ggl.ulaval.ca/cgi-bin/isotope/generisotope.cgi
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| [[Category:Isotope separation]]
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| [[Category:Geochemistry]]
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