Equilibrium fractionation

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 effects) forms the basis of the most widely used isotopic paleothermometers (or climate proxies): D/H and ¹⁸O/¹⁶O records from ice cores, and ¹⁸O/¹⁶O records from calcium carbonate. It is thus important for the construction of geologic temperature records. Isotopic fractionations attributed to equilibrium processes have been observed in many elements, from hydrogen (D/H) to uranium (²³⁸U/²³⁵U). 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.

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.

In a reaction involving the exchange of two isotopes, ^lX and ^hX, of element “X” in molecules AX and BX,

\[A^lX + B^hX \rightleftharpoons A^hX + B^lX\]

each reactant molecule is identical to a product except for the distribution of isotopes (i.e., they are isotopologues). The amount of isotopic fractionation in an exchange reaction can be expressed as a fractionation factor:

\[\alpha = \frac{(^hX/^lX)_{AX}}{(^hX/^lX)_{BX}}\]

\(\alpha = 1\) indicates that the isotopes are distributed evenly between AX and BX, with no isotopic fractionation. \(\alpha > 1\) indicates that ^hX is concentrated in substance AX, and \(\alpha < 1 \) indicates ^hX is concentrated in substance BX. \(\alpha\) is closely related to the equilibrium constant (K_eq):

\[\alpha = (K_{eq} \cdot \Pi \sigma_{Products}/ \Pi \sigma_{Reactants})^{1/n}\]

where \(\Pi\sigma_{Products}\) is the product of the rotational symmetry numbers of the products (right side of the exchange reaction), \(\Pi\sigma_{Reactants}\) is the product of the rotational symmetry numbers of the reactants (left side of the exchange reaction), and \(n\) is the number of atoms exchanged.

An example of equilibrium isotope fractionation is the concentration of heavy isotopes of oxygen in liquid water, relative to water vapor,

\[H_2^{16}O_{(l)} + H_2^{18}O_{(g)} \rightleftharpoons H_2^{18}O_{(l)} + H_2^{16}O_{(g)}\]

At 20^oC, the equilibrium fractionation factor for this reaction is

\[\alpha = \frac{(^{18}O/^{16}O)_{Liquid}}{(^{18}O/^{16}O)_{Vapor}} = 1.0098 \]

Equilibrium fractionation is a type of mass-dependent isotope fractionation, while mass-independent fractionation is usually assumed to be a non-equilibrium process.

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.

See also

Stable isotope
Isotope geochemistry
Kinetic isotope effect
Isotope analysis
Isotope electrochemistry
δ¹⁸O
Kinetic fractionation
Mass-independent fractionation
Transient kinetic isotope effect
Isotopic ratio
Isotopic composition
Fractionation factor
Isotopic enrichment

References

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.

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.

Links

AlphaDelta: Stable Isotope fractionation calculator - http://www2.ggl.ulaval.ca/cgi-bin/isotope/generisotope.cgi