Equilibrium fractionation

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,

${\displaystyle {\ce {{A^{\mathit {l}}X}+B^{\mathit {h}}X<=>{A^{\mathit {h}}X}+B^{\mathit {l}}X}}}$

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:

${\displaystyle \alpha ={\frac {(^{h}{\ce {X}}/^{l}{\ce {X}})_{{\ce {AX}}}}{(^{h}{\ce {X}}/^{l}{\ce {X}})_{{\ce {BX}}}}}}$

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

${\displaystyle \alpha =(K_{eq}\cdot \Pi \sigma _{Products}/\Pi \sigma _{Reactants})^{1/n}}$

where ${\displaystyle \Pi \sigma _{Products}}$ is the product of the rotational symmetry numbers of the products (right side of the exchange reaction), ${\displaystyle \Pi \sigma _{Reactants}}$ 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,

${\displaystyle {\ce {{H2{^{16}O}{(l)}}+{H2{^{18}O}{(g)}}<=>{H2{^{18}O}{(l)}}+{H2{^{16}O}{(g)}}}}}$

At 20 °C, the equilibrium fractionation factor for this reaction is

${\displaystyle \alpha ={\frac {{\ce {(^{18}O/^{16}O)_{Liquid}}}}{{\ce {(^{18}O/^{16}O)_{Vapor}}}}}=1.0098}$

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.[2]

When water vapor condenses (an equilibrium fractionation), the heavier water isotopes (H₂¹⁸O and ²H₂O) become enriched in the liquid phase while the lighter isotopes (H₂¹⁶O and ¹H₂O) tend toward the vapor phase.[3]

• Kinetic fractionation
• Mass-independent fractionation
• Transient kinetic isotope fractionation

• Equilibrium constant § Effect of isotopic substitution
• Isotope analysis
• Isotope electrochemistry
• Isotope geochemistry
• Kinetic isotope effect
• Stable isotope
• Standard electrode potential

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.

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