HR: 0800h
AN: A51C-0800 [Abstracts]
TI: Theoretical Calculations of Exchange Equilibria Involving Multiply-Substituted Isotopologues of
Molecular Gases
AU: * Wang, Z
EM: wzhr@gps.caltech.edu
AF: Caltech, Division of Geological and Planetary Sciences, M/C 100-23, Pasadena, CA 91125
United States
AU: John, E M
EM: eiler@gps.caltech.edu
AF: Caltech, Division of Geological and Planetary Sciences, M/C 100-23, Pasadena, CA 91125
United States
AU: Schauble, E A
EM: schauble@ess.ucla.edu
AF: UCLA, Department of Earth and Space Sciences, P.O. Box 951567, Los Angeles, CA 90095
United States
AB:
Heavy stable isotopes are not randomly distributed among molecules in thermodynamically equilibrated mono-molecular gases
(e.g., O$_{2}$, N$_{2}$, or CO$_{2}$), but instead preferentially concentrate into bonds with each other (e.g.,
$^{18}$O-$^{18}$O, $^{15}$N-$^{15}$N, etc.). This occurs because such bonds have exceptionally low zero point energies and
thus are comparatively more stable. This zero point energy effect is subtle (typically at per-mil level) but has recently
been shown to be measurable. The abundances of isotopologues of molecular gases containing more than one rare isotope
(`multiply-substituted isotopologues') could be used for a variety of geochemical applications, including geothermometry, and
such applications will require a sound understanding of these zero-point energy effects. This study presents methods and
data for theoretically estimating the strength of these effects, and discusses possible applications. Accompanying abstracts
by Afek et al., Eiler et al., Ghosh et al. and Schauble et al. provide analytical details, analogous models for condensed
phases, and illustrative applications.
We have derived a method for systematically evaluating the influence of the zero point energy effect in the abundances of all
isotopologues in thermodynamically equilibrated populations of O$_{2}, CO, N$_{2}$, NO, CO$_{2}$ and N$_{2}$O between 1000
and 193 to 77 K. This method uses Urey-type algorithms (based on simple harmonic oscillator and rigid rotor model) to
evaluate partition functions and equilibrium constants of isotope exchange reactions, and simultaneously solves for abundance
of each isotopologue of a given molecule constrained by all independent equilibria. We also examine the accuracy of the
Urey-type models by comparison with direct summations over all experimentally or empirically determined energy levels to
calculate partition functions. This comparison is only made for CO and CO$_{2}$ due to limitations in spectroscopic data, but
in these cases there are no significant differences among methods. Calculation results also show that, in most cases,
multiply-substituted isotopologues are predicted to be enriched relative to stochastic (random) distributions by ca. 1 to 2
per mil at earth-surface temperatures. This deviation, defined as \Delta$_{i}$ for isotopologue i, generally increases
linearly with 1/T at temperatures $<$ 500 K, and with 1/T$^{2}$ at temperatures $>$ 500 K. An exception is N$_{2}$O, which
shows complex temperature dependences and 10's of per-mil enrichments or depletions of abundances for some isotopologues.
These theoretical calculations provide a basis for discriminating between fractionations controlled by equilibrium
thermodynamics and other sorts of isotopic fractionations in the budgets of atmospheric gases. Moreover, because abundances
of multiply-substituted isotopologues in thermodynamically equilibrated populations of molecules vary systematically with
temperature, they can be used as geothermometers. Such thermometers are unusual in that they involve homogeneous rather than
heterogeneous equilibria (e.g., isotopic distribution in gaseous CO$_{2}$ alone, rather than difference in isotopic
composition between CO$_{2}$ and coexisting water). Also, multiple, independent thermometers exist for all molecules having
more than one multiply-substituted isotopologue (e.g., thermometers based on abundances of $^{18}$O$^{13}$C$^{16}$O and
$^{18}$O$^{12}$C$^{18}$O are independent); thus temperatures estimated by this method can be tested for internal consistency.
DE: 4825 Geochemistry
DE: 4870 Stable isotopes
DE: 1040 Isotopic composition/chemistry
DE: 0300 ATMOSPHERIC COMPOSITION AND STRUCTURE
DE: 0345 Pollution--urban and regional (0305)
SC: Atmospheric Sciences [A]
MN: 2004 AGU Fall Meeting